The muon g-2 anomaly dates back to the late 1990s and early 2000s, when measurements at Brookhaven National Laboratory (BNL) uncovered a possible discrepancy by comparison to theoretical predictions of the so-called muon anomaly, a_μ = (g-2)/2. a_μ expresses the magnitude of quantum loop corrections to the leading-order prediction of the Dirac equation, which multiplies the classical gyromagnetic ratio of fundamental fermions by a “g-factor” of precisely two. Loop corrections of a_μ ~ 0.1% quantify the extent to which virtual particles emitted by the muon further increase the strength of its interaction with magnetic fields. Were measurements to be shown to deviate from SM predictions, this would indicate the influence of virtual fields beyond the SM.

Move on up

In 2013, the BNL experiment’s magnetic storage ring was transported from Long Island, New York, to Fermilab in Batavia, Illinois. After years of upgrades and improvements, the new experiment began in 2017. It now reports a final precision of 127 parts per billion (ppb), bettering the experiment’s design precision of 140 ppb, and a factor of four more sensitive than the BNL result.

“First and foremost, an increase in the number of stored muons allowed us to reduce our statistical uncertainty to 98 ppb compared to 460 ppb for BNL,” explains co-spokesperson Peter Winter of Argonne National Laboratory, “but a lot of technical improvements to our calorimetry, tracking, detector calibration and magnetic-field mapping were also needed to improve on the systematic uncertainties from 280 ppb at BNL to 78 ppb at Fermilab.”

This formidable experimental precision throws down the gauntlet to the theory community

The final Fermilab measurement is (116592070.5 ± 11.4 (stat.) ± 9.1(syst.) ± 2.1 (ext.)) × 10^–11, fully consistent with the previous BNL measurement. This formidable precision throws down the gauntlet to the Muon g-2 Theory Initiative (TI), which was founded to achieve an international consensus on the theoretical prediction.

The calculation is difficult, featuring contributions from all sectors of the SM (CERN Courier March/April 2025 p21). The TI published its first whitepaper in 2020, reporting a_μ = (116591810 ± 43) × 10^–11, based exclusively on a data-driven analysis of cross-section measurements at electron–positron colliders (WP20). In May, the TI updated its prediction, publishing a value a_μ = (116592033 ± 62) × 10^–11, statistically incompatible with the previous prediction at the level of three standard deviations, and with an increased uncertainty of 530 ppb (WP25). The new prediction is based exclusively on numerical SM calculations. This was made possible by rapid progress in the use of lattice QCD to control the dominant source of uncertainty, which arises due to the contribution of so-called hadronic vacuum polarisation (HVP). In HVP, the photon representing the magnetic field interacts with the muon during a brief moment when a virtual photon erupts into a difficult-to-model cloud of quarks and gluons.

Significant shift

“The switch from using the data-driven method for HVP in WP20 to lattice QCD in WP25 results in a significant shift in the SM prediction,” confirms Aida El-Khadra of the University of Illinois, chair of the TI, who believes that it is not unreasonable to expect significant error reductions in the next couple of years. “There still are puzzles to resolve, particularly around the experimental measurements that are used in the data-driven method for HVP, which prevent us, at this point in time, from obtaining a new prediction for HVP in the data-driven method. This means that we also don’t yet know if the data-driven HVP evaluation will agree or disagree with lattice–QCD calculations. However, given the ongoing dedicated efforts to resolve the puzzles, we are confident we will soon know what the data-driven method has to say about HVP. Regardless of the outcome of the comparison with lattice QCD, this will yield profound insights.”

We are making plans to improve experimental precision beyond the Fermilab experiment

On the experimental side, attention now turns to the Muon g-2/EDM experiment at J-PARC in Tokai, Japan. While the Fermilab experiment used the “magic gamma” method first employed at CERN in the 1970s to cancel the effect of electric fields on spin precession in a magnetic field (CERN Courier September/October 2024 p53), the J-PARC experiment seeks to control systematic uncertainties by exercising particularly tight control of its muon beam. In the Japanese experiment, antimatter muons will be captured by atomic electrons to form muonium, ionised using a laser, and reaccelerated for a traditional precession measurement with sensitivity to both the muon’s magnetic moment and its electric dipole moment (CERN Courier July/August 2024 p8).

“We are making plans to improve experimental precision beyond the Fermilab experiment, though their precision is quite tough to beat,” says spokesperson Tsutomu Mibe of KEK. “We also plan to search for the electric dipole moment of the muon with an unprecedented precision of roughly 10^–21 e cm, improving the sensitivity of the last results from BNL by a factor of 70.”

With theoretical predictions from high-order loop processes expected to be of the order 10^–38 e cm, any observation of an electric dipole moment would be a clear indication of new physics.

“Construction of the experimental facility is currently ongoing,” says Mibe. “We plan to start data taking in 2030.”

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Particle physics today benefits from a wealth of high-quality data at the same time as powerful new ideas are boosting the accuracy of theoretical predictions. These are particularly important while the international community discusses future projects, basing projections on current results and technology. The conference heard how theoretical investigations of specific models and “catch all” effective field theories are being sharpened to constrain a broader spectrum of possible extensions of the Standard Model. Theoretical parametric uncertainties are being greatly reduced by collider precision measurements and lattice QCD. Perturbative calculations of short-distance amplitudes are reaching to percent-level precision, while hadronic long-distance effects are being investigated both in B-, D- and K-meson decays, as well as in the modelling of collider events.

Comprehensive searches

Throughout Moriond 2025 we heard how a broad spectrum of experiments at the LHC, B factories, neutrino facilities, and astrophysical and cosmological observatories are planning upgrades to search for new physics at both low- and high-energy scales. Several fields promise qualitative progress in understanding nature in the coming years. Neutrino experiments will measure the neutrino mass hierarchy and CP violation in the neutrino sector. Flavour experiments will exclude or confirm flavour anomalies. Searches for QCD axions and axion-like particles will seek hints to the solution of the strong CP problem and possible dark-matter candidates.

The Standard Model has so far been confirmed to be the theory that describes physics at the electroweak scale (up to a few hundred GeV) to a remarkable level of precision. All the particles predicted by the theory have been discovered, and the consistency of the theory has been proven with high precision, including all calculable quantum effects. No direct evidence of new physics has been found so far. Still, big open questions remain that the Standard Model cannot answer, from understanding the origin of neutrino masses and their hierarchy, to identifying the origin and nature of dark matter and dark energy, and explaining the dynamics behind the baryon asymmetry of the universe.

Several fields promise qualitative progress in understanding nature in the coming years

The discovery of the Higgs boson has been crucial to confirming the Standard Model as the theory of particle physics at the electroweak scale, but it does not explain why the scalar Brout–Englert–Higgs (BEH) potential takes the form of a Mexican hat, why the electroweak scale is set by a Higgs vacuum expectation value of 246 GeV, or what the nature of the Yukawa force is that results in the bizarre hierarchy of masses coupling the BEH field to quarks and leptons. Gravity is also not a component of the Standard Model, and a unified theory escapes us.

At the LHC today, the ATLAS and CMS collaborations are delivering Run 1 and 2 results with beyond-expectation accuracies on Higgs-boson properties and electroweak precision measurements. Projections for the high-luminosity phase of the LHC are being updated and Run 3 analyses are in full swing. The LHCb collaboration presented another milestone in flavour physics for the first time at Moriond 2025: the first observation of CP violation in baryon decays. Its rebuilt Run 3 detector with triggerless readout and full software trigger reported its first results at this conference.

Several talks presented scenarios of new physics that could be revealed in today’s data given theoretical guidance of sufficient accuracy. These included models with light weakly interacting particles, vector-like fermions and additional scalar particles. Other talks discussed how revisiting established quantum properties such as entanglement with fresh eyes could offer unexplored avenues to new theoretical paradigms and overlooked new-physics effects.

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Among the fundamental particles, tau leptons occupy a curious spot. They participate in the same sort of reactions as their lighter lepton cousins, electrons and muons, but their large mass means that they can also decay into a shower of pions and they interact more strongly with the Higgs boson. In many new-physics theories, Higgs-like particles – beyond that of the Standard Model – are introduced in order to explain the mass hierarchy or as possible portals to dark matter.

Because of their large mass, tau leptons are especially useful in searches for new physics. However, identifying taus is challenging, as in most cases they decay into a final state of one or more pions and an undetected neutrino. A crucial step in the identification of a tau lepton in the CMS experiment is the hadrons-plus-strips (HPS) algorithm. In the standard CMS reconstruction, a minimum momentum threshold of 20 GeV is imposed, such that the taus have enough momentum to make their decay products fall into narrow cones. However, this requirement reduces sensitivity to low-momentum taus. As a result, previous searches for a Higgs-like resonance φ decaying into two tau leptons required a φ-mass of more than 60 GeV.

The CMS experiment has now been able to extend the φ-mass range down to 20 GeV. To improve sensitivity to low-momentum tau decays, machine learning is used to determine a dynamic cone algorithm that expands the cone size as needed. The new algorithm, requiring one tau decaying into a muon and two neutrinos and one tau decaying into hadrons and a neutrino, is implemented in the CMS Scouting trigger system. Scouting extends CMS’s reach into previously inaccessible phase space by retaining only the most relevant information about the event, and thus facilitating much higher event rates.

The sensitivity of the new algorithm is so high that even the upsilon (Υ) meson, a bound state of the bottom quark and its antiquark, can be seen. Figure 1 shows the distribution of the mass of the visible decay products of tau (M_vis), in this case a muon from one tau lepton and either one or three pions from the other. A clear resonance structure is visible at M_vis = 6 GeV, in agreement with the expectation for the Υ meson. The peak is not at the actual mass of the Υ meson (9.46 GeV) due to the presence of neutrinos in the decay. While Υ → ττ decays have been observed at electron–positron colliders, this marks the first evidence at a hadron collider and serves as an important benchmark for the analysis.

Given the high sensitivity of the new algorithm, CMS performed a search for a possible resonance in the range between 20 and 60 GeV using the data recorded in the years 2022 and 2023, and set competitive exclusion limits (see figure 2). For the 2024 and 2025 data taking, the algorithm was further improved, enhancing the sensitivity even more.

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CERN’s Large Hadron Collider continues to deliver surprises. While searching for additional Higgs bosons, the CMS collaboration may have instead uncovered evidence for the smallest composite particle yet observed in nature – a “quasi-bound” hadron made up of the most massive and shortest-lived fundamental particle known to science and its antimatter counterpart. The findings, which do not yet constitute a discovery claim and could also be susceptible to other explanations, were reported this week at the Rencontres de Moriond conference in the Italian Alps.

Almost all of the Standard Model’s shortcomings motivate the search for additional Higgs bosons. Their properties are usually assumed to be simple. Much as the 125 GeV Higgs boson discovered in 2012 appears to interact with each fundamental fermion with a strength proportional to the fermion’s mass, theories postulating additional Higgs bosons generally expect them to couple more strongly to heavier quarks. This puts the singularly massive top quark at centre stage. If an additional Higgs boson has a mass greater than about 345 GeV and can therefore decay to a top quark–antiquark pair, this should dominate the way it decays inside detectors. Hunting for bumps in the invariant mass spectrum of top–antitop pairs is therefore often considered to be the key experimental signature of additional Higgs bosons above the top–antitop production threshold.

The CMS experiment has observed just such a bump. Intriguingly, however, it is located at the lower limit of the search, right at the top-quark pair production threshold itself, leading CMS to also consider an alternative hypothesis long considered difficult to detect: a top–antitop quasi-bound state known as toponium (see “Threshold excess” figure).

The toponium hypothesis is very exciting as we previously did not expect to be able to see it at the LHC

“When we started the project, toponium was not even considered as a background to this search,” explains CMS physics coordinator Andreas Meyer (DESY). “In our analysis today we are only using a simplified model for toponium – just a generic spin-0 colour-singlet state with a pseudoscalar coupling to top quarks. The toponium hypothesis is very exciting as we previously did not expect to be able to see it at the LHC.”

Though other explanations can’t be ruled out, CMS finds the toponium hypothesis to be sufficient to explain the observed excess. The size of the excess is consistent with the latest theoretical estimate of the cross section to produce pseudoscalar toponium of around 6.4 pb.

“The cross section we obtain for our simplified hypothesis is 8.8 pb with an uncertainty of about 15%,” explains Meyer. “One can infer that this is significantly above five sigma.”

The smallest hadron

If confirmed, toponium would be the final example of quarkonium – a term for quark–antiquark states formed from heavy charm, bottom and perhaps top quarks. Charmonium (charm–anticharm) mesons were discovered at SLAC and Brookhaven National Laboratory in the November Revolution of 1974. Bottomonium (bottom–antibottom) mesons were discovered at Fermilab in 1977. These heavy quarks move relatively slowly compared to the speed of light, allowing the strong interaction to be modelled by a static potential as a function of the separation between them. When the quarks are far apart, the potential is proportional to their separation due to the self-interacting gluons forming an elongating flux tube, yielding a constant force of attraction. At close separations, the potential is due to the exchange of individual gluons and is Coulomb-like in form, and inversely proportional to separation, leading to an inverse-square force of attraction. This is the domain where compact quarkonium states are formed, in a near perfect QCD analogy to positronium, wherein an electron and a positron are bound by photon exchange. The Bohr radii of the ground states of charmonium and bottomonium are approximately 0.3 fm and 0.2 fm, and bottomonium is thought to be the smallest hadron yet discovered. Given its larger mass, toponium’s Bohr radius would be an order of magnitude smaller.

For a long time it was thought that toponium bound states were unlikely to be detected in hadron–hadron collisions. The top quark is the most massive and the shortest-lived of the known fundamental particles. It decays into a bottom quark and a real W boson in the time it takes light to travel just 0.1 fm, leaving little time for a hadron to form. Toponium would be unique among quarkonia in that its decay would be triggered by the weak decay of one of its constituent quarks rather than the annihilation of its constituent quarks into photons or gluons. Toponium is expected to decay at twice the rate of the top quark itself, with a width of approximately 3 GeV.

CMS first saw a 3.5 sigma excess in a 2019 search studying the mass range above 400 GeV, based on 35.9 fb⁻¹ of proton–proton collisions at 13 TeV from 2016. Now armed with 138 fb^–1 of collisions from 2016 to 2018, the collaboration extended the search down to the top–antitop production threshold at 345 GeV. Searches are complicated by the possibility that quantum interference between background and Higgs signal processes could generate an experimentally challenging peak–dip structure with a more or less pronounced bump.

“The signal reported by CMS, if confirmed, could be due either to a quasi-bound top–antitop meson, commonly called ‘toponium’, or possibly an elementary spin-zero boson such as appears in models with additional Higgs bosons, or conceivably even a combination of the two,” says theorist John Ellis of King’s College London. “The mass of the lowest-lying toponium state can be calculated quite accurately in QCD, and is expected to lie just below the nominal top–antitop threshold. However, this threshold is smeared out by the short lifetime of the top quark, as well as the mass resolution of an LHC detector, so toponium would appear spread out as a broad excess of events in the final states with leptons and jets that generally appear in top decays.”

Quantum numbers

An important task of the analysis is to investigate the quantum numbers of the signal. It could be a scalar particle, like the Higgs boson discovered in 2012, or a pseudoscalar particle – a different type of spin-0 object with odd rather than even parity. To measure its spin-parity, CMS studied the angular correlations of the top-quark-pair decay products, which retain information on the original quantum state. The decays bear all the experimental hallmarks of a pseudoscalar particle, consistent with toponium (see “Angular analysis” figure) or the pseudoscalar Higgs bosons common to many theories featuring extended Higgs sectors.

“The toponium state produced at the LHC would be a pseudoscalar boson, whose decays into these final states would have characteristic angular distributions, and the excess of events reported by CMS exhibits the angular correlations expected for such a pseudoscalar state,” explains Ellis. “Similar angular correlations would be expected in the decays of an elementary pseudoscalar boson, whereas scalar-boson decays would exhibit different angular correlations that are disfavoured by the CMS analysis.”

Whatever the true cause of the excess, the analyses reflect a vibrant programme of sensitive measurements at the LHC – and the possibility of a timely discovery

Two main challenges now stand in the way of definitively identifying the nature of the excess. The first is to improve the modelling of the creation of top-quark pairs at the LHC, including the creation of bound states at the threshold. The second challenge is to obtain consistency with the ATLAS experiment. “ATLAS had similar studies in the past but with a more conservative approach on the systematic uncertainties,” says ATLAS physics coordinator Fabio Cerutti (LBNL). “This included, for example, larger uncertainties related to parton showers and other top-modelling effects. To shed more light on the CMS observation, be it a new boson, a top quasi-bound state, or some limited understanding of the modelling of top–antitop production at threshold, further studies are needed on our side. We have several analysis teams working on that. We expect to have new results with improved modelling of the top-pair production at threshold and additional variables sensitive to both a new pseudo-scalar boson or a top quasi-bounded state very soon.”

Whatever the true cause of the excess, the analyses reflect a vibrant programme of sensitive measurements at the LHC – and the possibility of a timely discovery.

“Discovering toponium 50 years after the November Revolution would be an unanticipated and welcome golden anniversary present for its charmonium cousin that was discovered in 1974,” concludes Ellis. “The prospective observation and measurement of the vector state of toponium in e⁺e^– collisions around 350 GeV have been studied in considerable theoretical detail, but there have been rather fewer studies of the observability of pseudoscalar toponium at the LHC. In addition to the angular correlations observed by CMS, the effective production cross section of the observed threshold effect is consistent with non-relativistic QCD calculations. More detailed calculations will be desirable for confirmation that another quarkonium family member has made its appearance, though the omens are promising.”

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Fundamental charged particles have spins that wobble in a magnetic field. This is just one of the insights that emerged from the equation Paul Dirac wrote down in 1928. Almost 100 years later, calculating how much they wobble – their “magnetic moment” – strains the computational sinews of theoretical physicists to a level rarely matched. The challenge is to sum all the possible ways in which the quantum fluctuations of the vacuum affect their wobbling.

The particle in question here is the muon. Discovered in cosmic rays in 1936, muons are more massive but ephemeral cousins of the electron. Their greater mass is expected to amplify the effect of any undiscovered new particles shimmering in the quantum haze around them, and measurements have disagreed with theoretical predictions for nearly 20 years. This suggests a possible gap in the Standard Model (SM) of particle physics, potentially providing a glimpse of deeper truths beyond it.

In the coming weeks, Fermilab is expected to present the final results of a seven-year campaign to measure this property, reducing uncertainties to a remarkable one part in 10¹⁰ on the magnetic moment of the muon, and 0.1 parts per million on the quantum corrections. Theorists are racing to match this with an updated prediction of comparable precision. The calculation is in good shape, except for the incredibly unusual eventuality that the muon briefly emits a cloud of quarks and gluons at just the moment it absorbs a photon from the magnetic field. But in quantum mechanics all possibilities count all the time, and the experimental precision is such that the fine details of “hadronic vacuum polarisation” (HVP) could be the difference between reinforcing the SM and challenging it.

Quantum fluctuations

The Dirac equation predicts that fundamental spin s = ½ particles have a magnetic moment given by g(eħ/2m)s, where the gyromagnetic ratio (g) is precisely equal to two. For the electron, this remarkable result was soon confirmed by atomic spectroscopy, before more precise experiments in 1947 indicated a deviation from g = 2 of a few parts per thousand. Expressed as a = (g-2)/2, the shift was a surprise and was named the magnetic anomaly or the anomalous magnetic moment.

This marked the beginning of an enduring dialogue between experiment and theory. It became clear that a relativistic field theory like the developing quantum electrodynamics (QED) could produce quantum fluctuations, shifting g from two. In 1948, Julian Schwinger calculated the first correction to be a = α/2π ≈ 0.00116, aligning beautifully with 1947 experimental results. The emission and absorption of a virtual photon creates a cloud around the electron, altering its interaction with the external magnetic field (see “Quantum fluctuation” figure). Soon, other particles would be seen to influence the calculations. The SM’s limitations suggest that undiscovered particles could also affect these calculations. Their existence might be revealed by a discrepancy between the SM prediction for a particle’s anomalous magnetic moment and its measured value.

As noted, the muon is an even more promising target than the electron, as its sensitivity to physics beyond QED is generically enhanced by the square of the ratio of their masses: a factor of around 43,000. In 1957, inspired by Tsung-Dao Lee and Chen-Ning Yang’s proposal that parity is violated in the weak interaction, Richard Garwin, Leon Lederman and Marcel Weinrich studied the decay of muons brought to rest in a magnetic field at the Nevis cyclotron at Columbia University. As well as showing that parity is broken in both pion and muon decays, they found g to be close to two for muons by studying their “precession” in the magnetic field as their spins circled around the field lines.

This iconic experiment was the prototype of muon-precession projects at CERN (see CERN Courier September/October 2024 p53), later at Brookhaven National Laboratory and now Fermilab (see “Precision” figure). By the end of the Brookhaven project, a disagreement between the measured value of “a_μ” – the subscript indicating g-2 for the muon rather than the electron – and the SM prediction was too large to ignore, motivating the present round of measurements at Fermilab and rapidly improving theory refinements.

g-2 and the Standard Model

Today, a prediction for a_μ must include the effects of all three of the SM’s interactions and all of its elementary particles. The leading contributions are from electrons, muons and tau leptons interacting electromagnetically. These QED contributions can be computed in an expansion where each successive term contributes only around 1% of the previous one. QED effects have been computed to fifth order, yielding an extraordinary precision of 0.9 parts per billion – significantly more precise than needed to match measurements of the muon’s g-2, though not the electron’s. It took over half a century to achieve this theoretical tour de force.

The weak interaction gives the smallest contribution to a_μ, a million times less than QED. These contributions can also be computed in an expansion. Second order suffices. All SM particles except gluons need to be taken into account.

Gluons are responsible for the strong interaction and appear in the third and last set of contributions. These are described by QCD and are called “hadronic” because quarks and gluons form hadrons at the low energies relevant for the muon g-2 (see “Hadronic contributions” figure). HVP is the largest, though 10,000 times smaller than the corrections due to QED. “Hadronic light-by-light scattering” (HLbL) is a further 100 times smaller due to the exchange of an additional photon. The challenge is that the strong-interaction effects cannot be approximated by a perturbative expansion. QCD is highly nonlinear and different methods are needed.

Data or the lattice?

Even before QCD was formulated, theorists sought to subdue the wildness of the strong force using experimental data. In the case of HVP, this triggered experimental investigations of e⁺e^– annihilation into hadrons and later hadronic tau–lepton decays. Though apparently disparate, the production of hadrons in these processes can be related to the clouds of virtual quarks and gluons that are responsible for HVP.

A more recent alternative makes use of massively parallel numerical simulations to directly solve the equations of QCD. To compute quantities such as HVP or HLbL, “lattice QCD” requires hundreds of millions of processor-core hours on the world’s largest supercomputers.

In preparation for Fermilab’s first measurement in 2021, the Muon g-2 Theory Initiative, spanning more than 120 collaborators from over 80 institutions, was formed to provide a reference SM prediction that was published in a 2020 white paper. The HVP contribution was obtained with a precision of a few parts per thousand using a compilation of measurements of e⁺e^– annihilation into hadrons. The HLbL contribution was determined from a combination of data-driven and lattice–QCD methods. Though even more complex to compute, HLbL is needed only to 10% precision, as its contribution is smaller.

After summing all contributions, the prediction of the 2020 white paper sits over five standard deviations below the most recent experimental world average (see “Landscape of muon g-2” figure). Such a deviation would usually be interpreted as a discovery of physics beyond the SM. However, in 2021 the result of the first lattice calculation of the HVP contribution with a precision comparable to that of the data-driven white paper was published by the Budapest–Marseille–Wuppertal collaboration (BMW). The result, labelled BMW 2020 as it was uploaded to the preprint archive the previous year, is much closer to the experimental average (green band on the figure), suggesting that the SM may still be in the race. The calculation relied on methods developed by dozens of physicists since the seminal work of Tom Blum (University of Connecticut) in 2002 (see CERN Courier May/June 2021 p25).

In 2020, the uncertainties on the data-driven and lattice-QCD predictions for the HVP contribution were still large enough that both could be correct, but BMW’s 2021 paper showed them to be explicitly incompatible in an “intermediate-distance window” accounting for approximately 35% of the HVP contribution, where lattice QCD is most reliable.

This disagreement was the first sign that the 2020 consensus had to be revised. To move forward, the sources of the various disagreements – more numerous now – and the relative limitations of the different approaches must be understood better. Moreover, uncertainty on HVP already dominated the SM prediction in 2020. As well as resolving these discrepancies, its uncertainty must be reduced by a factor of three to fully leverage the coming measurement from Fermilab. Work on the HVP is therefore even more critical than before, as elsewhere the theory house is in order: Sergey Volkov (KITP) recently verified the fifth-order QED calculation of Tatsumi Aoyama, Toichiro Kinoshita and Makiko Nio, identifying an oversight not numerically relevant at current experimental sensitivities; new HLbL calculations remain consistent; and weak contributions have already been checked and are precise enough for the foreseeable future.

News from the lattice

Since BMW’s 2020 lattice results, a further eight lattice-QCD computations of the dominant up-and-down-quark (u + d) contribution to HVP’s intermediate-distance window have been performed with similar precision, with four also including all other relevant contributions. Agreement is excellent and the verdict is clear: the disagreement between the lattice and data-driven approaches is confirmed (see “Intermediate window” figure).

Work on the short-distance window (about 10% of the HVP contribution) has also advanced rapidly. Seven computations of the u + d contribution have appeared, with four including all other relevant contributions. No significant disagreement is observed.

The long-distance window (around 55% of the total) is by far the most challenging, with the largest uncertainties. In recent weeks three calculations of the dominant u + d contribution have appeared, by the RBC–UKQCD, Mainz and FHM collaborations. Though some differences are present, none can be considered significant for the time being.

With all three windows cross-validated, the Muon g-2 Theory Initiative is combining results to obtain a robust lattice–QCD determination of the HVP contribution. The final uncertainty should be slightly below 1%, still quite far from the 0.2% ultimately needed.

The BMW–DMZ and Mainz collaborations have also presented new results for the full HVP contribution to a_μ, and the RBC–UKQCD collaboration, which first proposed the multi-window approach, is also in a position to make a full calculation. (The corresponding result in the “Landscape of muon g-2” figure combines contributions reported in their publications.) Mainz obtained a result with 1% precision using the three windows described above. BMW–DMZ divided its new calculation into five windows and replaced the lattice–QCD computation of the longest distance window – “the tail”, encompassing just 5% of the total – with a data-driven result. This pragmatic approach allows a total uncertainty of just 0.46%, with the collaboration showing that all e⁺e^– datasets contributing to this long-distance tail are entirely consistent. This new prediction differs from the experimental measurement of a_μ by only 0.9 standard deviations.

These new lattice results, which have not yet been published in refereed journals, make the disagreement with the 2020 data-driven result even more blatant. However, the analysis of the annihilation of e⁺e^– into hadrons is also evolving rapidly.

News from electron–positron annihilation

Many experiments have measured the cross-section for e⁺e^– annihilation to hadrons as a function of centre-of-mass energy (√s). The dominant contribution to a data-driven calculation of a_μ, and over 70% of its uncertainty budget, is provided by the e⁺e^– → π⁺π^– process, in which the final-state pions are produced via the ρ resonance (see “Two-pion channel” figure).

The most recent measurement, by the CMD-3 energy-scan experiment in Novosibirsk, obtained a cross-section on the peak of the ρ resonance that is larger than all previous ones, significantly changing the picture in the π⁺π^– channel. Scrutiny by the Theory Initiative has identified no major problem.

CMD-3’s approach contrasts that used by KLOE, BaBar and BESIII, which study e⁺e^– annihilation with a hard photon emitted from the initial state (radiative return) at facilities with fixed √s. BaBar has innovated by calibrating the luminosity of the initial-state radiation using the μ⁺μ^– channel and using a unique “next-to-leading-order” approach that accounts for extra radiation from either the initial or the final state – a necessary step at the required level of precision.

In 1997, Ricard Alemany, Michel Davier and Andreas Höcker proposed an alternative method that employs τ^– → π^–π⁰ν decay while requiring some additional theoretical input. The decay rate has been precisely measured as a function of the two-pion invariant mass by the ALEPH and OPAL experiments at LEP, as well as by the Belle and CLEO experiments at B factories, under very different conditions. The measurements are in good agreement. ALEPH offers the best normalisation and Belle the best shape measurement.

KLOE and CMD-3 differ by more than five standard deviations on the ρ peak, precluding a combined analysis of e⁺e^– → π⁺π^– cross-sections. BaBar and τ data lie between them. All measurements are in good agreement at low energies, below the ρ peak. BaBar, CMD-3 and τ data are also in agreement above the ρ peak. To help clarify this unsatisfactory situation, in 2023 BaBar performed a careful study of radiative corrections to e⁺e^– → π⁺π^–. That study points to the possible underestimate of systematic uncertainties in radiative-return experiments that rely on Monte Carlo simulations to describe extra radiation, as opposed to the in situ studies performed by BaBar.

The future

While most contributions to the SM prediction of the muon g-2 are under control at the level of precision required to match the forthcoming Fermilab measurement, in trying to reduce the uncertainties of the HVP contribution to a commensurate degree, theorists and experimentalists shattered a 20 year consensus. This has triggered an intense collective effort that is still in progress.

The prospect of testing the limits of the SM through high-precision measurements generates considerable impetus

New analyses of e⁺e^– are underway at BaBar, Belle II, BES III and KLOE, experiments are continuing at CMD-3, and Belle II is also studying τ decays. At CERN, the longer term “MUonE” project will extract HVP by analysing how muons scatter off electrons – a very challenging endeavour regarding the unusual accuracy required both in the control of experimental systematic uncertainties and also theoretically, for the radiative corrections.

At the same time, lattice-QCD calculations have made enormous progress in the last five years and provide a very competitive alternative. The fact that several groups are involved with somewhat independent techniques is allowing detailed cross checks. The complementarity of the data-driven and lattice-QCD approaches should soon provide a reliable value for the g-2 theoretical prediction at unprecedented levels of precision.

There is still some way to go to reach that point, but the prospect of testing the limits of the SM through high-precision measurements generates considerable impetus. A new white paper is expected in the coming weeks. The ultimate aim is to reach a level of precision in the SM prediction that allows us to fully leverage the potential of the muon anomalous magnetic moment in the search for new fundamental physics, in concert with the final results of Fermilab’s Muon g-2 experiment and the projected Muon g-2/EDM experiment at J-PARC in Japan, which will implement a novel technique.

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Triggering systems play a crucial role in filtering the vast amounts of data generated by modern collider experiments. A good trigger design selects features in the event sample that greatly enrich the proportion of the desired physics processes in the recorded data. The key considerations are timing and selectivity. Timing has long been at the core of experiment design – detectors must capture data at the appropriate time to record an event. Selectivity has been a feature of triggering for almost as long. Recording an event makes demands on running time and data-acquisition bandwidth, both of which are limited.

Evolving architecture

Thanks to detector upgrades and major changes in the cost and availability of fast data links and storage, the past 10 years have seen an evolution in LHC triggers away from hardware-based decisions using coarse-grain information.

Detector upgrades mean higher granularity and better time resolution, improving the precision of the trigger algorithms and the ability to resolve the problem of having multiple events in a single LHC bunch crossing (“pileup”). Such upgrades allow more precise initial-level hardware triggering, bringing the event rate down to a level where events can be reconstructed for further selection via high-level trigger (HLT) systems.

To take advantage of modern computer architecture more fully, HLTs use both graphics processing units (GPUs) and central processing units (CPUs) to process events. In ALICE and LHCb this leads to essentially triggerless access to all events, while in ATLAS and CMS hardware selections are still important. All HLTs now use machine learning (ML) algorithms, with the ATLAS and CMS experiments even considering their use at the first hardware level.

ATLAS and CMS are primarily designed to search for new physics. At the end of Run 3, upgrades to both experiments will significantly enhance granularity and time resolution to handle the high-luminosity environment of the HL-LHC, which will deliver up to 200 interactions per LHC bunch crossing. Both experiments achieved efficient triggering in Run 3, but higher luminosities, difficult-to-distinguish physics signatures, upgraded detectors and increasingly ambitious physics goals call for advanced new techniques. The step change will be significant. At HL-LHC, the first-level hardware trigger rate will increase from the current 100 kHz to 1 MHz in ATLAS and 760 kHz in CMS. The price to pay is increasing the latency – the time delay between input and output – to 10 µsec in ATLAS and 12.5 µsec in CMS.

The proposed trigger systems for ATLAS and CMS are predominantly FPGA-based, employing highly parallelised processing to crunch huge data streams efficiently in real time. Both will be two-level triggers: a hardware trigger followed by a software-based HLT. The ATLAS hardware trigger will utilise full-granularity calorimeter and muon signals in the global-trigger-event processor, using advanced ML techniques for real-time event selection. In addition to calorimeter and muon data, CMS will introduce a global track trigger, enabling real-time tracking at the first trigger level. All information will be integrated within the global-correlator trigger, which will extensively utilise ML to enhance event selection and background suppression.

Substantial upgrades

The other two big LHC experiments already implemented substantial trigger upgrades at the beginning of Run 3. The ALICE experiment is dedicated to studying the strong interactions of the quark–gluon plasma – a state of matter in which quarks and gluons are not confined in hadrons. The detector was upgraded significantly for Run 3, including the trigger and data-acquisition systems. The ALICE continuous readout can cope with 50 kHz for lead ion–lead ion (PbPb) collisions and several MHz for proton–proton (pp) collisions. In PbPb collisions the full data is continuously recorded and stored for offline analysis, while for pp collisions the data is filtered.

Unlike in Run 2, where the hardware trigger reduced the data rate to several kHz, Run 3 uses an online software trigger that is a natural part of the common online–offline computing framework. The raw data from detectors is streamed continuously and processed in real time using high-performance FPGAs and GPUs. ML plays a crucial role in the heavy-flavour software trigger, which is one of the main physics interests. Boosted decision trees are used to identify displaced vertices from heavy quark decays. The full chain from saving raw data in a 100 PB buffer to selecting events of interest and removing the original raw data takes about three weeks and was fully employed last year.

The third edition of TDHEP suggests that innovation in this field is only set to accelerate

The LHCb experiment focuses on precision measurements in heavy-flavour physics. A typical example is measuring the probability of a particle decaying into a certain decay channel. In Run 2 the hardware trigger tended to saturate in many hadronic channels when the luminosity was instantaneously increased. To solve this issue for Run 3 a high-level software trigger was developed that can handle 30 MHz event readout with 4 TB/s data flow. A GPU-based partial event reconstruction and primary selection of displaced tracks and vertices (HLT1) reduces the output data rate to 1 MHz. The calibration and detector alignment (embedded into the trigger system) are calculated during data taking just after HLT1 and feed full-event reconstruction (HLT2), which reduces the output rate to 20 kHz. This represents 10 GB/s written to disk for later analysis.

Away from the LHC, trigger requirements differ considerably. Contributions from other areas covered heavy-ion physics at Brookhaven National Laboratory’s Relativistic Heavy Ion Collider (RHIC), fixed-target physics at CERN and future experiments at the Facility for Antiproton and Ion Research at GSI Darmstadt and Brookhaven’s Electron–Ion Collider (EIC). NA62 at CERN and STAR at RHIC both use conventional trigger strategies to arrive at their final event samples. The forthcoming CBM experiment at FAIR and the ePIC experiment at the EIC deal with high intensities but aim for “triggerless” operation.

Requirements were reported to be even more diverse in astroparticle physics. The Pierre Auger Observatory combines local and global trigger decisions at three levels to manage the problem of trigger distribution and data collection over 3000 km² of fluorescence and Cherenkov detectors.

These diverse requirements will lead to new approaches being taken, and evolution as the experiments are finalised. The third edition of TDHEP suggests that innovation in this field is only set to accelerate.

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Space Oddities takes readers on a journey through the mysteries of modern physics, from the smallest subatomic particles to the vast expanse of stars and space. Harry Cliff – an experimental particle physicist at Cambridge University – unravels some of the most perplexing anomalies challenging the Standard Model (SM), with behind-the-scenes scoops from eight different experiments. The most intriguing stories concern lepton universality and the magnetic moment of the muon.

Theoretical predictions have demonstrated an extremely precise value for the muon’s magnetic moment, experimentally verified to an astonishing 11 significant figures. Over the last few years, however, experimental measurements have suggested a slight discrepancy – the devil lying in the 12th digit. 2021 measurements at Fermilab disagreed with theory predictions at 4σ. Not enough to cause a “scientific earthquake”, as Cliff puts it, but enough to suggest that new physics might be at play.

Just as everything seemed to be edging towards a new discovery, Cliff introduces the “villains” of the piece. Groundbreaking lattice–QCD predictions from the Budapest–Marseille–Wuppertal collaboration were published on the same day as a new measurement from Fermilab. If correct, these would destroy the anomaly by contradicting the data-driven theory consensus. (“Yeah, bullshit,” said one experimentalist to Cliff when put to him that the timing wasn’t intended to steal the experiment’s thunder.) The situation is still unresolved, though many new theoretical predictions have been made and a new theoretical consensus is imminent (see “Do muons wobble faster than expected“). Regardless of the outcome, Cliff emphasises that this research will pave the way for future discoveries, and none of it should be taken for granted – even if the anomaly disappears.

“One of the challenging aspects of being part of a large international project is that your colleagues are both collaborators and competitors,” Cliff notes. “When it comes to analysing the data with the ultimate goal of making discoveries, each research group will fight to claim ownership of the most interesting topics.”

This spirit of spurring collaborator- competitors on to greater heights of precision is echoed throughout Cliff’s own experience of working in the LHCb collaboration, where he studies “lepton universality”. All three lepton flavours – electron, muon and tau – should interact almost identically, except for small differences due to their masses. However, over the past decade several experimental results suggested that this theory might not hold in B-meson decays, where muons seemed to be appearing less frequently than electrons. If confirmed, this would point to physics beyond the SM.

Having been involved himself in a complementary but less sensitive analy­sis of B-meson decay channels involving strange quarks, Cliff recalls the emotional rollercoaster experienced by some of the key protagonists: the “RK” team from Imperial College London. After a year of rigorous testing, RK unblinded a sanity check of their new computational toolkit: a reanalysis of the prior measurement that yielded a perfectly consistent R value of 0.72 with an uncertainty of about 0.08, upholding a 3σ discrepancy. Now was the time to put the data collected since then through the same pasta machine: if it agreed, the tension between the SM and their overall measurement would cross the 5σ threshold. After an anxious wait while the numbers were crunched, the team received the results for the new data: 0.93 with an uncertainty of 0.09.

“Dreams of a major discovery evaporated in an instant,” recalls Cliff. “Anyone who saw the RK team in the CERN cafeteria that day could read the result from their faces.” The lead on the RK team, Mitesh Patel, told Cliff that they felt “emotionally train wrecked”.

One day we might make the right mistake and escape the claustrophobic clutches of the SM

With both results combined, the ratio averaged out to 0.85 ± 0.06, just shy of 3σ away from unity. While the experimentalists were deflated, Cliff notes that for theorists this result may have been more exciting than the initial anomaly, as it was easier to explain using new particles or forces. “It was as if we were spying the footprints of a great, unknown beast as it crashed about in a dark jungle,” writes Cliff.

Space Oddities is a great defence of irrepressible experimentation. Even “failed” anomalies are far from useless: if they evaporate, the effort required to investigate them pushes the boundaries of experimental precision, enhances collaboration between scientists across the world, and refines theoretical frameworks. Through retellings and interviews, Cliff helps the public experience the excitement of near breakthroughs, the heartbreak of failed experiments, and the dynamic interactions between theoretical and experimental physicists. Thwarting myths that physicists are cold, calculating figures working in isolation, Cliff sheds light on a community driven by curiosity, ambition and (healthy) competition. His book is a story of hope that one day we might make the right mistake and escape the claustrophobic clutches of the SM.

“I’ve learned so much from my mistakes,” read a poster above Cliff’s undergraduate tutor’s desk. “I think I’ll make another.”

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What motivates you to be CERN’s next Director-General?

CERN is an incredibly important organisation. I believe my deep passion for particle physics, coupled with the experience I have accumulated in recent years, including leading the Deep Underground Neutrino Experiment, DUNE, through a formative phase, and running the Science and Technology Facilities Council in the UK, has equipped me with the right skill set to lead CERN though a particularly important period.

How would you describe your management style?

That’s a good question. My overarching approach is built around delegating and trusting my team. This has two advantages. First, it builds an empowering culture, which in my experience provides the right environment for people to thrive. Second, it frees me up to focus on strategic planning and engagement with numerous key stakeholders. I like to focus on transparency and openness, to build trust both internally and externally.

How will you spend your familiarisation year before you take over in 2026?

First, by getting a deep understanding of CERN “from within”, to plan how I want to approach my mandate. Second, by lending my voice to the scientific discussion that will underpin the third update to the European strategy for particle physics. The European strategy process is a key opportunity for the particle-physics community to provide genuine bottom-up input and shape the future. This is going to be a really varied and exciting year.

What open question in fundamental physics would you most like to see answered in your lifetime?

I am going to have to pick two. I would really like to understand the nature of dark matter. There are a wide range of possibilities, and we are addressing this question from multiple angles; the search for dark matter is an area where the collider and non-collider experiments can both contribute enormously. The second question is the nature of the Higgs field. The Higgs boson is just so different from anything else we’ve ever seen. It’s not just unique – it’s unique and very strange. There are just so many deep questions, such as whether it is fundamental or composite. I am confident that we will make progress in the coming years. I believe the High-Luminosity LHC will be able to make meaningful measurements of the self-coupling at the heart of the Higgs potential. If you’d asked me five years ago whether this was possible, I would have been doubtful. But today I am very optimistic because of the rapid progress with advanced analysis techniques being developed by the brilliant scientists on the LHC experiments.

What areas of R&D are most in need of innovation to meet our science goals?

Artificial intelligence is changing how we look at data in all areas of science. Particle physics is the ideal testing ground for artificial intelligence, because our data is complex there are none of the issues around the sensitive nature of the data that exist in other fields. Complex multidimensional datasets are where you’ll benefit the most from artificial intelligence. I’m also excited by the emergence of new quantum technologies, which will open up fresh opportunities for our detector systems and also new ways of doing experiments in fundamental physics. We’ve only scratched the surface of what can be achieved with entangled quantum systems.

How about in accelerator R&D?

There are two areas that I would like to highlight: making our current technologies more sustainable, and the development of high-field magnets based on high-temperature superconductivity. This connects to the question of innovation more broadly. To quote one example among many, high-temperature superconducting magnets are likely to be an important component of fusion reactors just as much as particle accelerators, making this a very exciting area where CERN can deploy its engineering expertise and really push that programme forward. That’s not just a benefit for particle physics, but a benefit for wider society.

How has CERN changed since you were a fellow back in 1994?

The biggest change is that the collider experiments are larger and more complex, and the scientific and technical skills required have become more specialised. When I first came to CERN, I worked on the OPAL experiment at LEP – a collaboration of less than 400 people. Everybody knew everybody, and it was relatively easy to understand the science of the whole experiment.

My overarching approach is built around delegating and trusting my team

But I don’t think the scientific culture of CERN and the particle-physics community has changed much. When I visit CERN and meet with the younger scientists, I see the same levels of excitement and enthusiasm. People are driven by the wonderful mission of discovery. When planning the future, we need to ensure that early-career researchers can see a clear way forward with opportunities in all periods of their career. This is essential for the long-term health of particle physics. Today we have an amazing machine that’s running beautifully: the LHC. I also don’t think it is possible to overstate the excitement of the High-Luminosity LHC. So there’s a clear and exciting future out to the early 2040s for today’s early-career researchers. The question is what happens beyond that? This is one reason to ensure that there is not a large gap between the end of the High-Luminosity LHC and the start of whatever comes next.

Should the world be aligning on a single project?

Given the increasing scale of investment, we do have to focus as a global community, but that doesn’t necessarily mean a single project. We saw something similar about 10 years ago when the global neutrino community decided to focus its efforts on two complementary long-baseline projects, DUNE and Hyper-Kamiokande. From the perspective of today’s European strategy, the Future Circular Collider (FCC) is an extremely appealing project that would map out an exciting future for CERN for many decades. I think we’ll see this come through strongly in an open and science-driven European strategy process.

How do you see the scientific case for the FCC?

For me, there are two key points. First, gaining a deep understanding of the Higgs boson is the natural next step in our field. We have discovered something truly unique, and we should now explore its properties to gain deeper insights into fundamental physics. Scientifically, the FCC provides everything you want from a Higgs factory, both in terms of luminosity and the opportunity to support multiple experiments.

Second, investment in the FCC tunnel will provide a route to hadron–hadron collisions at the 100 TeV scale. I find it difficult to foresee a future where we will not want this capability.

These two aspects make the FCC a very attractive proposition.

How successful do you believe particle physics is in communicating science and societal impacts to the public and to policymakers?

I think we communicate science well. After all, we’ve got a great story. People get the idea that we work to understand the universe at its most basic level. It’s a simple and profound message.

Going beyond the science, the way we communicate the wider industrial and societal impact is probably equally important. Here we also have a good story. In our experiments we are always pushing beyond the limits of current technology, doing things that have not been done before. The technologies we develop to do this almost always find their way back into something that will have wider applications. Of course, when we start, we don’t know what the impact will be. That’s the strength and beauty of pushing the boundaries of technology for science.

Would the FCC give a strong return on investment to the member states?

Absolutely. Part of the return is the science, part is the investment in technology, and we should not underestimate the importance of the training opportunities for young people across Europe. CERN provides such an amazing and inspiring environment for young people. The scale of the FCC will provide a huge number of opportunities for young scientists and engineers.

We need to ensure that early-career researchers can see a clear way forward with opportunities in all periods of their career. This is essential for the long-term health of particle physics

In terms of technology development, the detectors for the electron–positron collider will provide an opportunity for pushing forward and deploying new, advanced technologies to deliver the precision required for the science programme. In parallel, the development of the magnet technologies for the future hadron collider will be really exciting, particularly the potential use of high-temperature superconductors, as I said before.

It is always difficult to predict the specific “return on investment” on the technologies for big scientific research infrastructure. Part of this challenge is that some of that benefits might be 20, 30, 40 years down the line. Nevertheless, every retrospective that has tried, has demonstrated that you get a huge downstream benefit.

Do we reward technical innovation well enough in high-energy physics?

There needs to be a bit of a culture shift within our community. Engineering and technology innovation are critical to the future of science and critical to the prosperity of Europe. We should be striving to reward individuals working in these areas.

Should the field make it more flexible for physicists and engineers to work in industry and return to the field having worked there?

This is an important question. I actually think things are changing. The fluidity between academia and industry is increasing in both directions. For example, an early-career researcher in particle physics with a background in deep artificial-intelligence techniques is valued incredibly highly by industry. It also works the other way around, and I experienced this myself in my career when one of my post-doctoral researchers joined from an industry background after a PhD in particle physics. The software skills they picked up from industry were incredibly impactful.

I don’t think there is much we need to do to directly increase flexibility – it’s more about culture change, to recognise that fluidity between industry and academia is important and beneficial. Career trajectories are evolving across many sectors. People move around much more than they did in the past.

Does CERN have a future as a global laboratory?

CERN already is a global laboratory. The amazing range of nationalities working here is both inspiring and a huge benefit to CERN.

How can we open up opportunities in low- and middle-income countries?

I am really passionate about the importance of diversity in all its forms and this includes national and regional inclusivity. It is an agenda that I pursued in my last two positions. At the Deep Underground Neutrino Experiment, I was really keen to engage the scientific community from Latin America, and I believe this has been mutually beneficial. At STFC, we used physics as a way to provide opportunities for people across Africa to gain high-tech skills. Going beyond the training, one of the challenges is to ensure that people use these skills in their home nations. Otherwise, you’re not really helping low- and middle-income countries to develop.

What message would you like to leave with readers?

That we have really only just started the LHC programme. With more than a factor of 10 increase in data to come, coupled with new data tools and upgraded detectors, the High-Luminosity LHC represents a major opportunity for a new discovery. Its nature could be a complete surprise. That’s the whole point of exploring the unknown: you don’t know what’s out there. This alone is incredibly exciting, and it is just a part of CERN’s amazing future.

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Since the LHC began operations in 2008, the CMS experiment has been searching for signs of supersymmetry (SUSY) – the only remaining spacetime symmetry not yet observed to have consequences for physics. It has explored higher and higher masses of supersymmetric particles (sparticles) with increasing collision energies and growing datasets. No evidence has been observed so far. A new CMS analysis using data recorded between 2016 and 2018 continues this search in an often overlooked, difficult corner of SUSY manifestations: compressed sparticle mass spectra.

The masses of SUSY sparticles have very important implications for both the physics of our universe and how they could be potentially produced and observed at experiments like CMS. The heavier the sparticle, the rarer its appearance. On the other hand, when heavy sparticles decay, their mass is converted to the masses and momenta of SM particles, like leptons and jets. These particles are detected by CMS, with large masses leaving potentially spectacular (and conspicuous) signatures. Each heavy sparticle is expected to continue to decay to lighter ones, ending with the lightest SUSY particles (LSPs). LSPs, though massive, are stable and do not decay in the detector. Instead, they appear as missing momentum. In cases of compressed sparticle mass spectra, the mass difference between the initially produced sparticles and LSPs is small. This means the low rates of production of massive sparticles are not accompanied by high-momentum decay products in the detector. Most of their mass ends up escaping in the form of invisible particles, significantly complicating observation.

This new CMS result turns this difficulty on its head, using a kinematic observable R_ISR, which is directly sensitive to the mass of LSPs as opposed to the mass difference between parent sparticles and LSPs. The result is even better discrimination between SUSY and SM backgrounds when sparticle spectra are more compressed.

This approach focuses on events where putative SUSY candidates receive a significant “kick” from initial-state radiation (ISR) – additional jets recoiling opposite the system of sparticles. When the sparticle masses are highly compressed, the invisible, massive LSPs receive most of the ISR momentum-kick, with this fraction telling us about the LSP masses through the R_ISR observable.

Given the generic applicability of the approach, the analysis is able to systematically probe a large class of possible scenarios. This includes events with various numbers of leptons (0, 1, 2 or 3) and jets (including those from heavy-flavour quarks), with a focus on objects with low momentum. These multiplicities, along with R_ISR and other selected discriminating variables, are used to categorise recorded events and a comprehensive fit is performed to all these regions. Compressed SUSY signals would appear at larger values of R_ISR, while bins at lower values are used to model and constrain SM backgrounds. With more than 2000 different bins in R_ISR, over several hundred object-based categ­ories, a significant fraction of the experimental phase space in which compressed SUSY could hide is scrutinised.

In the absence of significant observed deviations in data yields from SM expectations, a large collection of SUSY scenarios can be excluded at high confidence level (CL), including those with the production of stop quarks, EWKinos and sleptons. As can be seen in the results for stop quarks (figure 1), the analysis is able to achieve excellent sensitivity to compressed SUSY. Here, as for many of the SUSY scenarios considered, the analy­sis provides the world’s most stringent constraints on compressed SUSY, further narrowing the space it could be hiding.

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Magnetic monopoles are hypothetical particles that would carry magnetic charge, a concept first proposed by Paul Dirac in 1931. He pointed out that if monopoles exist, electric charge must be quantised, meaning that particle charges must be integer multiples of a fundamental charge. Electric charge quantisation is indeed observed in nature, with no other known explanation for this striking phenomenon. The ATLAS collaboration performed a search for these elusive particles using lead–lead (PbPb) collisions at 5.36 TeV from Run 3 of the Large Hadron Collider.

The search targeted the production of monopole–antimonopole pairs via photon–photon interactions, a process enhanced in heavy-ion collisions due to the strong electromagnetic fields (∝Z²) generated by the Z = 82 lead nuclei. Ultraperipheral collisions are ideal for this search, as they feature electromagnetic interactions without direct nuclear contact, allowing rare processes like monopole production to dominate in visible signatures. The ATLAS study employed a novel detection technique exploiting the expected highly ionising nature of these particles, leaving a characteristic signal in the innermost silicon detectors of the ATLAS experiment (figure 1).

The analysis employed a non-perturbative semiclassical model to estimate monopole production. Traditional perturbative models, which rely on Feynman diagrams, are inadequate due to the large coupling constant of magnetic monopoles. Instead, the study used a model based on the Schwinger mechanism, adapted for magnetic fields, to predict monopole production in the ultraperipheral collisions’ strong magnetic fields. This approach offers a more robust
theoretical framework for the search.

The experiment’s trigger system was critical to the search. Given the high ionisation signature of monopoles, traditional calorimeter-based triggers were unsuitable, as even high-momentum monopoles lose energy rapidly through ionisation and do not reach the calorimeter. Instead, the trigger, newly introduced for the 2023 PbPb data-taking campaign, focused on detecting the forward neutrons emitted during electromagnetic interactions. The level-1 trigger system identified neutrons using the Zero-Degree Calorimeter, while the high-level trigger required more than 100 clusters of pixel-detector hits in the inner detector – an approach sensitive to monopoles due to their high ionisation signatures.

Additionally, the analysis examined the topology of pixel clusters to further refine the search, as a more aligned azimuthal distribution in the data would indicate a signature consistent with monopoles (figure 1), while the uniform distribution typically associated with beam-induced backgrounds could be identified and suppressed.

No significant monopole signal is observed beyond the expected background, with the latter being estimated using a data-driven technique. Consequently, the analysis set new upper limits on the cross-section for magnetic monopole production (figure 2), significantly improving existing limits for low-mass monopoles in the 20–150 GeV range. Assuming a non-perturbative semiclassical model, the search excludes monopoles with a single Dirac magnetic charge and masses below 120 GeV. The techniques developed in this search will open new possibilities to study other highly ionising particles that may emerge from beyond-Standard Model physics.

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The accidental symmetries observed between the three generations of leptons are poorly understood, with no compelling theoretical motivation in the framework of the Standard Model (SM). The b → cτ^–ν_τ transition has the potential to reveal new particles or forces that interact primarily with third-generation particles, which are subject to the less stringent experimental constraints at present. As a tree-level SM process mediated by W-boson exchange, its amplitude is large, resulting in large branching fractions and significant data samples to analyse.

The observable under scrutiny is the ratio of decay rates between the signal mode involving τ and ν_τ leptons from the third generation of fermions and the normalisation mode containing μ and ν_μ leptons from the second generation. Within the SM, this lepton flavour universality (LFU) ratio deviates from unity only due to the different mass of the charged leptons – but new contributions could change the value of the ratios. A longstanding tension exists between the SM prediction and the experimental measurements, requiring further input to clarify the source of the discrepancy.

The LHCb collaboration analysed four decay modes: B⁰ → D^(*)+ℓ^–ν_ℓ, with ℓ representing τ or μ. Each is selected using the same visible final state of one muon and light hadrons from the decay of the charm meson. In the normalisation mode, the muon originates directly from the B-hadron decay, while in the signal mode, it arises from the decay of the τ lepton. The four contributions are analysed simultaneously, yielding two LFU ratios between taus and muons – one using the ground state of the D⁺ meson and one the excited state D^*+.

The control of the background contributions is particularly complicated in this analysis as the final state is not fully reconstructible, limiting the resolution on some of the discriminating variables. Instead, a three-dimensional template fit separates the signal and the normalisation from the background versus: the momentum transferred to the lepton pair (q²); the energy of the muon in the rest frame of the B meson (E_μ^*); and the invariant mass missing from the visible system. Each contribution is modelled using a template histogram derived either from simulation or from selected control samples in data.

This constitutes the world’s second most precise measurement of R(D)

To prevent the simulated data sample size from becoming a limiting factor in the precision of the measurement, a fast tracker-only simulation technique was exploited for the first time in LHCb. Another novel aspect of this work is the use of the HAMMER software tool during the minimisation procedure of the likelihood fit, which enables a fast, but exact, variation of a template as a function of the decay-model parameters. This variation is important to allow the form factors of both the signal and normalisation channels to vary as the constraints derived from the predictions that use precise lattice calculations can have larger uncertainties than those obtained from the fit.

The fit projection over one of the discriminating variables is shown in figure 1, illustrating the complexity of the analysed data sample but nonetheless showcasing LHCb’s ability to distinguish the signal modes (red and orange) from the normalisation modes (two shades of blue) and background contributions.

The measured LFU ratios are in good agreement with the current world average and the predictions of the SM: R(D⁺) = 0.249 ± 0.043 (stat.) ± 0.047 (syst.) and R(D^*+) = 0.402 ± 0.081(stat.) ± 0.085 (syst.). Under isospin symmetry assumptions, this constitutes the world’s second most precise measurement of R(D), following a 2019 measurement by the Belle collaboration. This analysis complements other ongoing efforts at LHCb and other experiments to test LFU across different decay channels. The precision of the measurements reported here is primarily limited by the size of the signal and control samples, so more precise measurements are expected with future LHCb datasets.

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Changing flavour

The discussion on rare B decays continued in the session on flavour-changing neutral-currents. With new lattice-QCD results pinning down short-distance local hadronic contributions, the discussion focused on understanding the long-distance contributions arising from hadronic resonances and charm rescattering. Arianna Tinari (Zurich) and Martin Hoferichter (Bern) judged the latter not to be dramatic in magnitude. Lakshan Madhan (Cambridge) presented a new amplitude analysis in which the long and short-distance contributions are separated via the kinematic dependence of the decay amplitudes. New theo­retical analyses of the nonlocal form factors for B → K^(*)μ⁺μ^– and B → K^(*)e⁺e^– were representative of the workshop as a whole: truly the bee’s knees.

Another challenge to accurate theory predictions for rare decays, the widths of vector final states, snuck its way into the flavour-changing charged-currents session, where Luka Leskovec (Ljubljana) presented a comprehensive overview of lattice methods for decays to resonances. Leskovec’s optimistic outlook for semileptonic decays with two mesons in the final state stood in contrast to prospects for applying lattice methods to D-D mixing: such studies are currently limited to the SU(3)-flavour symmetric point of equal light-quark masses, explained Felix Erben (CERN), though he offered a glimmer of hope in the form of spectral reconstruction methods currently under development.

LHCb’s beauty and charm physics programme reported substantial progress. Novel techniques have been implemented in the most recent CP-violation studies, potentially leading to an impressive uncertainty of just 1° in future measurements of the CKM angle gamma. LHCb has recently placed a special emphasis on beauty and charm baryons, where the experiment offers unique capabilities to perform many interesting measurements ranging from CP violation to searches for very rare decays and their form factors. Going from three quarks to four and five, the spectroscopy session illustrated the rich and complex debate around tetraquark and pentaquark states with a big open discussion on the underlying structure of the 20 or so discovered at LHCb: which are bound states of quarks and which are simply meson molecules? (CERN Courier November/December 2024 p26 and p33.)

LHCb’s ability to do unique physics was further highlighted in the QCD, electroweak (EW) and exotica session, where the collaboration has shown the most recent publicly available measurement of the weak-mixing angle in conjunction with W/Z-boson production cross-sections and other EW observables. LHCb have put an emphasis on combined QCD + QED and effective-field-theory calculations, and the interplay between EW precision observables and new-physics effects in couplings to the third generation. By studying phase space inaccessible to any other experiment, a study of hypothetical dark photons decaying to electrons showed the LHCb experiment to be a unique environment for direct searches for long-lived and low-mass particles.

Attendees left the workshop with a fresh perspective

Parallel to Implications 2024, the inaugural LHCb Open Data and Ntuple Wizard Workshop, took place on 22 October as a satellite event, providing theorists and phenomenologists with a first look at a novel software application for on-demand access to custom ntuples from the experiment’s open data. The LHCb Ntupling Service will offer a step-by-step wizard for requesting custom ntuples and a dashboard to monitor the status of requests, communicate with the LHCb open data team and retrieve data. The beta version was released at the workshop in advance of the anticipated public release of the application in 2025, which promises open access to LHCb’s Run 2 dataset for the first time.

A recurring satellite event features lectures by theorists on topics following LHCb’s scientific output. This year, Simon Kuberski (CERN) and Saša Prelovšek (Ljubljana) took the audience on a guided tour through lattice QCD and spectroscopy.

With LHCb’s integrated luminosity in 2024 exceeding all previous years combined, excitement was heightened. Attendees left the workshop with a fresh perspective on how to approach the challenges faced by our community.

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This text is a hefty volume of around 1000 pages describing the two-component formalism of spinors and its applications to particle physics, quantum field theory and supersymmetry. The authors of this volume, Herbi Dreiner, Howard Haber and Stephen Martin, are household names in the phenomenology of particle physics with many original contributions in the topics that are covered in the book. Haber is also well known at CERN as a co-author of the legendary Higgs Hunter’s Guide (Perseus Books, 1990), a book that most collider physicists of the pre and early LHC eras are very familiar with.

The book starts with a 250-page introduction (chapters one to five) to the Standard Model (SM), covering more or less the theory material that one finds in standard advanced textbooks. The emphasis is on the theoretical side, with no discussion on experimental results, providing a succinct discussion of topics ranging from how to obtain Feynman rules to anomaly-cancellation calculations. In chapter six, extensions of the SM are discussed, starting with the seesaw-extended SM, moving on to a very detailed exposition of the two-Higgs-doublet model and finishing with grand unification theories (GUTs).

The second part of the book (from chapter seven onwards) is about supersymmetry in general. It begins with an accessible introduction that is also applicable to other beyond-SM-physics scenarios. This gentle and very pedagogical pattern continues to chapter eight, before proceeding to a more demanding supersymmetry-algebra discussion in chapter nine. Superfields, supersymmetric radiative corrections and supersymmetry symmetry breaking, which are discussed in the subsequent chapters, are more advanced topics that will be of interest to specialists in these areas.

The third part (chapter 13 onwards) discusses realistic supersymmetric models starting from the minimal supersymmetric SM (MSSM). After some preliminaries, chapter 15 provides a general presentation of MSSM phenomenology, discussing signatures relevant for proton–proton and electron–positron collisions, as well as direct dark-matter searches. A short discussion on beyond-MSSM scenarios is given in chapter 16, including NMSSM, seesaw, GUTs and R-parity violating theories. Phenomenological implications, for example their impact on proton decay, are also discussed.

Part four includes basic Feynman diagram calculations in the SM and MSSM using two-component spinor formalism. Starting from very simple tree-level SM processes, like Bhabha scattering and Z-boson decays, it proceeds with tree-level supersymmetric processes, standard one-loop calculations and their supersymmetric counterparts, and Higgs-boson mass corrections. The presentation of this is very practical and useful for those who want to see how to perform easy calculations in SM or MSSM using two-component spinor formalism. The material is accessible and detailed enough to be used for teaching master’s or graduate-level students.

A valuable resource for all those who are interested in the extensions of the SM, especially if they include supersymmetry

The book finishes with almost 200 pages of appendices covering all sorts of useful topics, from notation to commonly used identity lists and group theory.

The book requires some familiarity with master’s-level particle-physics concepts, for example via Halzen and Martin’s Quarks and Leptons or Paganini’s Fundamentals of Particle Physics. Some familiarity with quantum field theory is helpful but not needed for large parts of the book. No effort is made to be brief: two-component spinor formalism is discussed in all its detail in a very pedagogic and clear way. Parts two and three are a significant enhancement to the well known A Supersymmetry Primer (arXiv:hep-ph/9709356), which is very popular among beginners to supersymmetry and written by Stephen Martin, one of authors of this volume. A rich collection of exercises is included in every chapter, and the appendix chapters are no exception to this.

Do not let the word supersymmetry in the title to fool you: even if you are not interested in supersymmetric extensions you can find a detailed exposition on two-component formalism for spinors, SM calculations with this formalism and a detailed discussion on how to design extensions of the scalar sector of the SM. Chapter three is particularly useful, describing in 54 pages how to get from the two-component to the four-component spinor formalism that is more familiar to many of us.

This is a book for advanced graduate students and researchers in particle-physics phenomenology, which nevertheless contains much that will be of interest to advanced physics students and particle-physics researchers in boththeory and experiment. This is because the size of the volume allows the authors to start from the basics and dwell in topics that most other books of that type cover in less detail, making them less accessible. I expect that Dreiner, Haber and Martin will become a valuable resource for all those who are interested in the extensions of the SM, especially if they include supersymmetry.

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The CDF experiment at the Tevatron observed just such a departure in 2022, plunging the boson into a midlife crisis 39 years after it was discovered at CERN’s SpSS collider (CERN Courier September/October 2023 p27). A new measurement from the CMS experiment at the LHC now contradicts the anomaly reported by CDF. While the CDF result stands seven standard deviations above the SM, CMS’s measurement aligns with the SM prediction and previous results at the LHC. The CMS and CDF results claim joint first place in precision, provoking a dilemma for phenomenologists.

New-physics puzzle

“The result by CDF remains puzzling, as it is extremely difficult to explain the discrepancy with the three LHC measurements by the presence of new physics, in particular as there is also a discrepancy with D0 at the same facility,” says Jens Erler of Johannes Gutenberg-Universität Mainz. “Together with measurements of the weak mixing angle, the CMS result confirms the validity of the SM up to new physics scales well into the TeV region.”

“I would not call this ‘case closed’,” agrees Sven Heinemeyer of the Universidad Autónoma de Madrid. “There must be a reason why CDF got such an anomalously high value, and understanding what is going on may be very beneficial for future investigations. We know that the SM is not the last word, and there are clear cases that require physics beyond the SM (BSM). The question is at which scale BSM physics appears, or how strongly it is coupled to the SM particles.”

The result confirms the validity of the SM up to new physics scales well into the TeV region

To obtain their result, CDF analysed four million W-boson decays originating from 1.96 TeV proton–antiproton collisions at Fermilab’s Tevatron collider between 1984 and 2011. In stark disagreement with the SM, the analysis yielded a mass of 80,433.5 ± 9.4 MeV. This result induced the ATLAS collaboration to revisit its 2017 analysis of W → μν and W → eνdecays in 7 TeV proton–proton collisions using the latest global data on parton distribution functions, which describe the probable momenta of quarks and gluons inside the proton. A newly developed fit was also implemented. The central value remained consistent with the SM, with a reduced uncertainty of 16 MeV increasing its tension with the new CDF result. A less precise measurement by the LHCb collaboration also favoured the SM (CERN Courier May/June 2023 p10).

CMS now reports m_W to be 80,360.2 ± 9.9 MeV, concluding a study of W → μν decays begun eight years ago.

“One of the main strategic choices of this analysis is to use a large dataset of Run 2 data,” says CMS spokesperson Gautier Hamel de Monchenault. “We are using 16.8 fb^–1 of 13 TeV data at a relatively high pileup of on average 25 interactions per bunch crossing, leading to very large samples of about 7.5 million Z bosons and 90 million W bosons.”

With high pileup and high energies come additional challenges. The measurement uses an innovative analysis tech­nique that benchmarks W → μν decay systematics using Z → μμ decays as independent validation wherein one muon is treated as a neutrino. The ultimate precision of the measurement relies on reconstructing the muon’s momentum in the detector’s silicon tracker to better than one part in 10,000 – a groundbreaking level of accuracy built on minutely modelling energy loss, multiple scattering, magnetic-field inhomogeneities and misalignments. “What is remarkable is that this incredible level of precision on the muon momentum measurement is obtained without using Z → μμ as a calibration candle, but only using a huge sample of J/ψ → μμ events,” says Hamel de Monchenault. “In this way, the Z → μμ sample can be used for an independent closure test, which also provides a competitive measurement of the Z mass.”

Measurement matters

Measuring m_W using W → μν decays is challenging because the neutrino escapes undetected. m_W must be inferred from either the distribution of the transverse mass visible in the events (m_T) or the distribution of the transverse momentum of the muons (p_T). The m_T approach used by CDF is the most precise option at the Tevatron, but typically less precise at the LHC, where hadronic recoil is difficult to distinguish from pileup. The LHC experiments also face a greater challenge when reconstructing m_W from distributions of p_T. In proton–antiproton collisions at the Tevatron, W bosons could be created via the annihilation of pairs of valence quarks. In proton–proton collisions at the LHC, the antiquark in the annihilating pair must come from the less well understood sea; and at LHC energies, the partons have lower fractions of the proton’s momentum – a less well constrained domain of parton distribution functions.

“Instead of exploiting the Z → μμ sample to tune the parameters of W-boson production, CMS is using the W data themselves to constrain the theory parameters of the prediction for the p_T spectrum, and using the independent Z → μμ sample to validate this procedure,” explains Hamel de Monchenault. “This validation gives us great confidence in our theory modelling.”

“The CDF collaboration doesn’t have an explanation for the incompatibility of the results,” says spokesperson David Toback of Texas A&M University. “Our focus is on the checks of our own analysis and understanding of the ATLAS and CMS methods so we can provide useful critiques that might be helpful in future dialogues. On the one hand, the consistency of the ATLAS and CMS results must be taken seriously. On the other, given the number of iterations and improvements needed over decades for our own analysis – CDF has published five times over 30 years – we still consider both LHC results ‘early days’ and look forward to more details, improved methodology and additional measurements.”

The LHC experiments each plan improvements using new data. The results will build on a legacy of electroweak precision at the LHC that was not anticipated to be possible at a hadron collider (CERN Courier September/October 2024 p29).

“The ATLAS collaboration is extremely impressed with the new measurement by CMS and the extraordinary precision achieved using high-pileup data,” says spokesperson Andreas Hoecker. “It is a tour de force, accomplished by means of a highly complex fit, for which we applaud the CMS collaboration.” ATLAS’s next measurement of m_W will focus on low-pileup data, to improve sensitivity to m_T relative to their previous result.

The ATLAS collaboration is extremely impressed with the new measurement by CMS

The LHCb collaboration is working on an update of their measurement using its full Run 2 data set. LHCb’s forward acceptance may prove to be powerful in a global fit. “LHCb probes parton density functions in different phase space regions, and that makes the measurements from LHCb anticorrelated with those of ATLAS and CMS, promising a significant impact on the average, even if the overall uncertainty is larger,” says spokesperson Vincenzo Vagnoni. The goal is to progress LHC measurements towards a combined precision of 5 MeV. CMS plans several improvements to their own analysis.

“There is still a significant factor to be gained on the momentum scale, with which we could reach the same precision on the Z-boson mass as LEP,” says Hamel de Monchenault. “We are confident that we can also use a future, large low-pileup run to exploit the W recoil and m_T to complement the muon p_T spectrum. Electrons can also be used, although in this case the Z sample could not be kept independent in the energy calibration.”

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The Dirac equation predicts the magnetic moment of the muon (g) to be precisely two in units of the Bohr magneton. Virtual lines and loops add roughly 0.1% to this value, giving rise to a so-called anomalous contribution often quantified by a_μ = (g–2)/2. Countless electromagnetic loops dominate the calculation, spontaneous symmetry breaking is evident in the effect of weak interactions, and contributions from the strong force are non-perturbative. Despite this formidable complexity, theoretical calculations of a_μ have been experimentally verified to nine significant figures.

The devil is in the 10th digit. The experimental world average for a_μ currently stands more than 5σ above the Standard Model (SM) prediction published by the Muon g-2 Theory Initiative in a 2020 white paper. But two recent results may ease this tension in advance of a new showdown with experiment next year.

The first new input is data from the CMD-3 experiment at the Budker Institute of Nuclear Physics, which yields a_μconsistent with experimental data. Comparable electron–positron (e⁺e^–) collider data from the KLOE experiment at the National Laboratory of Frascati, the BaBar experiment at SLAC, the BESIII experiment at IHEP Beijing and CMD-3’s predecessor CMD-2, were the backbone of the 2020 theory white paper. With KLOE and CMD-3 now incompatible at the level of 5σ, theorists are exploring alternative bases for the theoretical prediction, such as an ab-initio approach based on lattice QCD and a data-driven approach using tau–lepton decays.

The second new result is an updated theory calculation of a_μ by the Budapest–Marseille–Wuppertal (BMW) collaboration. BMW’s ab-initio lattice–QCD calculation of 2020 was the first to challenge the data-driven consensus expressed in the 2020 white paper. The recent update now claims a superior precision, driven in part by the pragmatic implementation of a data-driven approach in the low-mass region, where experiments are in good agreement. Though only accounting for 5% of the hadronic contribution to a_μ, this “long distance” region is often the largest source of error in lattice–QCD calculations, and relatively insensitive to the use of finer lattices.

The new BMW result is fully compatible with the experimental world average, and incompatible with the 2020 white paper at the level of 4σ.

“It seems to me that the 0.9σ agreement between the direct experimental measurement of the magnetic moment of the muon and the ab-initio calculation of BMW has most probably postponed the possible discovery of new physics in this process,” says BMW spokesperson Zoltán Fodor (Wuppertal). “It is important to mention that other groups have partial results, too, so-called window results, and they all agree with us and in several cases disagree with the result of the data-driven method.”

These two analyses were among the many discussed at the seventh plenary workshop of the Muon g-2 Theory Initiative held in Tsukuba, Japan from 9 to 13 September. The theory initiative is planning to release an updated prediction in a white paper due to be published in early 2025. With multiple mature e⁺e^– and lattice–QCD analyses underway for several years, attention now turns to tau decays – the subject of a soon-to-be-announced mini-workshop to ensure their full availability for consideration as a possible basis for the 2025 white paper. Input data would likely originate from tau decays recorded by the Belle experiment at KEK and the ALEPH experiment at CERN, both now decommissioned.

I am hopeful we will be able to establish consolidation between independent lattice calculations at the sub-percent level

“From a theoretical point of view, the challenge for including the tau data is the isospin rotation that is needed to convert the weak hadronic tau decay to the desired input for hadronic vacuum polarisation,” explains theory-initiative chair Aida X El-Khadra (University of Illinois). Hadronic vacuum polarisation (HVP) is the most challenging part of the calculation of a_μ, accounting for the effect of a muon emitting a virtual photon that briefly transforms into a flurry of quarks and gluons just before it absorbs the photon representing the magnetic field (CERN Courier May/June 2021 p25).

Lattice QCD offers the possibility of a purely theoretical calculation of HVP. While BMW remains the only group to have published a full lattice-QCD calculation, multiple groups are zeroing in on its most sensitive aspects (CERN CourierSeptember/October 2024 p21).

“The main challenge in lattice-QCD calculations of HVP is improving the precision to the desired sub-percent level, especially at long distances,” continues El-Khadra. “With the new results for the long-distance contribution by the RBC/UKQCD and Mainz collaborations that were already reported this year, and the results that are still expected to be released this fall, I am hopeful that we will be able to establish consolidation between independent lattice calculations at the sub-percent level. In this case we will provide a lattice-only determination of HVP in the second white paper.”

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Particle-physics experiments typically produce large amounts of highly complex data. Extracting information about the properties of fundamental physics interactions from these data is a non-trivial task. The general availability of simulation frameworks makes it relatively straightforward to model the forward process of data analysis: to go from an analytically formulated theory of nature to a sample of simulated events that describe the observation of that theory for a given particle collider and detector in minute detail. The inverse process – to infer from a set of observed data what is learned about a theory – is much harder as the predictions at the detector level are only available as “point clouds” of simulated events, rather than as the analytically formulated distributions that are needed by most statistical-inference methods.

Traditionally, statistical techniques have found a variety of ways to deal with this problem, mostly centered on simplifying the data via summary statistics that can be modelled empirically in an analytical form. A wide range of ML algorithms, ranging from neural networks to boosted decision trees trained to classify events as signal- or background-like, have been used in the past 25 years to construct such summary statistics.

The broader field of ML has experienced a very rapid development in recent years, moving from relatively straightforward models capable of describing a handful of observable quantities, to neural models with advanced architectures such as normalising flows, diffusion models and transformers. These boast millions to billions of parameters that are potentially capable of describing hundreds to thousands of observables – and can now extract features from the data with an order-of-magnitude better performance than traditional approaches. 

New generation

These advances are driven by newly available computation strategies that not only calculate the learned functions, but also their analytical derivatives with respect to all model parameters, greatly speeding up training times, in particular in combination with modern computing hardware with graphics processing units (GPUs) that facilitate massively parallel calculations. This new generation of ML models offers great potential for novel uses in physics data analyses, but have not yet found their way to the mainstream of published physics results on a large scale. Nevertheless, significant progress has been made in the particle-physics community in learning the technology needed, and many new developments using this technology were shown at the workshop.

This new generation of machine-learning models offers great potential for novel uses in physics data analyses

Many of these ML developments showcase the ability of modern ML architectures to learn multidimensional distributions from point-cloud training samples to a very good approximation, even when the number of dimensions is large, for example between 20 and 100. 

A prime use-case of such ML models is an emerging statistical analysis strategy known as simulation-based inference (SBI), where learned approximations of the probability density of signal and background over the full high-dimensional observables space are used, dispensing with the notion of summary statistics to simplify the data. Many examples were shown at the workshop, with applications ranging from particle physics to astronomy, pointing to significant improvements in sensitivity. Work is ongoing on procedures to model systematic uncertainties, and no published results in particle physics exist to date. Examples from astronomy showed that SBI can give results of comparable precision to the default Markov chain Monte Carlo approach for Bayesian computations, but with orders of magnitude faster computation times.

Beyond binning

A commonly used alternative approach to the full-fledged theory parameter inference from observed data is known as deconvolution or unfolding. Here the goal is publishing intermediate results in a form where the detector response has been taken out, but stopping short of interpreting this result in a particular theory framework. The classical approach to unfolding requires estimating a response matrix that captures the smearing effect of the detector on a particular observable, and applying the inverse of that to obtain an estimate of a theory-level distribution – however, this approach is challenging and limited in scope, as the inversion is numerically unstable, and requires a low dimensionality binning of the data. Results on several ML-based approaches were presented, which either learn the response matrix from modelling distributions outright (the generative approach) or learn classifiers that reweight simulated samples (the discriminative approach). Both approaches show very promising results that do not have the limitations on the binning and dimensionality of the distribution of the classical response-inversion approach.

A third domain where ML is facilitating great progress is that of anomaly searches, where an anomaly can either be a single observation that doesn’t fit the distribution (mostly in astronomy), or a collection of events that together don’t fit the distribution (mostly in particle physics). Several analyses highlighted both the power of ML models in such searches and the bounds from statistical theory: it is impossible to optimise sensitivity for single-event anomalies without knowing the outlier distribution, and unsupervised anomaly detectors require a semi-supervised statistical model to interpret ensembles of outliers.

A final application of machine-learned distributions that was much discussed is data augmentation – sampling a new, larger data sample from a learned distribution. If the synthetic data is significantly larger than the training sample, its statistical power will be greater, but will derive this statistical power from the smooth interpolation of the model, potentially generating so-called inductive bias. The validity of the assumed smoothness depends on its realism in a particular setting, for which there is no generic validation strategy. The use of a generative model amounts to a tradeoff between bias and variance.

Interpretable and explainable

Beyond the various novel applications of ML, there were lively discussions on the more fundamental aspects of artificial intelligence (AI), notably on the notion of and need for AI to be interpretable or explainable. Explainable AI aims to elucidate what input information was used, and its relative importance, but this goal has no unambiguous definition. The discussion on the need for explainability centres to a large extent on trust: would you trust a discovery if it is unclear what information the model used and how it was used? Can you convince peers of the validity of your result? The notion of interpretable AI goes beyond that. It is an often-desired quality by scientists, as human knowledge resulting from AI-based science is generally desired to be interpretable, for example in the form of theories based on symmetries, or structures that are simple, or “low-rank”. However, interpretability has no formal criteria, which makes it an impractical requirement. Beyond practicality, there is also a fundamental point: why should nature be simple? Why should models that describe it be restricted to being interpretable? The almost philosophical nature of this question made the discussion on interpretability one of the liveliest ones in the workshop, but for now without conclusion.

Human knowledge resulting from AI-based science is generally desired to be interpretable

For the longer-term future there are several interesting developments in the pipeline. In the design and training of new neural models, two techniques were shown to have great promise. The first one is the concept of foundation models, which are very large models that are pre-trained by very large datasets to learn generic features of the data. When these pre-trained generic models are retrained to perform a specific task, they are shown to outperform purpose-trained models for that same task. The second is on encoding domain knowledge in the network. Networks that have known symmetry principles encoded in the model can significantly outperform models that are generically trained on the same data.

The evaluation of systematic effects is still mostly taken care of in the statistical post-processing step. Future ML techniques may more fully integrate systematic uncertainties, for example by reducing the sensitivity to these uncertainties through adversarial training or pivoting methods. Beyond that, future methods may also integrate the currently separate step of propagating systematic uncertainties (“learning the profiling”) into the training of the procedure. A truly global end-to-end optimisation of the full analysis chain may ultimately become feasible and computationally tractable for models that provide analytical derivatives.

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With the long shutdown on the horizon, the third run of the LHC is progressing in earnest. Its high-availability operation and mastery of operational risks were highly praised. Run 3 data is of immense importance as it will be the dataset that experiments will work with for the next decade. With the newly collected data at 13.6 TeV, the LHC experiments showed new measurements of Higgs and di-electroweak-boson production, though of course most of the LHC results were based on the Run 2 (2014 to 2018) dataset, which is by now impeccably well calibrated and understood. This also allowed ATLAS and CMS to bring in-depth improvements to reconstruction algorithms.

AI algorithms

A highlight of the conference was the improvements brought by state-of-the-art artificial-intelligence algorithms such as graph neural networks, both at the trigger and reconstruction level. A striking example of this is the ATLAS and CMS flavour-tagging algorithms, which have improved their rejection of light jets by a factor of up to four. This has important consequences. Two outstanding examples are: di-Higgs-boson production, which is fundamental for the measurement of the Higgs boson self-coupling (CERN Courier July/August 2024 p7); and the Higgs boson’s Yukawa coupling to charm quarks. Di-Higgs-boson production should be independently observable by both general-purpose experiments at the HL-LHC, and an observation of the Higgs boson’s coupling to charm quarks is getting closer to being within reach.

The LHC experiments continue to push the limits of precision at hadron colliders. CMS and LHCb presented new measurements of the weak mixing angle. The per-mille precision reached is close to that of LEP and SLD measurements (CERN Courier September/October 2024 p29). ATLAS presented the most precise measurement to date (0.8%) of the strong coupling constant extracted from the measurement of the transverse momentum differential cross section of Drell–Yan Z-boson production. LHCb provided a comprehensive analysis of the B⁰ → K^0* μ⁺μ^– angular distributions, which had previously presented discrepancies at the level of 3σ. Taking into account long-distance contributions significantly weakens the tension down to 2.1σ.

Pioneering the highest luminosities ever reached at colliders (setting a record at 4.7 × 10³⁴ cm^–2 s^–1), SuperKEKB has been facing challenging conditions with repeated sudden beam losses. This is currently an obstacle to further progress to higher luminosities. Possible causes have been identified and are currently under investigation. Meanwhile, with the already substantial data set collected so far, the Belle II experiment has produced a host of new results. In addition to improved CKM angle measurements (alongside LHCb), in particular of the γ angle, Belle II (alongside BaBar) presented interesting new insights in the long standing |V_cb| and |V_ub| inclusive versus exclusive measurements puzzle (CERN Courier July/August 2024 p30), with new |V_cb| exclusive measurements that significantly reduce the previous 3σ tension.

ATLAS and CMS furthered their systematic journey in the search for new phenomena to leave no stone unturned at the energy frontier, with 20 new results presented at the conference. This landmark outcome of the LHC puts further pressure on the naturalness paradigm.

A highlight of the conference was the overall progress in neutrino physics. Accelerator-based experiments NOvA and T2K presented a first combined measurement of the mass difference, neutrino mixing and CP parameters. Neutrino telescopes IceCube with DeepCore and KM3NeT with ORCA (Oscillation Research with Cosmics in the Abyss) also presented results with impressive precision. Neutrino physics is now at the dawn of a bright new era of precision with the next-generation accelerator-based long baseline experiments DUNE and Hyper Kamiokande, the upgrade of DeepCore, the completion of ORCA and the medium baseline JUNO experiment. These experiments will bring definitive conclusions on the measurement of the CP phase in the neutrino sector and the neutrino mass hierarchy – two of the outstanding goals in the field.

The KATRIN experiment presented a new upper limit on the effective electron–anti-neutrino mass of 0.45 eV, well en route towards their ultimate sensitivity of 0.2 eV. Neutrinoless double-beta-decay search experiments KamLAND-Zen and LEGEND-200 presented limits on the effective neutrino mass of approximately 100 meV; the sensitivity of the next-generation experiments LEGEND-1T, KamLAND-Zen-1T and nEXO should reach 20 meV and either fully exclude the inverted ordering hypothesis or discover this long-sought process. Progress on the reactor neutrino anomaly was reported, with recent fission data suggesting that the fluxes are overestimated, thus weakening the significance of the anti-neutrino deficits.

Neutrinos were also a highlight for direct-dark-matter experiments as Xenon announced the observation of nuclear recoil events from⁸B solar neutrino coherent elastic scattering on nuclei, thus signalling that experiments are now reaching the neutrino fog. The conference also highlighted the considerable progress across the board on the roadmap laid out by Kathryn Zurek at the conference to search for dark matter in an extraordinarily large range of possibilities, spanning 89 orders of magnitude in mass from 10^–23 eV to 10⁵⁷ GeV. The roadmap includes cosmological and astrophysical observations, broad searches at the energy and intensity frontier, direct searches at low masses to cover relic abundance motivated scenarios, building a suite of axion searches, and pursuing indirect-detection experiments.

Neutrinos also made the headlines in multi-messenger astrophysics experiments with the announcement by the KM3Net ARCA (Astroparticle Research with Cosmics in the Abyss) collaboration of a muon-neutrino event that could be the most energetic ever found. The energy of the muon from the interaction of the neutrino is compatible with having an energy of approximately 100 PeV, thus opening a fascinating window on astrophysical processes at energies well beyond the reach of colliders. The conference showed that we are now well within the era of multi-messenger astrophysics, via beautiful neutrinos, gamma rays and gravitational-wave results.

The conference saw new bridges across fields being built. The birth of collider-neutrino physics with the beautiful results from FASERν and SND fill the missing gap in neutrino–nucleon cross sections between accelerator neutrinos and neutrino astronomy. ALICE and LHCb presented new results on He³ production that complement the AMS results. Astrophysical He³ could signal the annihilation of dark matter. ALICE also presented a broad, comprehensive review of the progress in understanding strongly interacting matter at extreme energy densities.

The highlight in the field of observational cosmology was the recent data from DESI, the Dark Energy Spectroscopic Instrument in operation since 2021, which bring splendid new data on baryon acoustic oscillation measurements. These precious new data agree with previous indirect measurements of the Hubble constant, keeping the tension with direct measurements in excess of 2.5σ. In combination with CMB measurements, the DESI measurements also set an upper limit on the sum of neutrino masses at 0.072 eV, in tension with the inverted ordering of neutrino masses hypothesis. This limit is dependent on the cosmological model.

In everyone’s mind at the conference, and indeed across the domain of high-energy physics, it is clear that the field is at a defining moment in its history: we will soon have to decide what new flagship project to build. To this end, the conference organised a thrilling panel discussion featuring the directors of all the major laboratories in the world. “We need to continue to be bold and ambitious and dream big,” said Fermilab’s Lia Merminga, summarising the spirit of the discussion.

“As we have seen at this conference, the field is extremely vibrant and exciting,” said CERN’s Fabiola Gianotti at the conclusion of the panel. In these defining times for the future of our field, ICHEP 2024 was an important success. The progress in all areas is remarkable and manifest through the outstanding number of beautiful new results shown at the conference.

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The trick is to study hadron decays that are highly suppressed by the GIM mechanism (see “Charming clues for existence“). Should massive particles beyond the Standard Model (SM) exist at the right energy scale, they could disrupt the delicate cancellations expected in the SM by making brief virtual appearances according to the limits imposed by Heisenberg’s uncertainty principle. In a recent featured article, Andrzej Buras (Technical University Munich) identified the six most promising rare decays where new physics might be discovered before the end of the decade (CERN Courier July/August 2024 p30). Among them is K⁺ → π⁺νν, the ultra-rare decay sought by NA62. In the SM, fewer than one K⁺in 10 billion decays this way, requiring the team to exercise meticulous attention to detail in excluding backgrounds. The collaboration has now announced that it has observed the process with 5σ significance.

“This observation is the culmination of a project that started more than a decade ago,” says spokesperson Giuseppe Ruggiero of INFN and the University of Florence. “Looking for effects in nature that have probabilities of happening of the order of 10^–11 is both fascinating and challenging. After rigorous and painstaking work, we have finally seen the process NA62 was designed and built to observe.”

In the NA62 experiment, kaons are produced by colliding a high-intensity proton beam from CERN’s Super Proton Synchrotron into a stationary beryllium target. Almost a billion secondary particles are produced each second. Of these, about 6% are positively charged kaons that are tagged and matched with positively charged pions from the decay K⁺ → π⁺νν, with the neutrinos escaping undetected. Upgrades to NA62 during Long Shutdown 2 increased the experiment’s signal efficiency while maintaining its sample purity, allowing the collaboration to double the expected signal of their previous measurement using new data collected between 2021 and 2022. A total of 51 events pass the stringent selection criteria, over an expected background of 18⁺³_–2, definitely establishing the existence of this decay for the first time.

NA62 measures the branching ratio for K⁺ → π⁺νν to be 13.0^+3.3_–2.9 × 10^–11 – the most precise measurement to date and about 50% higher than the SM prediction, though compatible with it within 1.7σ at the current level of precision. NA62’s full data set will be required to test the validity of the SM in this decay. Data taking is ongoing.

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Let’s consider two with starkly contrasting experimental prospects. The coupling of the Higgs boson to two Z bosons (HZZ) has been measured with a precision of around 5%, increasing to around 1.3% by the end of High-Luminosity LHC (HL-LHC) operations. The Higgs boson’s self-coupling (HHH) has so far only been measured with a precision of the order of several hundred percent, improving to around the 50% level by the end of HL-LHC operations – though it’s now rumoured that this latter estimate may be too pessimistic.

Good motives

As HZZ can be measured much more precisely than HHH, is it the more promising window beyond the Standard Model (SM)? An agnostic might say that both measurements are equally valuable, while a “top down” theorist might seek to judge which theories are well motivated, and ask how they modify the two couplings. In supersymmetry and minimal composite Higgs models, for example, modifications to HZZ and HHH are typically of a similar magnitude. But “well motivated” is a slippery notion and I don’t entirely trust it.

Fortunately there is a happy compromise between these perspectives, using the tool of choice of the informed agnostic: effective field theory. It’s really the same physical principle as trying to look within an object when your microscope operates on wavelengths greater than its physical extent. Just as the microscopic structure of an atom is imprinted, at low energies, in its multipolar (dipole, quadrupole and so forth) interactions with photons, so too would the microscopic structure of the Higgs boson leave its trace in modifications to its SM interactions.

All possible coupling modifications from microscopic new physics can be captured by effective field theory and organised into classes of “UV-completion”. UV-completions are the concrete microscopic scenarios that could exist. (Here, ultraviolet light is a metaphor for the short-wavelength probes needed to study the Higgs boson’s microscopic origins in detail.) Scenarios with similar patterns are said to live in the same universality class. Families of universality classes can be identified from the bottom up. A powerful tool for this is naïve dimensional analysis (NDA).

One particularly sharp arrow in the NDA quiver is ℏ counting, which establishes how many couplings and/or ℏs must be present in the EFT modification of an interaction. Couplings tell you the number of fundamental interactions involved. ℏs establish the need for quantum effects. For instance, NDA tells us that the coefficient of the Fermi interaction must have two couplings, which the electroweak theory duly supplies – a W boson transforms a neutron into a proton, and then decays into an electron and a neutrino.

For our purposes, NDA tells us that modifications to HZZ must necessarily involve one more ℏ or two fewer couplings than any underlying EFT interaction that modifies HHH. In the case of one more ℏ, modifications to HZZ could potentially be an entire quantum loop factor smaller than modifications to HHH. In the case of two fewer couplings, modifications to HHH could be as large as a factor g² greater than for HZZ, where g is a generic coupling. Either way, it is theoretically possible that the BSM modifications could be up to a couple of orders of magnitude greater for HHH than for HZZ. (Naively, a loop factor counts as around 1/16 π² or about 0.01, and in the most strongly interacting scenarios, g² can rise to about 16 π².)

Why does this contrast so strongly with supersymmetry and the minimal composite Higgs? They are simply in universality classes where modifications to HZZ and HHH are comparable in magnitude. But there are more universality classes in heaven and Earth than are dreamt of in our well-motivated scenarios.

Faced with the theoretical possibility of a large hierarchy in coupling modifications, it behoves the effective theorist to provide an existence proof of a concrete UV-completion where this happens, or we may have revealed a universality class of measure zero. But such an example exists: the custodial quadruplet model. I often say it’s a model that only a mother could love, but it could exist in nature, and gives rise to coupling modifications a full loop factor of about 200 greater for HHH than HZZ.

When confronted with theories beyond the SM, all Higgs couplings are not born equal: UV-completions matter. Though HZZ measurements are arguably the most powerful general probe, future measurements of HHH will explore new territory that is inaccessible to other coupling measurements. This territory is largely uncharted, exotic and beyond the best guesses of theorists. Not bad circumstances for the start of any adventure.

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Supersymmetry (SUSY) provides elegant solutions to many of the problems of the Standard Model (SM) by introducing new boson/fermion partners for each SM fermion/boson, and by extending the Higgs sector. If SUSY is realised in nature at the TeV scale, it would accommodate a light Higgs boson without excessive fine-tuning. It could furthermore provide a viable dark-matter candidate, and be a key ingredient to the unification of the electroweak and strong forces at high energy. The SUSY partners of the SM bosons can mix to form what are called charginos and neutralinos, collectively referred to as electroweakinos.

Electroweakinos would be produced only through the electroweak interaction, where their production cross sections in proton–proton collisions are orders of magnitude smaller than strongly produced squarks and gluinos (the supersymmetric partners of quarks and gluons). Therefore, while extensive searches using the Run 1 (7–8 TeV) and Run 2 (13 TeV) LHC datasets have turned up null results, the corresponding chargino/neutralino exclusion limits remain substantially weaker than those for strongly interacting SUSY particles.

The ATLAS collaboration has recently released a comprehensive analysis of the electroweak SUSY landscape based on its Run 2 searches. Each individual search targeted specific chargino/neutralino production mechanisms and subsequent decay modes. The analyses were originally interpreted in so-called “simplified models”, where only one production mechanism is considered, and only one possible decay. However, if SUSY is realised in nature, its particles will have many possible production and decay modes, with rates depending on the SUSY parameters. The new ATLAS analysis brings these pieces together by reinterpreting 10 searches in the phenomenological Minimal Supersymmetric Standard Model (pMSSM), which includes a range of SUSY particles, production mechanisms and decay modes governed by 19 SUSY parameters. The results provide a global picture of ATLAS’s sensitivity to electroweak SUSY and, importantly, reveals the gaps that remain to be explored.

The 19-dimensional pMSSM parameter space was randomly sampled to produce a set of 20,000 SUSY model points. The 10 selected ATLAS searches were then performed on each model point to determine whether it is excluded with at least 95% confidence level. This involved simulating datasets for each SUSY model, and re-running the corresponding analyses and statistical fits. An extensive suite of reinterpretation tools was employed to achieve this, including preserved likelihoods and RECAST – a framework for preserving analysis workflows and re-applying them to new signal models.

The results show that, while electro­weakino masses have been excluded up to 1 TeV in simplified models, the coverage with regard to the pMSSM is not exhaustive. Numerous scenarios remain viable, including mass regions nominally covered by previous searches (inside the dashed line in figure 1). The pMSSM models may evade detection due to smaller production cross-sections and decay probabilities compared to simplified models. Scenarios with small mass-splittings between the lightest and next-to-lightest neutralino can reproduce the dark-matter relic density, but are particularly elusive at the LHC. The decays in these models produce challenging event features with low-momentum particles that are difficult to reconstruct and separate from SM events.

Beyond ATLAS, experiments such as LZ aim at detecting relic dark-matter particles through their scattering by target nuclei. This provides a complementary probe to ATLAS searches for dark matter produced in the LHC collisions. Figure 2 shows the LZ sensitivity to the pMSSM models considered by ATLAS, compared to the sensitivity of its SUSY searches. ATLAS is particularly sensitive to the region where the dark-matter candidate is around half the Z/Higgs-boson mass, causing enhanced dark-matter annihilation that could have reduced the otherwise overabundant dark-matter relic density to the observed value.

The new ATLAS results demonstrate the breadth and depth of its search programme for supersymmetry, while uncovering its gaps. Supersymmetry may still be hiding in the data, and several scenarios have been identified that will be targeted, benefiting from the incoming Run 3 data.

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The basic constituents of matter interact through forces which are mediated by virtual particles that ping back and forth, delivering momentum and quantum numbers. The gluon mediates the strong interaction, the photon mediates the electromagnetic interaction, and the W and Z bosons mediate the weak interaction. Although the electromagnetic and weak forces operate very differently to each other in everyday life, in the Standard Model they are two manifestations of the broken electroweak interaction – an interaction that broke when the Higgs field switched on throughout the universe, giving mass to matter particles, the W and Z bosons, and the Higgs boson itself, via the Brout–Englert–Higgs (BEH) mechanism. The electroweak theory has been extraordinarily successful in describing experimental results, but it remains mysterious – and the BEH mechanism is the origin of some of those free parameters. The best way to test the electroweak model is to over-constrain its free parameters using precision measurements and try to find a breaking point.

Ever since the late 1960s, when Steven Weinberg, Sheldon Glashow and Abdus Salam unified the electromagnetic and weak forces using the BEH mechanism, CERN has had an intimate experimental relationship with the electroweak theory. In 1973 the Z boson was indirectly discovered by observing “neutral current” events in the Gargamelle bubble chamber, using a neutrino beam from the Proton Synchrotron. The W boson was discovered in 1983 at the Super Proton Synchrotron collider, followed by the direct observation of the Z boson in the same machine soon after. The 1990s witnessed a decade of exquisite electroweak precision measurements at the Large Electron Positron (LEP) collider at CERN and the Stanford Linear Collider (SLC) at SLAC National Accelerator Laboratory in the US, before the crown jewel of the electroweak sector, the Higgs boson, was discovered by the ATLAS and CMS collaborations at the Large Hadron Collider (LHC) in 2012 – a remarkable success that delivered the last to be observed, and arguably most mysterious, missing piece of the Standard Model.

What was not expected, was that the ATLAS, CMS and LHCb experiments at the LHC would go on to make electroweak measurements that rival in precision those made at lepton colliders.

Discovery or precision?

Studying the electroweak interaction requires a supply of W and Z bosons. For that, you need a collider. Electrons and positrons are ideally suited for the task as they interact exclusively via the electroweak interaction. By precisely tuning the energy of electron–positron collisions, experiments at LEP and the SLC tested the electroweak sector with an unprecedented 0.1% accuracy at the energy scale of the Z-boson mass (m_Z).

Hadron colliders like the LHC have different strengths and weaknesses. Equipped to copiously produce all known Standard Model particles – and perhaps also hypothetical new ones – they are the ultimate instruments for probing the high-energy frontier of our understanding of the microscopic world. The protons they collide are not elementary, but a haze of constituent quarks and gluons that bubble and fizz with quantum fluctuations. Each constituent “parton” carries an unpredictable fraction of the proton’s energy. This injects unavoidable uncertainty into studies of hadron collisions that physicists attempt to encode in probabilistic parton distribution functions. What’s more, when a pair of partons from the two opposing protons interact in an interesting way, the result is overlaid by numerous background particles originating from the remaining partons that were untouched by the original collision – a complexity that is exacerbated by the difficult-to-model strong force which governs the behaviour of quarks and gluons. As a result, hadron colliders have a reputation for being discovery machines with limited precision.

The LHC has collided protons at the energy frontier since 2010, delivering far more collisions than comparable previous machines such as the Tevatron at Fermilab in the US. This has enabled a comprehensive search and measurement programme. Following the discovery of the Higgs boson in 2012, measurements have so far verified its place in the electroweak sector of the Standard Model, although the relative precisions of many measurements are currently far lower than those achieved for the W and Z bosons at LEP. But in defiance of expectations, the capabilities of the LHC experiments and the ingenuity of analysts have also enabled many of the world’s most precise measurements of the electroweak interaction. Here, we highlight five.

1. Producing W and Z bosons

When two streams of objects meet, how many strike each other depends on their cross-sectional area. Though quarks and other partons are thought to be fundamental objects with zero extent, particle physicists borrow this logic for particle beams, and extend it by subdividing the metaphorical cross section according to the resulting interactions. The range of processes used to study W and Z bosons at the LHC spans a remarkable eight orders of magnitude in cross section.

The most common interaction is the production of single W and Z bosons through the annihilation of a quark and an antiquark in the colliding protons. Measurements with single W and Z boson events have now reached a precision well below 1% thanks to the excellent calibration of the detector performance. They are a prodigious tool for testing and improving the modelling of the underlying process, for example using parton distribution functions.

The second most common interaction is the simultaneous production of two bosons. Measurements of “diboson” processes now routinely reach a precision better than 5%. Since the start of the LHC operation, the accelerator has operated at several collision energies, allowing the experiments to map diboson cross sections as a function of energy. Measurements of the cross sections for creating WW, WZ and ZZ pairs exhibit remarkable agreement with state-of-the art Standard Model predictions (see “Diboson production” figure).

The large amount of collected data at the LHC has recently allowed us to move the frontier to the observation of extremely infrequent “triboson” processes with three W or Z bosons, or photons, produced simultaneously – the first step towards confirming the existence of the quartic self-interaction between the electroweak bosons.

2. The weak mixing angle

The Higgs potential is famously thought to resemble a Mexican hat. The Higgs field that permeates space could in principle exist with a strength corresponding to any point on its surface. Theorists believe it settled somewhere in the brim a picosecond or so after the Big Bang, breaking the perfect symmetry of the hat’s apex, where its value was zero. This switched the Higgs field on throughout the universe – and the massless gauge bosons of the unified electroweak theory mixed to form the photon and W and Z boson mass eigenstates that mediate the broken electroweak interaction today. The weak mixing angle θ_W is the free parameter of the Standard Model which defines that mixing.

The θ_W angle can be studied using a beautifully simple interaction: the annihilation of a quark and its antiquark to create an electron and a positron or a muon and an antimuon. When the pair has an invariant mass in the vicinity of m_Z, there is a small preference for the negatively charged lepton to be produced in the same direction as the initial quark. This arises due to quantum interference between the Z boson’s vector and axial-vector couplings, whose relative strengths depend on θ_W.

The unique challenge at a proton–proton collider like the LHC is that the initial directions of the quark and the antiquark can only be inferred using our limited knowledge of parton distribution functions. These systematic uncertainties currently dominate the total uncertainty, although they can be reduced somewhat by using information on lepton pairs produced away from the Z resonance. The CMS and LHCb collaborations have recently released new measurements consistent with the Standard Model prediction with a precision comparable to that of the LEP and SLC experiments (see “Weak mixing angle” figure).

Quantum physics effects play an interesting role here. In practice, it is not possible to experimentally isolate “tree level” properties like θ_W, which describe the simplest interactions that can be drawn on a Feynman diagram. Measurements are in fact sensitive to the effective weak mixing angle, which includes the effect of quantum interference from higher-order diagrams.

A crucial prediction of electroweak theory is that the masses of the W and Z bosons are, at leading order, related by the electroweak mixing angle: sin²θ_W = 1–m²_W/m²_Z, where m_W and m_Z are the masses of the W and Z bosons. This relationship is modified by quantum loops involving the Higgs boson, the top quark and possibly new particles. Measuring the parameters of the electroweak theory precisely, therefore, allows us to test for any gaps in our understanding of nature.

Surprisingly, combining this relationship with the m_Z measurement from LEP and the CMS measurement of θ_W also allows a competitive measurement of m_W. A measurement of sin²θ_W with a precision of 0.0003 translates into a prediction of m_W with 15 MeV precision, which is comparable to the best direct measurements.

3. The mass and width of the W boson

Precisely measuring the mass of the W boson is of paramount importance to efforts to further constrain the relationships between the parameters of the electroweak theory, and probe possible beyond-the-Standard Model contributions. Particle lifetimes also offer a sensitive test of the electroweak theory. Because of their large masses and numerous decay channels, the W and Z bosons have mean lifetimes of less than 10^–24 s. Though this is an impossibly brief time interval to measure directly, Heisenberg’s uncertainty principle smudges a particle’s observed mass by a certain “width” when it is produced in a collider. This width can be measured by fitting the mass distribution of many virtual particles. It is reciprocally related to the particle’s lifetime.

While lepton-collider measurements of the properties of the Z boson were extensive and achieved remarkable precision, the same is not quite true for the W boson. The mass of the Z boson was measured with a precision of 0.002%, but the mass of the W boson was measured with a precision of only 0.04% – a factor 20 worse. The reason is that while single Z bosons were copiously produced at LEP and SLC, W bosons could not be produced singly, due to charge conservation. W⁺W^– pairs were produced, though only at low rates at LEP energies.

In contrast to LEP, hadron colliders produce large quantities of single W bosons through quark–antiquark annihilation. The LHC produces more single W bosons in a minute than all the W-boson pairs produced in the entire lifetime of LEP. Even when only considering decays to electrons or muons and their respective neutrinos – the most precise measurements – the LHC experiments have recorded billions of W-boson events.

But there are obstacles to overcome. The neutrino in the final state escapes undetected. Its transverse momentum with respect to the beam direction can only be measured indirectly, by measuring all other products of the collision – a major experimental challenge in an environment with not just one, but up to 60 simultaneous proton–proton collisions. Its longitudinal momentum cannot be measured at all. And as the W bosons are not produced at rest, extensive theoretical calculations and ancillary measurements are needed to model their momenta, incurring uncertainties from parton distribution functions.

Despite these challenges, the latest measurement of the W boson’s mass by the ATLAS collaboration achieved a precision of roughly 0.02% (see “Mass and width” figure, top). The LHCb collaboration also recently produced its first measurement of the W-boson mass using W bosons produced close to the beam line with a precision at the 0.04% level, dominated for now by the size of the data sample. Owing to the complementary detector coverage of the LHCb experiment with respect to the ATLAS and CMS experiments, several uncertainties are reduced when these measurements are combined.

The Tevatron experiments CDF and D0 also made precise W-boson measurements using proton–antiproton collisions at a lower centre-of-mass energy. The single most precise mass measurement, at the 0.01% level, comes from CDF. It is in stark disagreement with the Standard Model prediction and disagrees with the combination of other measurements.

A highly anticipated measurement by the CMS collaboration may soon weigh in decisively in favour either of the CDF measurement or the Standard Model. The CMS measurement will combine innovative analysis techniques using the Z boson with a larger 13 TeV data set than the 7 TeV data used by the recent ATLAS measurement, enabling more powerful validation samples and thereby greater power to reduce systematic uncertainties.

Measurements of the W boson’s width are not yet sufficiently precise to constrain the Standard Model significantly, though the strongest constraint so far comes from the ATLAS collaboration (see “Mass and width” figure, bottom). Further measurements are a promising avenue to test the Standard Model. If the W boson decays into any hitherto undiscovered particles, its lifetime should be shorter than predicted, and its width greater, potentially indicating the presence of new physics.

4. Couplings of the W boson to leptons

Within the Standard Model, the W and Z bosons have equal couplings to leptons of each of the three generations – a property known as lepton flavour universality (LFU). Any experimental deviation from LFU would indicate new physics.

As with mass and width, lepton colliders’ precision was superior for the Z boson than the W boson. LEP confirmed LFU in leptonic Z-boson decays to about 0.3%. Comparing the three branching fractions of the W boson in the electron, muon and tau–lepton decay channels, the combination of the four LEP experiments reached a precision of only about 2%.

At the LHC, the large cross section for producing top quark–antiquark pairs that both decay into a W boson and a bottom quark offers a unique sample of W-boson pairs for high-precision studies of their decays. The resulting measurements are the most precise tests of LFU for all three possible comparisons of the coupling of the lepton flavours to the W boson (see “Couplings to leptons” figure).

Regarding the tau lepton to muon ratio, the ATLAS collaboration observed 0.992 ± 0.013 decays to a tau for every one decay to a muon. This result favours LFU and is twice as precise than the corresponding LEP result of 1.066 ± 0.025, which exhibits a deviation of 2.6 standard deviations from unity. Because of the relatively long tau lifetime, ATLAS was able to separate muons produced in the decay of tau leptons from those produced promptly by observing the tau decay length of the order of 2 mm.

The best tau to electron measurement is provided by a simultaneous CMS measurement of all the leptonic and hadronic decay branching fractions of the W boson. The analysis splits the top quark–antiquark pair events based on the multiplicity and flavour of reconstructed leptons, the number of jets, and the number of jets identified as originating from the hadronisation of b quarks. All CMS ratios are consistent with the LFU hypothesis and reduce tension with the Standard Model prediction.

Regarding the muon to electron ratio, measurements have been performed by several LHC and Tevatron experiments. The observed results are consistent with LFU, with the most precise measurement from the ATLAS experiment boasting a precision better than 0.5%.

5. The invisible width of the Z boson

A groundbreaking measurement at LEP deduced how often a particle that cannot be directly observed decays to particles that cannot be detected. The particle in question is the Z boson. By scanning the energy of electron–positron collisions and measuring the broadness of the “lineshape” of the smudged bump in interactions around the mass of the Z, LEP physicists precisely measured its width. As previously noted, a particle’s width is reciprocal to its lifetime and therefore proportional to its decay rate – something that can also be measured by directly accounting for the observed rate of decays to visible particles of all types. The difference between the two numbers is due to Z-boson decays to so-called invisible particles that cannot be reconstructed in the detector. A seminal measurement concluded that exactly three species of light neutrino couple to the Z boson.

The LEP experiments also measured the invisible width of the Z boson using an ingenious method that searched for solitary “recoils”. Here, the trick was to look for the rare occasion when the colliding electron or positron emitted a photon just before creating a virtual Z boson that decayed invisibly. Such events would yield nothing more than a single photon recoiling from an otherwise invisible Z-boson decay.

The ATLAS and CMS collaborations recently performed similar measurements, requiring the invisibly decaying Z boson to be produced alongside a highly energetic jet in place of a recoil photon. By taking the ratio with equivalent recoil decays to electrons and muons, they achieved remarkable uncertainties of around 2%, equivalent to LEP, despite the much more challenging environment (see “Invisible width” figure). The results are consistent with the Standard Model’s three generations of light neutrinos.

Future outlook

Building on these achievements, the LHC experiments are now readying themselves for a more than comparable experimental programme, which is yet to begin. Following the ongoing run of the LHC, a high-luminosity upgrade (HL-LHC) is scheduled to operate throughout the 2030s, delivering a total integrated luminosity of 3 ab^–1 to both ATLAS and CMS. The LHCb experiment also foresees a major upgrade to collect an integrated luminosity of more than 300 fb^–1 by the end of the LHC operations. A tenfold data set, upgraded detectors and experimental methods, and improvements to theoretical modelling will greatly extend both experimental precision and the reach of direct and indirect searches for new physics. Unprecedented energy scales will be probed and anomalies with respect to the Standard Model may become apparent.

Despite the significant challenges posed by systematic uncertainties, there are good prospects to further improve uncertainties in precision electroweak observables such as the mass of the W boson and the effective weak mixing angle, thanks to the larger angular acceptances of the new inner tracking devices currently under production by ATLAS and CMS. A possible programme of high-precision measurements in electron–proton collisions, the LHeC, could deliver crucial input to reduce uncertainties such as from parton distribution functions. The LHeC has been proposed to run concurrently with the HL-LHC by adding an electron beam to the LHC.

Beyond the HL-LHC programme, several proposals for future particle colliders have captured the imagination of the global particle-physics community – and not least the two phases of the Future Circular Collider (FCC) being studied at CERN. With a circumference three to four times greater than that of the LEP/LHC tunnel, electron–positron collisions could be delivered with very high luminosity and centre-of-mass energies from 90 to 365 GeV in the initial FCC-ee phase. The FCC-ee would facilitate an impressive leap in the precision of most electroweak observables. Projections estimate a factor of 10 improvement for Z-boson measurements and up to 100 for W-boson measurements. For the first time, the top quark could be produced in an environment where it is not colour-connected to initial hadrons, in some cases reducing uncertainties by a factor of 10 or more.

The LHC collaborations have made remarkable strides forward in probing the electroweak theory – a theory of great beauty and consequence for the universe. But its most fundamental workings are subtle and elusive. Our exploration is only just beginning.

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The simplest possible interaction in nature is when three identical particle lines, with the same quantum numbers, meet at a single vertex. The Higgs boson is the only known elementary particle that can exhibit such behaviour. More importantly, the strength of the coupling between three or even four Higgs bosons will reveal the first picture of the shape of the Brout–Englert–Higgs potential, responsible for the evolution of the universe in its first moments as well as possibly its fate.

Since the discovery of the Higgs boson at the LHC in 2012, the ATLAS and CMS collaborations have measured its properties and interactions with increasing precision. This includes its couplings to the gauge bosons and to third-generation fermions, its production cross sections, mass and width. So far, the boson appears as the Standard Model (SM) says it should. But the picture is still fuzzy, and many more measurements are needed. After all, the Higgs boson may interact with new particles suggested by theories beyond the SM to shed light on mysteries including the nature of the electroweak phase transition.

Line of attack

“The Higgs self-coupling is the next big thing since the Higgs discovery, and di-Higgs production is our main line of attack,” says Jana Schaarschmidt of ATLAS. “The experiments are making tremendous progress towards measuring Higgs-boson pair production at the LHC – far more than was imagined would be possible 12 years ago – thanks to improvements in analysis techniques and machine learning in particular.”

The dominant process for di-Higgs production at the LHC, gluon–gluon fusion, proceeds via a box or triangle diagram, the latter offering access to the trilinear Higgs coupling constant λ (see figure). Destructive interference between the two processes makes di-Higgs production extremely rare, with a cross section at the LHC about 1000 times smaller than that for single-Higgs production. Many different decay channels are available to ATLAS and CMS. Those with a high probability to occur are chosen if they can also provide a clean way to be distinguished from backgrounds. The most sensitive channels are those with one Higgs boson decaying to a b-quark pair and the other decaying either to a pair of photons, τ leptons or b quarks.

During this year’s Rencontres de Moriond, ATLAS presented new results in the HH → bbbb and HH → multileptons channels and CMS in the HH → γγττ channel. In May, ATLAS released a combination of searches for HH production in five channels using the complete LHC Run 2 dataset. The combination provides the best expected sensitivities to HH production (excluding values more than 2.4 times the SM prediction) and to the Higgs boson self-coupling. A combination of HH searches published by CMS in 2022 obtains a similar sensitivity to the di-Higgs cross-section limits. “In late 2023 we put out a preliminary result combining single-Higgs and di-Higgs analyses to constrain the Higgs self-coupling, and further work on combining all the latest analyses is ongoing,” explains Nadjieh Jafari of CMS.

The Higgs self-coupling is the next big thing since the Higgs discovery

Considerable improvements are expected with the LHC Run 3 and much larger High-Luminosity LHC (HL-LHC) datasets. Based on extrapolations of early subsets of its Run 2 analyses, ATLAS expects to detect SM di-Higgs production with a significance of 3.2σ (4.6σ) with (without) systematic uncertainties by the end of the HL-LHC era. With similar progress at CMS, a di-Higgs observation is expected to be possible at the HL-LHC even with current analy­sis techniques, along with improved knowledge of λ. ATLAS, for example, expects to be able to constrain λ to be between 0.5 and 1.6 times the SM expectation at the level of 1σ.

Testing the foundations

Physicists are also starting to place limits on possible new-physics contributions to HH production, which can originate either from loop corrections involving new particles or from non-standard couplings between the Higgs boson and other SM particles. Several theories beyond the SM, including two-Higgs-doublet and composite-Higgs models, also predict the existence of heavy scalar particles that can decay resonantly into a pair of Higgs bosons. “Large anomalous values of λ are already excluded, and the window of possible values continues to shrink towards the SM as the sensitivity grows,” says Schaarschmidt. “Furthermore, in recent di-Higgs analyses ATLAS and CMS have been able to establish a strong constraint on the coupling between two Higgs bosons and two vector bosons.”

For Christophe Grojean of the DESY theory group, the principal interest in di-Higgs production is to test the foundations of quantum field theory: “The basic principles of the SM are telling us that the way the Higgs boson interacts with itself is mostly dictated by its expectation value (linked to the Fermi constant, i.e. the muon and neutron lifetimes) and its mass. Verifying this prediction experimentally is therefore of prime importance.”

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The key concept is the quantum fluctuation. Just because a collision doesn’t have enough energy to bring a new particle into existence does not mean that a very heavy new particle cannot inform us about its existence. Thanks to Heisenberg’s uncertainty principle, new particles could be virtually exchanged between the other particles involved in the collisions, modifying the probabilities for the processes we observe in our detectors. The effect of massive new particles could be unmistakable, giving physicists a powerful tool for exploring more deeply into the unknown than accelerator technology and economic considerations allow direct searches to go.

The effect of massive new particles could be unmistakable

The search for new particles and forces beyond those of the Standard Model is strongly motivated by the need to explain dark matter, the huge range of particle masses from the tiny neutrino to the massive top quark, and the asymmetry between matter and antimatter that is responsible for our very existence. As direct searches at the LHC have not yet provided any clue as to what these new particles and forces might be, indirect searches are growing in importance. Studying very rare processes could allow us to see imprints of new particles and forces acting at much shorter distance scales than it is possible to explore at current and future colliders.

Anticipating the November Revolution

The charm quark is a good example. The story of its direct discovery unfolded 50 years ago, in November 1974, when teams at SLAC and MIT simultaneously discovered a charm–anticharm meson in particle collisions. But four years earlier, Sheldon Glashow, John Iliopoulos and Luciano Maiani had already predicted the existence of the charm quark thanks to the surprising suppression of the neutral kaon’s decay into two muons.

Neutral kaons are made up of a strange quark and a down antiquark, or vice versa. In the Standard Model, their decay to two muons can proceed most simply through the virtual exchange of two W bosons, one virtual up quark and a virtual neutrino. The trouble was that the rate for the neutral kaon decay to two muons predicted in this  manner turned out to be many orders of magnitude larger than observed experimentally.

Glashow, Iliopoulos and Maiani (GIM) proposed a simple solution. With visionary insight, they hypothesised a new quark, the charm quark, which would totally cancel the contribution of the up quark to this decay if their masses were equal to each other. As the rate was non-vanishing and the charm quark had not yet been observed experimentally, they concluded that the mass of the charm quark must be significantly larger than that of the up quark.

Their hunch was correct. In early 1974, months before its direct discovery, Mary K Gaillard and Benjamin Lee predicted the charm quark’s mass by analysing another highly suppressed quantity, the mass difference in K⁰–K⁰ mixing.

As modifications to the GIM mechanism by new heavy particles are still a hot prospect for discovering new physics in the 2020s, the details merit a closer look. Years earlier, Nicola Cabibbo had correctly guessed that weak interactions act between up quarks and a mixture (d cos θ + s sin θ) of the down and strange quarks. We now know that charm quarks interact with the mixture (–d sin θ + s cos θ). This is just a rotation of the down and strange quarks through this Cabibbo angle. The minus sign causes the destructive interference observed in the GIM mechanism.

With the discovery of a third generation of quarks, quark mixing is now described by the Cabibbo–Kobayashi–Maskawa (CKM) matrix – a unitary three-dimensional rotation with complex phases that parameterise CP violation. Understanding its parameters may prove central to our ability to discover new physics this decade.

On to the 1980s

The story of indirect discoveries continued in the late 1980s, when the magnitude of B⁰_d – B⁰_d mixing implied the existence of a heavy top quark, which was confirmed in 1995, completing the third generation of quarks. The W, Z and Higgs bosons were also predicted well in advance of their discoveries. It’s only natural to expect that indirect searches for new physics will be successful at even shorter distance scales.

Rare weak decays of kaons and B mesons that are strongly suppressed by the GIM mechanism are expected to play a crucial role. Many channels of interest are predicted by the Standard Model to have branching ratios as low as 10^–11, often being further suppressed by small elements of the CKM matrix. If the GIM mechanism is violated by new-physics contributions, these branching ratios – the fraction of times a particle decays that way – could be much larger.

Measuring suppressed branching ratios with respectable precision this decade is therefore an exciting prospect. Correlations between different branching ratios can be particularly sensitive to new physics and could provide the first hints of physics beyond the Standard Model. A good example is the search for the violation of lepton-flavour universality (CERN Courier May/June 2019 p33). Though hints of departures from muon–electron universality seem to be receding, hints that muon–tau universality may be violated still remain, and the measured branching ratios for B → K(K^*)µ⁺µ^– differ visibly from Standard Model predictions.

The first step in this indirect strategy is to search for discrepancies between theoretical predictions and experimental observables. The main challenge for experimentalists is the low branching ratios for the rare decays in question. However, there are very good prospects for measuring many of these highly suppressed branching ratios in the coming years.

Six channels for the 2020s

Six channels stand out today for their superb potential to observe new physics this decade. If their decay rates defy expectations, the nature of any new physics could be identified by studying the correlations between these six decays and others.

The first two channels are kaon decays: the measurements of K⁺ → π⁺νν by the NA62 collaboration at CERN (see “Needle in a haystack” image), and the measurement of K_L → π⁰νν by the KOTO collaboration at J-PARC in Japan. The branching ratios for these decays are predicted to be in the ballpark of 8 × 10^–11 and 3 × 10^–11, respectively.

The second two are measurements of B → Kνν and B → K^*νν by the Belle II collaboration at KEK in Japan. Branching ratios for these decays are expected to be much higher, in the ballpark of 10^–5.

The final two channels, which are only accessible at the LHC, are measurements of the dimuon decays B_s → µ⁺µ^– and B_d → µ⁺µ^– by the LHCb, CMS and ATLAS collaborations. Their branching ratios are about 4 × 10^–9 and 10^–10 in the Standard Model. Though the decays B → K(K^*)µ⁺µ^–are also promising, they are less theoretically clean than these six.

The main challenge for theorists is to control quantum-chromodynamics (QCD) effects, both below 10^–16 m, where strong interactions weaken, and in the non-perturbative region at distance scales of about 10^–15 m, where quarks are confined in hadrons and calculations become particularly tricky. While satisfactory precision has been achieved at short-distance scales over the past three decades, the situation for non-perturbative computations is expected to improve significantly in the coming years, thanks to lattice QCD and analytic approaches such as dual QCD and chiral perturbation theory for kaon decays, and heavy-quark effective field theory for B decays.

Another challenge is that Standard Model predictions for the branching ratios require values for four CKM parameters that are not predicted by the Standard Model, and which must be measured using kaon and B-meson decays. These are the magnitude of the up-strange (V_us) and charm-bottom (V_cb) couplings and the CP-violating phases β and γ. The current precision on measurements of V_us and β is fully satisfactory, and the error on γ = (63.8 ± 3.5)° should be reduced to 1° by LHCb and Belle II in the coming years. The stumbling block is V_cb, where measurements currently disagree. Though experimental problems have not been excluded, the tension is thought to originate in QCD calculations. While measurements of exclusive decays to specific channels yield 39.21(62) × 10^–3, inclusive measurements integrated over final states yield 41.96(50) × 10^–3. This discrepancy makes the predicted branching ratios differ by 16% for the four B-meson decays, and by 25% and 35% for K⁺ → π⁺νν and K_L → π⁰νν. These discrepancies are a disaster for the theorists who had succeeded over many years of work to reduce QCD uncertainties in these decays to the level of a few percent.

One solution is to replace the CKM dependence of the branching ratios with observables where QCD uncertainties are under good control, for example: the mass differences in B⁰_s −  B⁰_s and B⁰_d −  B⁰_d mixing (∆M_s and ∆M_d); a parameter that measures CP violation in K⁰ – K⁰ mixing (ε_K); and the CP-asymmetry that yields the angle β. Fitting these observables to the experimental data avoids us being forced to choose between inclusive and exclusive values for the charm-bottom coupling, and avoids the 3.5° uncertainty on γ, which in this strategy is reduced to 1.6°. Uncertainty on the predicted branching ratios is thereby reduced to 6% and 9% for B → Kνν and B → K^*νν, to 5% for the two kaon decays, and to 4% for B_s → µ⁺µ^– and B_d → µ⁺µ^–.

So what is the current experimental situation for the six channels? The latest NA62 measurement of K⁺ → π⁺νν is 25% larger than the Standard Model prediction. Its 36% uncertainty signals full compatibility at present, and precludes any conclusions about the size of new physics contributing to this decay. Next year, when the full analysis has been completed, this could turn out to be possible. It is unfortunate that the HIKE proposal was not adopted (CERN Courier May/June 2024 p7), as NA62’s expected precision of 15% could have been reduced to 5%. This could turn out to be crucial for the discovery of new physics in this decay.

The present upper bound on K_L → π⁰νν from KOTO is still two orders of magnitude above the Standard Model prediction. This bound should be lowered by at least one order of magnitude in the coming years. As this decay is fully governed by CP violation, one may expect that new physics will impact it significantly more than CP-conserving decays such as K⁺ → π⁺νν.

Branching out from Belle

At present, the most interesting result concerns a 2023 update from Belle II to the measured branching ratio for B⁺ → K⁺νν (see “Interesting excess” image). The resulting central value from Belle II and BaBar is currently a factor of 2.6 above the Standard Model prediction. This has sparked many theoretical analyses around the world, but the experimental error of 30% once again does not allow for firm conclusions. Measurements of other charge and spin configurations of this decay are pending.

Finally, both dimuon B-meson decays are at present consistent with Standard Model predictions, but significant improvements in experimental precision could still reveal new physics at work, especially in the case of B_d.

It will take a few years to conclude if new physics contributions are evident in these six branching ratios, but the fact that all are now predicted accurately means that we can expect to observe or exclude new physics in them before the end of the decade. This would be much harder if measurements of the V_cb coupling were involved.

So far, so good. But what if the observables that replaced V_cb and γ are themselves affected by new physics? How can they be trusted to make predictions against which rare decay rates can be tested?

Here comes some surprisingly good news: new physics does not appear to be required to simultaneously fit them using our new basis of observables ΔM_d, ε_K and ΔM_s, as they intersect at a single point in the V_cb–γ plane (see “No new physics” figure). This analysis favours the inclusive determination of V_cb and yields a value for γ that is consistent with the experimental world average and a factor of two more accurate. It’s important to stress, though, that non-perturbative four-flavour lattice-QCD calculations of ∆M_s and ∆M_d by the HPQCD lattice collaboration played a key role here. It is crucial that another lattice QCD collaboration repeat these calculations, as the three curves cross at different points in three-flavour calculations that exclude charm.

Interesting years are ahead in the field of indirect searches for new physics

In this context, one realises the advantages of V_cb–γ plots compared to the usual unitarity-triangle plots, where V_cb is not seen and 1° improvements in the determination of γ are difficult to appreciate. In the late 2020s, determining V_cb and γ from tree-level decays will be a central issue, and a combination of V_cb-independent and V_cb-dependent approaches will be needed to identify any concrete model of new physics.

We should therefore hope that the tension between inclusive and exclusive determinations of V_cb will soon be conclusively resolved. Forthcoming measurements of our six rare decays may then reveal new physics at the energy frontier (see “New physics” figure). With a 1° precision measurement of γ on the horizon, and many V_cb-independent ratios available, interesting years are ahead in the field of indirect searches for new physics.

In 1676 Antonie van Leeuwenhoek discovered a microuniverse populated by bacteria, which he called animalcula, or little animals. Let us hope that we will, in this decade, discover new animalcula on our flavour expedition to the zeptouniverse.

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In a series of daring balloon flights in 1912, Victor Hess discovered radiation that intensified with altitude, implying extra-terrestrial origins. A century later, experiments with cosmic rays have reached low-Earth orbit, but physicists are still puzzled. Cosmic-ray spectra are difficult to explain using conventional models of galactic acceleration and propagation. Hypotheses for their sources range from supernova remnants, active galactic nuclei and pulsars to physics beyond the Standard Model. The study of cosmic rays in the 1940s and 1950s gave rise to particle physics as we know it. Could these cosmic messengers be about to unlock new secrets, potentially clarifying the nature of dark matter?

The cosmic-ray spectrum extends well into the EeV regime, far beyond what can be reached by particle colliders. For many decades, the spectrum was assumed to be broken into intervals, each following a power law, as Enrico Fermi had historically predicted. The junctures between intervals include: a steepening decline at about 3 × 10⁶ GeV known as the knee; a flattening at about 4 × 10⁹GeV known as the ankle; and a further steepening at the supposed end of the spectrum somewhere above 10¹⁰ GeV (10 EeV).

While the cosmic-ray population at EeV energies may include contributions from extra-galactic cosmic rays, and the end of the spectrum may be determined by collisions with relic cosmic-microwave-background photons – the Greisen–Zatsepin–Kuzmin cutoff – the knee is still controversial as the relative abundance of protons and other nuclei is largely unknown. What’s more, recent direct measurements by space-borne instruments have discovered “spectral curvatures” below the knee. These significant deviations from a pure power law range from a few hundred GeV to a few tens of TeV. Intriguing anomalies in the spectra of cosmic-ray electrons and positrons have also been observed below the knee.

Electron origins

The Calorimetric Electron Telescope (CALET; see “Calorimetric telescope” figure) on board the International Space Station (ISS) provides the highest-energy direct measurements of the spectrum of cosmic-ray electrons and positrons. Its goal is to observe discrete sources of high-energy particle acceleration in the local region of our galaxy. Led by the Japan Aerospace Exploration Agency, with the participation of the Italian Space Agency and NASA, CALET was launched from the Tanegashima Space Center in August 2015, becoming the second high-energy experiment operating on the ISS following the deployment of AMS-02 in 2011. During 2017 a third experiment, ISS-CREAM, joined AMS-02 and CALET, but its observation time ended prematurely.

As a result of radiative losses in space, high-energy cosmic-ray electrons are expected to originate just a few thousand light-years away, relatively close to Earth. CALET’s homogeneous calorimeter (fully active, with no absorbers) is optimised to reconstruct such particles (see “Energetic electron” figure). With the exception of the highest energies, anisotropies in their arrival direction are typically small due to deflections by turbulent interstellar magnetic fields.

Energy spectra also contain crucial information as to where and how cosmic-ray electrons are accelerated. And they could provide possible signatures of dark matter. For example, the presence of a peak in the spectrum could be a sign of dark-matter decay, or dark-matter annihilation into an electron–positron pair, with a detected electron or positron in the final state.

Direct measurements of the energy spectra of charged cosmic rays have recently achieved unprecedented precision thanks to long-term observations of electrons and positrons of cosmic origin, as well as of individual elements from hydrogen to nickel, and even beyond. Space-borne instruments such as CALET directly identify cosmic nuclei by measuring their electric charge. Ground-based experiments must do so indirectly by observing the showers they generate in the atmosphere, incurring large systematic uncertainties. Either way, hadronic cosmic rays can be assumed to be fully stripped of atomic electrons in their high-temperature regions of origin.

A rich phenomenology

The past decade has seen the discovery of unexpected features in the differential energy spectra of both leptonic and hadronic cosmic rays. The observation by PAMELA and AMS of an excess of positrons above 10 GeV has generated widespread interest and still calls for an unambiguous explanation (CERN Courier December 2016 p26). Possibilities include pair production in pulsars, in addition to the well known interactions with the interstellar gas, and the annihilation of dark matter into electron–positron pairs.

Regarding cosmic-ray nuclei, significant deviations of the fluxes from pure power-law spectra have been observed by several instruments in flight, including by CREAM on balloon launches from Antarctica, by PAMELA and DAMPE aboard satellites in low-Earth orbit, and by AMS-02 and CALET on the ISS. Direct measurements have also shown that the energy spectra of “primary” cosmic rays is different from those of “secondary” cosmic rays created by collisions of primaries with the interstellar medium. This rich phenomenology, which encodes information on cosmic-ray acceleration processes and the history of their propagation in the galaxy, is the subject of multiple theoretical models.

An unexpected discovery by PAMELA, which had been anticipated by CREAM and was later measured with greater precision by AMS-02, DAMPE and CALET, was the observation of a flattening of the differential energy spectra of protons and helium. Starting from energies of a few hundred GeV, the proton flux shows a smooth and progressive hardening (increase in gradient) of the spectrum that continues up to around 10 TeV, above which a completely different regime is established. A turning point was the subsequent discovery by CALET and DAMPE of an unexpected softening of proton and helium fluxes above about 10 TeV/Z, where the atomic number Z is one for protons and two for helium. The presence of a second break challenges the conventional “standard model” of cosmic-ray spectra and calls for a further extension of the observed energy range, currently limited to a few hundred TeV.

At present, only two experiments in low-Earth orbit have an energy reach beyond 100 TeV: CALET and DAMPE. They rely on a purely calorimetric measurement of the energy, while space-borne magnetic spectrometers are limited to a maximum magnetic “rigidity” – a particle’s momentum divided by its charge – of a few teravolts. Since the end of PAMELA’s operations in 2016, AMS-02 is now the only instrument in orbit with the ability to discriminate the sign of the charge. This allows separate measurements of the high-energy spectra of positrons and antiprotons – an important input to the observation of final states containing antiparticles for dark-matter searches. AMS-02 is also now preparing for an upgrade: an additional silicon tracker layer will be deployed at the top of the instrument to enable a significant increase in its acceptance and energy reach (CERN Courier March/April 2024 p7).

Pioneering observations

CALET was designed to extend the energy reach beyond the rigidity limit of present space-borne spectrometers, enabling measurements of electrons up to 20 TeV and measurements of hadrons up to 1 PeV. As an all-calorimetric instrument with no magnetic field, its main science goal is to perform precision measurements of the detailed shape of the inclusive spectra of electrons and positrons.

Thanks to its advanced imaging calorimeter, CALET can measure the kinetic energy of incident particles well into TeV energies, maintaining excellent proton–electron discrimination throughout. CALET’s homogeneous calorimeter has a total thickness of 30 radiation lengths, allowing for a full containment of electron showers. It is preceded by a high-granularity pre-shower detector with imaging capabilities that provide a redundant measurement of charge via multiple energy-loss measurements. The calibration of the two instruments is the key to controlling the energy scale, motivating beam tests at CERN before launch.

A first important deviation from a scale-invariant power-law spectrum was found for electrons near 1 TeV. Here, CALET and DAMPE observed a significant flux reduction, as expected from the large radiative losses of electrons during their travel in space. CALET has now published a high-statistics update up to 7.5 TeV, reporting the presence of candidate electrons above the 1 TeV spectral break (see “Electron break” figure).

This unexplored region may hold some surprises. For example, the detection of even higher energy electrons, such as the 12 TeV candidate recently found by CALET, may indicate the contribution of young and nearby sources such as the Vela supernova remnant, which is known to host a pulsar (see “Pulsar home” image).

CALET was designed to extend the energy reach beyond the rigidity limit of present space-borne spectrometers

A second unexpected finding is the observation of a significant reduction in the proton flux around 10 TeV. This bump and dip were also observed by DAMPE and anticipated by CREAM, albeit with low statistics (see “Proton bump” figure). A precise measurement of the flux has allowed CALET to fit the spectrum with a double-broken power law: after a spectral hardening starting at a few hundred GeV, which is also observed by AMS-02 and PAMELA, and which progressively increases above 500 GeV, a steep softening takes place above 10 TeV.

A similar bump and dip have been observed in the helium flux. These spectral features may result from a single physical process that generates a bump in the cosmic-ray spectrum. Theoretical models include an anomalous diffusive regime near the acceleration sources, the dominance of one or more nearby supernova remnants, the gradual release of cosmic rays from the source, and the presence of additional sources.

CALET is also a powerful hunter of heavier cosmic rays. Measurements of the spectra of boron, carbon and oxygen ions have been extended in energy reach and precision, providing evidence of a progressive spectral hardening for most of the primary elements above a few hundred GeV per nucleon. The boron-to-carbon flux ratio is an important input for understanding cosmic-ray propagation. This is because diffusion through the interstellar medium causes an additional softening of the flux of secondary cosmic rays such as boron with respect to primary cosmic rays such as carbon (see “Break in B/C?” figure). The collaboration also recently published the first high-resolution flux measurement of nickel (Z = 28), revealing the element to have a very similar spectrum to iron, suggesting similar acceleration and propagation behaviour.

CALET is also studying the spectra of sub-iron elements, which are poorly known above 10 GeV per nucleon, and ultra-heavy galactic cosmic rays such as zinc (Z = 30), which are quite rare. CALET studies abundances up to Z = 40 using a special trigger with a large acceptance, so far revealing an excellent match with previous measurements from ACE-CRIS (a satellite-based detector), SuperTIGER (a balloon-borne detector) and HEAO-3 (a satellite-based detector decommissioned in the 1980s). Ultra-heavy galactic cosmic rays provide insights into cosmic-ray production and acceleration in some of the most energetic processes in our galaxy, such as supernovae and binary-neutron-star mergers.

Gravitational-wave counterparts

In addition to charged particles, CALET can detect gamma rays with energies between 1 GeV and 10 TeV, and study the diffuse photon background as well as individual sources. To study electromagnetic transients related to complex phenomena such as gamma-ray bursts and neutron-star mergers, CALET is equipped with a dedicated monitor that to date has detected more than 300 gamma-ray bursts, 10% of which are short bursts in the energy range 7 keV to 20 MeV. The search for electromagnetic counterparts to gravitational waves proceeds around the clock by following alerts from LIGO, VIRGO and KAGRA. No X-ray or gamma-ray counterparts to gravitational waves have been detected so far.

On the low-energy side of cosmic-ray spectra, CALET has contributed a thorough study of the effect of solar activity on galactic cosmic rays, revealing charge dependence on the polarity of the Sun’s magnetic field due to the different paths taken by electrons and protons in the heliosphere. The instrument’s large-area charge detector has also proven to be ideal for space-weather studies of relativistic electron precipitation from the Van Allen belts in Earth’s magnetosphere.

The spectacular recent experimental advances in cosmic-ray research, and the powerful theoretical efforts that they are driving, are moving us closer to a solution to the century-old puzzle of cosmic rays. With more than four billion cosmic rays observed so far, and a planned extension of the mission to the nominal end of ISS operativity in 2030, CALET is expected to continue its campaign of direct measurements in space, contributing sharper and perhaps unexpected pictures of their complex phenomenology.

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The study of the Higgs boson remains central to the LHC programme. ATLAS reported a new result on Standard Model (SM) Higgs-boson production with decays to tau leptons, achieving the most precise single-channel measurement of the vector-boson-fusion production mode to date. Determining the production modes of the Higgs boson precisely may shed light on the existence of new physics that would be observed as deviations from the SM predictions.

Beyond single Higgs production, the di-Higgs production (HH) search is one of the most exciting and fundamental topics for LHC physics in the coming years as it directly probes the Higgs potential (see “Homing in on the Higgs self-interaction“). ATLAS has combined results for HH production in multiple final states, providing the best-expected sensitivity to the HH production cross-section and Higgs-boson self-coupling, allowing κ_λ (the Higgs self-coupling with respect to the SM value) to be within the range –1.2 < κ_λ < 7.2.

The search for beyond-the-SM (BSM) physics to explain the many unresolved questions about our universe is being conducted with innovative ideas and methods. CMS has presented new searches involving signatures with two tau leptons, examining the hypotheses of an excited tau lepton and a heavy neutral spin-1 gauge boson (Z′) produced via Drell-Yan and, for the first time, via vector boson fusion. These results set stringent constraints on BSM models with enhanced couplings to third-generation fermions.

Other new-physics theoretical models propose additional BSM Higgs bosons. ATLAS presented a search for such particles being produced in association with top quarks, setting limits on their cross-section that significantly improve upon previous ATLAS  results. Additional BSM Higgs bosons could explain puzzles such as dark matter, neutrino oscillations and the observed matter–antimatter asymmetry in the universe.

The dark side

Some BSM models imply that dark-matter particles could arise as composite mesons or baryons of a new strongly-coupled theory that is an extension of the SM. ATLAS investigated this dark sector through searches for high-multiplicity hadronic final states, providing the first direct collider constraints on this model to complement direct dark-matter-detection experimental results.

CMS have used low-pileup inelastic proton–proton collisions to measure event-shape variables related to the overall distribution of charged particles. These measurements showed the particle distribution to be more isotropic than predicted by theoretical models.

The LHC experiments also presented multiple analyses of proton–lead (p–Pb) and pp collisions, exploring the potential production of quark–gluon plasma (QGP) – a hot and dense phase of deconfined quarks and gluons found in the early universe that is frequently studied in heavy-ion Pb–Pb collisions, among others, at the LHC. Whether it can be created in smaller collision systems is still inconclusive.

ALICE reported a high-precision measurement of the elliptic flow of anti-helium-3 in QGP using the first Run-3 Pb–Pb run. The much larger data sample compared to the previous Run 2 measurement allowed ALICE to distinguish production models for these rarely produced particles for the first time. ALICE also reported the first measurement of an impact-parameter-dependent angular anisotropy in the decay of coherently photo-produced ρ⁰ mesons in ultra-peripheral Pb–Pb collisions. In these collisions, quantum interference effects cause a decay asymmetry that is inversely proportional to the impact parameter.

CMS reported its first measurement of the complete set of optimised CP-averaged observables from the process B⁰ → K^*0μ⁺μ^–. These measurements are significant because they could reveal indirect signs of new physics or subtle effects induced by low-energy strong interactions. By matching the current best experimental precision, CMS contributes to the ongoing investigation of this process.

LHCb presented measurements of the local and non-local contributions across the full invariant-mass spectrum of B^0* → K^*0μ⁺μ^–, tests of lepton flavour universality in semileptonic b decays, and mixing and CP violation in D → Kπ decays.

The future of the field was discussed in a well-attended panel session, which emphasised exploring the full potential of the HL-LHC and engaging younger generations

From a theoretical perspective, progress in precision calculations has exceeded expectations. Many processes are now known to next-to-next-to-leading order or even next-to-next-to-next-to-leading order (N³LO) accuracy. The first parton distribution functions approximating N³LO accuracy have been released and reported at LHCP, and modern parton showers have set new standards in perturbative accuracy.

In addition to these advances, several new ideas and observables are being proposed. Jet substructure, for instance, is becoming a precision science and valuable tool due to its excellent theoretical properties. Effective field theory (EFT) methods are continuously refined and automated, serving as crucial bridges to new theories as many ultraviolet theories share the same EFT operators. Synergies between flavour physics, electroweak effects and high-transverse-momentum processes at colliders are particularly evident within this framework. The use of the LHC as a photon collider showcases the extraordinary versatility of LHC experiments and their synergy with theoretical advancements.

Discovery machine

The HL-LHC upgrade was thoroughly discussed, with several speakers highlighting the importance and uniqueness of its physics programme. This includes fundamental insights into the Higgs potential, vector-boson scattering, and precise measurements of the Higgs boson and other SM parameters. Thanks to the endless efforts by the four collaborations to improve their performances, the LHC already rivals historic lepton colliders for electroweak precision in many channels, despite the cleaner signatures of lepton collisions. The HL-LHC will be capable of providing extraordinarily precise measurements while also serving as a discovery machine for many years to come.

The future of the field was discussed in a well-attended panel session, which emphasised exploring the full potential of the HL-LHC and engaging younger generations. Preserving the unique expertise and knowledge cultivated within the CERN community is imperative. Next year’s LHCP conference will be held at National Taiwan University in Taipei from 5 to 10 June.

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Being the most massive known elementary particle, top quarks are a focus for precision measurements and searches for new phenomena. At the LHC, they are copiously produced in pairs via quantum chromodynamic (QCD) interactions, and, to a much lesser extent, in single modes through the electroweak force. Precisely measuring the single-top cross section provides a stringent test for the electroweak sector of the Standard Model (SM) of particle physics.

In September 2022, only four months after the start of the Run 3, the CMS collaboration released the first measurement using data at the new collision energy of 13.6 TeV: the production cross section of a top quark together with its antiparticle (tt). The collaboration can now also report a measurement of the production of a single top quark in association with a W boson (tW) based on the full dataset recorded in 2022. As well as testing the electroweak sector, constraining tW allows it to be better disentangled from the dominant tt process – a channel where precision improves our knowledge of higher orders of accuracy in perturbative QCD.

tW is a challenging measurement as it is 10 times less likely than tt production but has almost the same detection signature. This analysis selects events where both the top quark and the W boson ultimately decay to leptons. The signal therefore consists of two leptons (electrons or muons), a jet initiated from a bottom quark, and possibly extra jets coming from additional radiation. No single observable can discriminate the signal from the background, so a random forest (RF) is employed in events that contain either one or two jets, one of which comes from a bottom quark. The RF is a collection of decision trees collaborating to distinguish the tW signal from the tt background. The output of the RF, for events with one jet identified as coming from a bottom quark, is shown in figure 1. The higher the RF discriminant, the higher the relative proportion of signal events.

To achieve a higher precision, an extra handle is used to control the tt background: information from events with two b-quark jets. Such events are more likely to come from the decay of a tt pair. The measurement yields a precise value for the tW cross section. Figure 2 shows tW cross-section measurements by CMS at different centre-of-mass energies, including the new measurement in proton–proton collisions of 13.6 TeV. All measurements are consistent with state-of-the-art theory calculations. The first tW measurement at the new LHC energy frontier uses only part of the data but is already as precise as the earlier measurement, which used the entire Run 2 sample at 13 TeV. Exploiting the full Run 3 data sample will push the precision frontier forward and provide an even more stringent SM probe in the top quark sector.

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Rare radiative b-hadron decays are powerful probes of the Standard Model (SM) sensitive to small deviations caused by potential new physics in virtual loops. One such process is the decay of B⁰_s → μ⁺μ^–γ. The dimuon decay of the B⁰_s meson is known to be extremely rare and has been measured with unprecedented precision by LHCb and CMS. While performing this measurement, LHCb also studied the B⁰_s → μ⁺μ^–γ decay, partially reconstructed due to the missing photon, as a background component of the B⁰_s → μ⁺μ^– process and set the first upper limit on its branching fraction to 2.0 × 10^–9 at 95% CL (red arrow in figure 1). However, this search was limited to the high-dimuon-mass region, whereas several theoretical extensions of the SM could manifest themselves in lower regions of the dimuon-mass spectrum. Reconstructing the photon is therefore essential to explore the spectrum thoroughly and probe a wide range of physics scenarios.

The LHCb collaboration now reports the first search for the B⁰_s → μ⁺μ^–γ decay with a reconstructed photon, exploring the full dimuon mass spectrum. Photon reconstruction poses additional experimental challenges, such as degrading the mass resolution of the B⁰_s candidate and introducing additional background contributions. To cope with this ambitious search, machine-learning algorithms and new variables have been specifically designed with the aim of discriminating the signal among background processes with similar signatures. The analysis is performed separately for three dimuon mass ranges to exploit any differences along the spectrum, such as the ϕ(1020) meson contribution in the low invariant mass region. The μ⁺μ^–γ invariant mass distributions of the selected candidates are fitted, including all background contributions and the B⁰_s → μ⁺μ^–γ signal component. Figure 2 shows the fit for the lowest dimuon mass region.

No significant signal of B⁰_s → μ⁺μ^–γ is found in any of the three dimuon mass regions, consistent with the background-only hypothesis. Upper bounds on the branching fraction are set and can be seen as the black arrows in figure 1. The mass fit is also performed for the combined candidates of the three dimuon mass regions to set a combined upper limit on the branching fraction to 2.8 × 10^–8 at 95% CL.

The SM theoretical predictions of b decays becomes particularly difficult to calculate when a photon is involved, and they have large uncertainties due to the B⁰_s → γ local form factors. The B⁰_s → μ⁺μ^–γ decay provides a unique opportunity to validate the different theoretical approaches, which do not agree with each other, as shown by the coloured bands in figure 1. Theoretical calculations of the branching fractions are currently below the experimental limits. The upgraded LHCb detector and the increased luminosity of the LHC’s Run 3 is currently providing conditions for studying rare radiative b-hadron decays with greater precision and, eventually, for finding evidence for the B⁰_s → μ⁺μ^–γ decay.

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This year, the PBC initiative has significantly strengthened CERN’s dark-sector searches, explained Mike Lamont and Joachim Mnich, directors for accelerators and technology, and research and computing, respectively. In particular, the newly approved SHiP proton beam-dump experiment (see SHiP to chart hidden sector) will complement the searches for light dark-sector particles that are presently conducted with NA64’s versatile setup, which is suitable for electron, positron, muon and hadron beams.

First-phase success

The FASER and SND experiments, now taking data in the LHC tunnel, are two of the successes of the PBC initiative’s first phase. Both search for new physics and study high-energy neutrinos along the LHC collision axis. FASER’s successor, FASER2, promises a 10,000-fold increase in sensitivity to beyond-the-Standard Model physics, said Jonathan Feng (UC Irvine). With the potential to detect thousands of TeV-scale neutrinos a day, it could also measure parton distribution functions and thereby enhance the physics reach of the high-luminosity LHC (HL-LHC). FASER2 may form part of the proposed Forward Physics Facility, set to be located 620 m away, along a tangent from the HL-LHC’s interaction point 1. A report on the facility’s technical infrastructure is scheduled for mid-2024, with a letter of intent foreseen in early 2025. By contrast, the CODEX-b and ANUBIS experiments are being designed to search for feebly interacting particles transverse to LHCb and ATLAS, respectively. In all these endeavours, the Feebly Interacting Particle Physics Centre will act as a hub for exchanges between experiment and theory.

Francesco Terranova (Milano-Bicocca) and Marc Andre Jebramcik (CERN) explained how ENUBET and NuTAG have been combined to optimise a “tagged” neutrino beam for cross-section measurements, where the neutrino flavour is known by studying the decay process of its parent hadron. In the realm of quantum chromodynamics, SPS experiments with lead ions (the new NA60+ experiment) and light ions (NA61/SHINE) are aiming to decode the phases of nuclear matter in the non-perturbative regime. Meanwhile, AMBER is proposing to determine the charge radii of kaons and pions, and to perform meson spectroscopy, in particularwith kaons.

The LHCspin collaboration presented a plan to open a new frontier of spin physics at the LHC building upon the successful operation of the SMOG2 gas cell that is upstream of the LHCb detector. Studying collective phenomena at the LHC in this way could probe the structure of the nucleon in a so-far little-explored kinematic domain and make use of new probes such as charm mesons, said Pasquale Di Nezza (INFN Frascati).

Measuring moments

The TWOCRYST collaboration aims to demonstrate the feasibility and the performance of a possible fixed-target experiment in the LHC to measure the electric and magnetic dipole moments (EDMs and MDMs) of charmed baryons, offering a complementary probe of searches for CP violation in the Standard Model. The technique would use two bent crystals: the first to deflect protons from the beam halo onto a target, with the resulting charm baryons then deflected by the second (precession) crystal onto a detector such as LHCb, while at the same time causing their spins to precess in the strong electric and magnetic fields of the deformed crystal lattice, explained Pascal Hermes (CERN).

New ideas ranged from the measurement of molecular electric dipole moments at ISOLDE to measuring the gravitational field of the LHC beam

Several projects to detect axion-like particles were discussed, including a dedicated superconducting cavity for heterodyne detection being jointly developed by PBC and CERN’s Quantum Technology Initiative. Atom interferometry is another subject of common interest, with PBC demonstrating the technical feasibility of installing an atom interferometer with a baseline of 100 m in one of the LHC’s access shafts. Other new ideas ranged from the measurement of molecular EDMs at ISOLDE to measuring the gravitational field of the LHC beam.

With the continued determination to fully exploit the scientific potential of the CERN accelerator complex and infrastructure for projects that are complementary to high-energy-frontier colliders testified by many fruitful discussions, the annual meeting concluded as a resounding success. The PBC community ended the workshop by thanking co-founder Claude Vallée (CPPM Marseille), who retired as a PBC convener after almost a decade of integral work, and welcomed Gunar Schnell (Ikerbasque and UPV/EHU Bilbao), who will take over as convener.

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In March, CERN selected a new experiment called SHiP to search for hidden particles using high-intensity proton beams from the SPS. First proposed in 2013, SHiP is scheduled to operate in the North Area’s ECN3 hall from 2031, where it will enable searches for new physics at the “coupling frontier” complementary to those at high-energy and precision-flavour experiments.

Interest in hidden sectors has grown in recent years, given the absence of evidence for non-Standard Model particles at the LHC, yet the existence of several phenomena (such as dark matter, neutrino masses and the cosmic baryon asymmetry) that require new particles or interactions. It is possible that the reason why such particles have not been seen is not that they are too heavy but that they are light and extremely feebly interacting. With such small couplings and mixings, and thus long lifetimes, hidden particles are extremely difficult to constrain. Operating in a beam-dump configuration that will produce copious quantities of photons and charm and beauty hadrons, SHiP will generically explore hidden-sector particles in the MeV to multiple-GeV mass range.

Optimised searching

SHiP is designed to search for signatures of models with hidden-sector particles, which include heavy neutral leptons, dark photons and dark scalars, by full reconstruction and particle identification of Standard Model final states. It will also search for light–dark-matter scattering signatures via the direct detection of atomic–electron or nuclear recoils in a high-density medium, and is optimised to make measurements of tau neutrinos and of neutrino-induced charm production by all three neutrinos species.

The experiment will be built in the existing TCC8/ECN3 experimental facility in the North Area. The beam-dump setup consists of a high-density proton target located in the target bunker, followed by a hadron stopper and a muon shield. Sharing the SPS beam time with other fixed-target experiments and the LHC should allow around 6 × 10²⁰ protons on target to be produced during 15 years of nominal operation. The detector itself consists of two parts that are designed to be sensitive to as many physics models and final states as possible. The scattering and neutrino detector will search for light dark matter and perform neutrino measurements. Further downstream is the much larger hidden-sector decay spectrometer, which is designed to reconstruct the decay vertex of a hidden-sector particle, measure its mass and provide particle identification of the decay products in an extremely low-background environment.

One of the most critical and challenging components of the facility is the proton target, which has to sustain an energy of 2.6 MJ impinging on it every 7.2 s. Another is the muon shield. To control the beam-induced background from muons, the flux in the detector acceptance must be reduced by some six orders of magnitude over the shortest possible distance, for which an active muon shield entirely based on magnetic deflection has been developed.

One of the most critical and challenging components of the facility is the proton target

The focus of the SHiP collaboration now is to produce technical design reports. “Given adequate funding, we believe that the TDR phase for BDF/SHiP will take us about three years, followed by production and construction, with the aim to commission the facility towards the end of 2030 and the detector in 2031,” says SHiP spokesperson Andrey Golutvin of Imperial College London. “This will allow up to two years of data-taking during Run 4, before the start of Long Shutdown 4, which would be the obvious opportunity to improve or consolidate, if necessary, following the experience of the first years of data taking.”

The decision to proceed with SHiP concluded a process that took more than a year, involving the Physics Beyond Colliders study group and the SPS and PS experiments committee. Two other experiments, HIKE and SHADOWS, were proposed to exploit the high-intensity beam from the SPS. Continuing the successful tradition of kaon experiments in the ECN3 hall, which currently hosts the NA62 experiment, HIKE (high-intensity kaon experiment) proposed to search for new physics in rare charged and neutral kaon decays while also allowing on-axis searches for hidden particles. For SHADOWS (search for hidden and dark objects with the SPS), which would have taken data concurrently with HIKE when the beamline is operated in beam-dump mode, the focus was low-background searches for off-axis hidden-sector particles in the MeV-GeV region.

“In terms of their science, SHiP and HIKE/SHADOWS were ranked equally by the relevant scientific committees,” explains CERN director for research and computing Joachim Mnich. “But a decision had to be made, and SHiP was a strategic choice for CERN.”

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Besides being a cornerstone of the Standard Model (SM), the Higgs boson (H) opens a very powerful path to search for physics beyond the SM. In particular, in the SM there are no particles that are sufficiently heavy to decay into two Higgs bosons. Therefore, if we observe the resonant production of HH pairs, for example, we have clear evidence for the existence of new physics, as predicted by models with an extended Higgs sector.

The CMS collaboration recently conducted a search for the resonant production of Higgs-boson pairs. The analysis combines six different analyses and five HH final states, targeting H decays into b quarks, photons, τ leptons and W bosons. As figure 1 shows for a spin-0 resonance (denoted X), the combination of the decay modes covers a wide mass range, from 280 GeV to 4 TeV. While no resonant signal is observed, stringent upper limits on the pp → X → HH cross section are obtained, which reach values of about 0.2 fb at the highest masses. These are the strongest observed limits to date for a scalar mass below 320 GeV or above 800 GeV.

One possible candidate for such a resonance is a heavy scalar from an extended Higgs sector, as predicted in the Minimal Supersymmetric Standard Model (MSSM), which features three neutral and two charged Higgs bosons. Figure 2 shows the excluded region of the model parameter tanβ (the ratio of vacuum expectation values of the two underlying Higgs doublets) as a function of the mass of the CP-odd Higgs boson, m_A. The HH combination is sensitive up to well beyond tanβ = 6, just above the HH threshold, and its exclusion extends up to beyond 600 GeV, outperforming the lower limits from the (also shown) searches of single heavy Higgs-boson production in this mass range. Compared to other direct searches, there is unique sensitivity for m_A > 450 GeV and tanβ < 5.

This result is part of a recent comprehensive review article on resonant Higgs-boson production searches by the CMS collaboration, covering the VH, HH and YH final states, with V denoting a W or Z boson and Y representing an additional new boson.

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The absence of LHC signals for new phenomena in the TeV range requires physicists to think differently about the open questions in fundamental physics. These include the abundance of matter over antimatter, the nature of dark matter, the quark and lepton flavour puzzle in general, and the non-zero nature of neutrino masses in particular. Solutions could be at even higher energies, at the price of either an unnatural value of the electroweak scale or an ingenious but still elusive structure. Radically new physics scenarios have been devised, often involving light and very-weakly coupled structures. Neither the mass scale (from meV to ZeV) of this new physics nor the intensity of its couplings (from 1 to 10^–12 or less) to the SM are known, calling for a versatile exploration tool.

By providing considerable advances in sensitivity, precision and, eventually, energy far above the TeV scale, the integrated Future Circular Collider (FCC) programme is the perfect vehicle with which to navigate this new landscape. Its first stage FCC-ee, an e⁺e^– collider operating at centre-of-mass energies ranging from below the Z pole (90 GeV) to beyond the top-quark pair-production threshold (365 GeV), would map the properties of the Higgs and electroweak gauge bosons and the top quark with precisions that are orders of magnitude better than today, acquiring sensitivity to the processes that led to the formation of the Brout–Englert–Higgs field a fraction of a nanosecond after the Big Bang. A comprehensive campaign of precision electroweak, QCD, flavour, tau, Higgs and top-quark measurements sensitive to tiny deviations from the predicted SM behaviour would probe energy scales far beyond the direct kinematic reach, while a subsequent pp collider (FCC-hh) would improve – by about an order of magnitude – the direct discovery reach for new particles. Both machines are strongly motivated in their own rights. Together, they offer the furthest physics reach of all proposed future colliders, and put the fundamental scalar sector of the universe centre-stage.

A scalar odyssey

The power of FCC-ee to probe the Higgs boson and other SM particles at much higher resolution would allow physicists to peer further into the cloud of quantum fluctuations surrounding them. The combination of results from previous lepton and hadron colliders at CERN and elsewhere has shown that electroweak symmetry breaking is consistent with its SM parameterisation, but its origin (and the origin of the Higgs boson itself) demands a deeper explanation. The FCC is uniquely placed to address this mystery via a combination of per-mil-level Higgs-boson and parts-per-millon gauge-boson measurements, along with direct high-energy exploration, to comprehensively probe symmetry-based explanations for an electroweak hierarchy. In particular, measurements of the Higgs boson’s self-coupling at the FCC would test whether the electroweak phase transition was first- or second-order, revealing whether it could have potentially played a role in setting the out-of-equilibrium condition necessary for creating the matter–antimatter asymmetry.

While the Brout–Englert–Higgs mechanism nicely explains the pattern of gauge-boson masses, the peculiar structure of quark and lepton masses (as well as the quark mixing angles) is ad hoc within the SM and could be the low-energy imprint of some new dynamics. The FCC will probe such potential new symmetries and forces, in particular via detailed studies of b and τ decays and of b → τ transitions, and significantly extend knowledge of flavour physics. A deeper understanding of approximate conservation laws such as baryon- and lepton-number conservation (or the absence thereof in the case of Majorana neutrinos) would test the limits of lepton-flavour universality and violation, for example, and could reveal new selection rules governing the fundamental laws. Measuring the first- and second-generation Yukawa couplings will also be crucial to complete our understanding, with a potential FCC-ee run at the s-channel Higgs resonance offering the best sensitivity to the electron Yukawa coupling. Stepping back, the FCC would sharpen understanding of the SM as a low-energy effective field theory approximation of a deeper, richer theory by extending the reach of direct and indirect exploration by about one order of magnitude.

The unprecedented statistics from FCC-ee also make it uniquely sensitive to exploring weakly coupled dark sectors and other candidates for new physics beyond the SM (such as heavy axions, dark photons and long-lived particles). Decades of searches across different experiments have pushed the mass of the initially favoured dark-matter candidate (weakly interacting massive particles, WIMPs) progressively beyond the reach of the highest energy e⁺e^– colliders. As a consequence, hidden sectors consisting of new particles that interact almost imperceptibly with the SM are rapidly gaining popularity as an alternative that could hold the answer not only to this problem but to a variety of others, such as the origin of neutrino masses. If dark matter is a doublet or a triplet WIMP, FCC-hh would cover the entire parameter space up to the upper mass limit for thermal relic. The FCC could also host a range of complementary detector facilities to extend its capabilities for neutrino physics, long-lived particles and forward physics.

For the first time since the Fermi theory almost a century ago, particle physicists are voyaging into completely uncharted territory

Completing this brief, high-level summary of the FCC physics reach are the origins of exotic astrophysical and cosmological signals, such as stochastic gravitational waves from cosmological phase transitions or astrophysical signatures of high-energy gamma rays. These phenomena, which include a modified electroweak phase transition, confining new physics in a dark sector, or annihilating TeV-scale WIMPs, could arise due to new physics which is directly accessible only to an energy-frontier facility.

Precision rules

Back in 2011, the original incarnation of a circular e⁺e^– collider to follow the LHC (dubbed LEP3) was to create a high-luminosity Higgs factory operating at 240 GeV in the LEP/LHC tunnel, providing similar precision to that at a linear collider running at the same centre-of-mass energy for a much smaller price tag. Choosing to build a larger 80–100 km version not only allows the tunnel and infrastructure to be reused for a 100 TeV hadron collider, but extends the FCC-ee scientific reach significantly beyond the study of the Higgs boson alone. The unparalleled control of the centre-of-mass energy via the use of resonant depolarisation and the unrivalled luminosity of an FCC-ee with four interaction points would produce around 6 × 10¹² Z bosons, 2.4 × 10⁸ W pairs (offering ppm precision on the Z and W masses and widths), 2 × 10⁶ Higgs bosons and 2 × 10⁶ top-quark pairs (impossible to produce with e⁺e^– collisions in the LEP/LHC tunnel) in as little as 16 years.

From the Fermi interaction to the discovery of the W and Z, and from electroweak measurements to the discovery of the top quark and the Higgs boson, greater precision has operated as a route to discoveries. Any deviation from the SM predictions, interpreted as the manifestation of new contact interactions, will point to a new energy scale that will be explored directly in a later stage. One of the findings of the FCC feasibility study is the richness of the FCC-ee Z-pole run, which promises comprehensive measurements of the Z lineshape and many electroweak observables with a 50-fold increase in precision, as well as direct and uniquely precise determinations of the electromagnetic and strong coupling constants. The comparison between these data and commensurately precise SM predictions would severely constrain the existence of new physics via virtual loops or mixing, corresponding to a factor-of-seven increase in energy scale – a jump similar to that from the LHC to FCC-hh. The Z-pole run also enables otherwise unreachable flavour (b, τ) physics, studies of QCD and hadronisation, searches for rare or forbidden decays, and exploration of the dark sector.

After the Z-pole run, the W boson provides a further precision tool at FCC-ee. Its mass is one of the most precisely measured parameters that can be calculated in the SM and is thus of utmost importance. In the planned WW-threshold run, current knowledge can be improved by more than an order of magnitude to test the SM as well as a plethora of new-physics models at a higher quantum level. Together, the very-high-luminosity Z and W runs will determine the gauge-boson sector with the sharpest precision ever.

Going to its highest energy, FCC-ee would explore physics associated with the heaviest known particle, the top quark, whose mass plays a fundamental role in the prediction of SM processes and for the cosmological fate of the vacuum. An improvement in precision by more than an order of magnitude will go hand in hand with a significant improvement in the strong coupling constant, and is crucial for precision exploration beyond the SM.

High-energy synergies

A later FCC-hh stage would complement and substantially extend the FCC-ee physics reach in nearly all areas. Compared to the LHC, it would increase the energy for direct exploration by a factor of seven, with the potential to observe new particles with masses up to 40 TeV (see “Direct exploration” figure). The day FCC-hh directly finds a signal for beyond-SM physics, the precision measurements from FCC-ee will be essential to pinpoint its microscopic origin. Indirectly, FCC-hh will be sensitive to energies of around 100 TeV, for example in the tails of Drell–Yan distributions. The large production of SM particles, including the Higgs boson, at large transverse momentum allows measurements to be performed in kinematic regions with optimal signal-to-background ratio and reduced experimental systematic uncertainties, testing the existence of effective contact interactions in ways that are complementary to what is accessible at lepton colliders. Dedicated FCC-hh experiments, for instance with forward detectors, would enrich further the new-physics opportunities and hunt for long-lived and millicharged particles.

Further increasing the synergies between FCC-ee and FCC-hh is the importance of operating four detectors (instead of two as in the conceptual design study), which has led to an optimised ring layout with a new four-fold period­icity. With four interaction points, FCC-ee provides a net gain in integrated luminosity for a given physics outcome. It also allows for a range of detector solutions to cover all physics opportunities, strengthens the robustness of systematic-uncertainty estimates and discovery claims, and opens several key physics targets that are tantalisingly close (but missed) with only two detectors. The latter include the first 5σ observation of the Higgs-boson self-coupling, and the opportunity to access the Higgs-boson coupling to electrons – one of FCC-ee’s toughest physics challenges.

No physics case for FCC would be complete without a thorough assessment of the corresponding detector challenges. A key deliverable of the feasibility study is a complete set of specifications ensuring that calorimeters, tracking and vertex detectors, muon detectors, luminometers and particle-identification devices meet the physics requirements. In the context of a Higgs factory operating at the ZH production threshold and above, these requirements have already been studied extensively for proposed linear colliders. However, the different experimental environment and the huge statistics of FCC-ee demand that they are revisited. The exquisite statistical uncertainties anticipated on key electroweak measurements at the Z peak and at the WW threshold call for a superb control of the systematic uncertainties, which will put considerable demands on the acceptance, construction quality and stability of the detectors. In addition, the specific discovery potential for very weakly coupled particles must be kept in mind.

The software and computing demands of FCC are an integral element of the feasibility study. From the outset, the driving consideration has been to develop a single software “ecosystem” adaptable to any future collider and usable by any future experiment, based on the best software available. Some tools, such as flavour tagging, significantly exceed the performance of algorithms previously used for linear-collider studies, but there is still much work needed  to bring the software to the level required by the FCC-ee. This includes the need for more accurate simulations of beam-related quantities, the machine-detector interface and the detectors themselves. In addition, various reconstruction and analysis tools for use by all collaborators need to be developed and implemented, reaping the benefits from the LHC experience and past linear-collider studies, and computing resources for regular simulated data production need to be evaluated.

Powerful plan

The alignment of stars – that from the initial concept in 2011/2012 of a 100 km-class electron–positron collider in the same tunnel as a future 100 TeV proton–proton collider led to the 2020 update of the European strategy for particle physics endorsing the FCC feasibility study as a top priority for CERN and its international partners – provides the global high-energy physics community with the most powerful exploration tool. FCC-ee offers ideal conditions (luminosity, centre-of-mass energy calibration, multiple experiments and possibly monochromatisation) for the study of the four heaviest particles of the SM with a flurry of opportunities for precision measurements, searches for rare or forbidden processes, and the possible discovery of feebly coupled particles. It is also the perfect springboard for a 100 TeV hadron collider, for which it provides a great part of the infrastructure. Strongly motivated in their own rights, together these two machines offer a uniquely powerful long-term plan for 21st-century particle physics.

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Magnetic monopoles are hypothetical particles that possess a magnetic charge. In 1864 James Clerk Maxwell assumed that magnetic monopoles didn’t exist because no one had ever observed one. Hence, he did not incorporate the concept of magnetic charges in his unified theory of electricity and magnetism, despite their being fully consistent with classical electrodynamics. Interest in magnetic monopoles intensified in 1931 when Dirac showed that quantum mechanics can accommodate magnetic charges, g, allowed by the quantisation condition g = N^e⁄_2α  = Ng_D, where e is the elementary electric charge, α is the fine structure constant, g_D is the fundamental magnetic charge and N is an integer. Grand unified theories predict very massive magnetic monopoles, but several recent extensions of the Standard Model feature monopoles in a mass range accessible at the LHC. Scientists have explored cosmic rays, particle collisions, polar volcanic rocks and lunar materials in their quest for magnetic monopoles, yet no experiment has found conclusive evidence thus far.

Signature strategy

The ATLAS collaboration recently reported the results of the search for magnetic monopoles using the full LHC Run 2 dataset recorded in 2015–2018. Magnetic charge conservation dictates that magnetic monopoles are stable and would be created in pairs of oppositely charged particles. Point-like magnetic monopoles could be produced in proton–proton collisions via two mechanisms: Drell–Yan, in which a virtual photon from the collision creates a magnetic mono­pole pair; or photon-fusion, whereby two virtual photons scattering off proton collisions interact to create a magnetic monopole pair. Dirac’s quantisation condition implies that a 1g_D monopole would ionise matter in a similar way as a high-electric-charge object (HECO) of charge 68.5e. Hence, magnetic monopoles and HECOs are expected to be highly ionising. In contrast to the behaviour of electrically charged particles, however, the Lorentz force on a monopole in the solenoidal magnetic field encompassing the ATLAS inner tracking detector would cause it to be accelerated in the direction of the field rather than in the orthogonal plane – a trajectory that precludes the application of usual track-reconstruction methods. The ATLAS detection strategy therefore relies on characterising the highly ionising signature of magnetic monopoles and HECOs in the electromagnetic calorimeter and in the transition radiation tracker.

This is the first ATLAS analysis to consider the photon-fusion production mechanism

The ATLAS search considered magnetic monopoles of magnetic charge 1g_D and 2g_D, and HECOs of 20e, 40e, 60e, 80e and 100e of both spin-0 and spin-½ in the mass range 0.2–4 TeV. ATLAS is not sensitive to higher charge monopoles or HECOs because they stop before the calorimeter due to their higher ionisation. Since particles in the considered mass range are too heavy to produce significant electromagnetic showers in the calorimeter, their narrow high-energy deposits are readily distinguished from the broader lower-energy ones of electrons and photons. Events with multiple high-energy deposits in the transition radiation tracker aligned with a narrow high-energy deposit in the calorimeter are therefore characteristic of magnetic monopoles and HECOs.

Random combinations of rare processes, such as superpositions of high-energy electrons, could potentially mimic such a signature. Since such rare processes cannot be easily simulated, the background in the signal region is estimated to be 0.15 ± 0.04 (stat) ± 0.05 (syst) events through extrapolation from the lower ionisation event yields in the data.

With no magnetic monopole or HECO candidate observed in the analysed ATLAS data, upper cross-section limits and lower mass limits on these particles were set at 95% confidence level. The Drell–Yan cross-section limits are approximately a factor of three better than those from the previous search using the 2015–2016 Run 2 data.

This is the first ATLAS analysis to consider the photon-fusion production mechanism, the results of which are shown in figure 1 (left) for spin-½ monopoles. ATLAS is also currently the most sensitive experiment to magnetic monopoles in the charge range 1-2g_D, as shown in figure 1 (right), and to HECOs in the charge range of 20–100e. The collaboration is further refining search techniques and developing new strategies to search for magnetic monopoles and HECOs in both Run 2 and Run 3 data.

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The congress started with parallel meetings on LHC physics, astroparticle physics, nuclear physics and theoretical physics. Two extra sessions were held, one covering technology transfer and the other discussing instrumentation R&D aimed at supporting the HL-LHC, future Higgs factories, and other developments in line with the European strategy for particle physics. The opening ceremony was followed by a lecture by Manuel Aguilar (CIEMAT), who gave an overview of the past 50 years of research in high-energy physics in Spain and the IMFP series. The first edition, held in Formigal (Spanish Pyrenees) in February 1973, was of great significance given the withdrawal of Spain from CERN in 1969, which put high-energy physics in Spain in a precarious position. The participation of prestigious foreign scientists in the first and subsequent editions undoubtedly contributed to the return of Spain to CERN in 1983.

LHC physics was one of the central themes of the event, in particular the first results from Run 3 as well as improvements in theoretical precision and Spain’s contribution to the HL-LHC upgrades. Other discussions and presentations focused on the search for new physics and especially dark-matter candidates, as well as new technologies such as quantum sensors. The conference also reviewed the status of studies related to neutrino oscillations and mass measurements, as well as searches for neutrinoless double beta decay and high-energy neutrinos in astrophysics. Results from gamma-ray and gravitational-wave observatories were discussed, as well as prospects for future experiments.

The programme included plenary sessions devoted to nuclear physics (such as the use of quantum computing to study the formation of nuclei), QCD studies in collisions of very high-energy heavy ions and in neutron stars, and nuclear reactions in storage rings. New technologies applied in nuclear and high-energy physics and their most relevant applications, especially in medical physics, complemented the programme alongside an overview of observational cosmology.

Roundtable discussions focused on grants offered by the European Research Council, R&D strategies and, following a clear presentation of the perspectives of future accelerators by ECFA chair Karl Jacobs (University of Freiburg), possible Spanish strategies for future projects with the participation of industry representatives. The congress also covered science policy, with the participation of the national programme manager Pilar Hernández (University of Valencia).

Prior to the opening of the conference, 170 students from various schools in Cantabria were welcomed to take part in an outreach activity “A morning among scientists” organised by IFCA and CPAN, while Álvaro de Rújula (University of Boston) gave a public talk on artificial intelligence. Finally, an excellent presentation by Antonio Pich (University of Valencia) on open questions in high-energy physics brought the conference to a close.

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While theorists are working hard to resolve this tension, the MUonE project aims to provide an independent determination of HVP using an intense muon beam from the CERN Super Proton Synchrotron. Whereas HVP is traditionally determined via hadron-production cross sections in e⁺e^– data, or via theory-based estimates from recent lattice calculations, MUonE would make a very precise measurement of the shape of the differential cross section of μ⁺e^– → μ⁺e^– scattering. This will enable a direct measurement of the hadronic contribution to the running of the electromagnetic coupling constant α, which governs the HVP process.

MUonE was first proposed in 2017 as part of the Physics Beyond Colliders initiative, and a test run in 2018 was performed to validate the basic idea of a detector. Following a decision by CERN in 2019 to carry out a three-week long pilot run to validate the experimental idea, the MUonE team collected data at the M2 beamline from 21 August to 10 September 2023, using a 160 GeV/c muon beam fired at atomic electrons in a fixed target located at CERN’s North Area. The main purpose of the run was to verify the system’s engineering and to attempt to measure the leptonic corrections to the running of α, for which an analysis is in progress.

The full experiment would have 40 stations comprising a 1.5 cm thick beryllium target followed by a tracking system, which can measure the scattering angles with high precision; further downstream lies an electromagnetic calorimeter and a muon detector. During the 2023 run, two MUonE stations followed by a calorimeter were installed, and a further tracking station without target was placed upstream of the apparatus to detect the incoming muons; the upstream station, towards the beam and without target, was dedicated to tracking the incoming muons. The next step is to install further detetor stations in stages.

“The original schedule has been delayed, partly due to the COVID pandemic, and the final measurement is expected to be performed after Long Shutdown 3,” explains MUonE collaboration board chair Clara Matteuzzi (INFN Milano Bicocca). “A first stage with a scaled detector, comprising a few stations followed by a calorimeter and a muon identifier, which could provide a very first measurement of HVP with low accuracy and a demonstration of the whole concept before the full final run, is under consideration.”

The overall goal of the experiment is to gather around 3.5 × 10¹² elastic scattering events with an electron energy larger than 1 GeV, during three years of data-taking at the M2 beam. This would allow the team to achieve a statistical error of 0.3% and thus make MUonE competitive with the latest HVP results computed by other means. The challenge, however, is to keep the systematic error at the level of the statistical one.

“This successful test run gives MUonE confidence that the final goal can be reached, and we are very much looking forward to submitting the proposal for the full run,” adds Matteuzzi.

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Kaons, which contain one strange and either a lighter up or down quark, have played a central role in the development of the Standard Model (SM). Augusto Ceccucci (CERN) pointed out that many of the SM’s salient features – including flavour mixing, parity violation, the charm quark and CP violation – were discovered through the study of kaons, leading to the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix. The full particle content of the SM was finally experimentally established at CERN with the Higgs-boson discovery in 2012, but many open questions remain.

The kaon’s special role in this context was the central topic of the workshop. The study of rare kaon decays provides a unique sensitivity to new physics, up to  scales higher than those at collider experiments. In the SM, the rare decay of a charged or neutral kaon into a pion plus a pair of charged or neutral leptons is strongly suppressed, even more so than the similar rare B-meson decays. This is due to the absence at tree-level of flavour-changing neutral current interactions (e.g. s → d) in the SM. Such a transition can only proceed at loop level involving the creation of at least one very heavy (virtual) electroweak gauge boson (figure “Decayed”, left). While experimentally this suppression constitutes a formidable challenge in identifying the decay products amongst a variety of background signals, new-physics contributions could leave a significantly measurable imprint through tree-level or virtual contributions. In contrast to rare B decays, the “gold-plated” rare kaon decay channels K⁺→π⁺νν and K_L→π⁰νν do not suffer from large hadronic uncertainties and are experimentally clean due to the limited number of possible decay channels.

The charged-kaon decay is currently being studied at NA62, and a measurement of its branching ratio with a precision of 15% is expected by 2025. However, as highlighted by NA62 physics coordinator Karim Massri (Lancaster University), to improve this measurement and thus significantly increase the  likelihood of a discovery, the experimental precision must be reduced to the level of the theoretical prediction, i.e. 5%. This can only be achieved with a next-generation experiment. The HIKE experiment, a proposed high-intensity kaon factory at CERN currently under approval, would reach the 5% precision goal on the measurement of K⁺→π⁺νν during its first phase of operation. experiment, a future high-intensity kaon factory at CERN currently under approval, will reach the 5% precision goal on the measurement of K⁺→π⁺νν during its first phase of operation. Afterwards, a second phase with a neutral K_L beam aiming at the first observation of the very rare decays K_L→π⁰ℓ⁺ℓ^– is foreseen. With a setup and detectors optimised for the measurement of the most challenging processes, the HIKE programme would be able to achieve unprecedented precision on most K⁺ and K_L decays.

For KOTO, Koji Shimi and Hashime Nanjo reported on the experimental progress on K_L→π⁰ℓ⁺ℓ^– and presented a new bound on its branching ratio. A planned phase two of KOTO, if funded, aims to measure the branching ratio with a precision of 20%. Although principally designed for the study of (rare) bottom-quark decays, LHCb can also provide information about the rare decay of the shorter-lived K_S.Radoslav Marchevski (EPFL Lausanne) presented the status and the prospects for a proposed LHCb-Phase II upgrade.

From the theory perspective, underpinned by impressive new perturbative, lattice QCD and effective-field-theory calculations presented at the workshop, the planned measurement of K⁺→π⁺νν at HIKE clearly has discovery potential, remarked Gino Isidori (University of Zurich). Together with other rare decay channels such as K_L→μ⁺μ^–, K_L→π⁰ℓ⁺ℓ^– and K⁺→π⁺ℓ⁺ℓ^– that would be measured by HIKE, added Giancarlo D’Ambrosio (INFN), the combined global theory analyses of experimental data will allow for discovering new physics if it exists within the reach of the experiment, and for providing solid constraints for new physics.

A decision on HIKE and other proposed experiments in CERN’s North Area will take place in early December.

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The participants were treated to many LHC Run 2 legacy results, as well as brand-new ones using freshly analysed Run 3 data. A large chunk of these results comprised precision measurements of the Higgs boson in view of gaining a deeper understanding of the origin of electroweak symmetry breaking. As the Higgs boson is deeply connected to many open questions potentially linked to physics beyond the Standard Model (SM), such as the origin of particle masses and flavour, studying it in the context of effective field theory is a particularly hot topic. A rich potential programme of “simplified” models for Higgs physics that can better quantify the reach of the LHC and offer new observables is also under development.

New frontiers

The ATLAS and CMS collaborations presented no fewer than 37 and 27 new preliminary results, respectively. Besides Higgs-sector physics, the experiments revealed their latest results of searches for physics beyond the SM, including new limits on the existence of supersymmetric and dark-matter particles. At the intensity frontier, the latest search for the ultra-rare decay K⁺ → π⁺e⁺e^–e⁺e^– from the NA62 experiment placed upper limits on dark-boson candidate masses, underlining the powerful complementarity between CERN’s fixed-target and LHC programmes. The Belle II collaboration presented first evidence of the decay B⁺ → K⁺ νν, as well as the result of their R(X) = Br(B → Xτν_τ)/Br(B → Xℓν_ℓ) measurement – the first at a B factory. The LHCb collaboration also presented an update of its recent R(D^*) = Br(B → D^*τν_τ)/Br(B → D^*ℓν_ℓ) measurement. Another highlight was LHCb’s observation of the hypernuclei antihypertriton and hypertriton.

Intense discussions took place on novel and potentially game-changing accelerator concepts

The state of the art in neutrino physics was presented, covering the vast landscape of experiments seeking to shed light on the three-flavour paradigm as well as the origin of the neutrino masses and mixings. So far, analyses by T2K and NOvA show a weak preference for a normal mass ordering, while the inverted mass ordering is not yet ruled out. With a joint analysis between T2K and NOvA in progress, updates are expected next year. At CERN the FASER experiment, which made the first observation of muon neutrinos at a collider earlier this year, presented the first observation of collider electron neutrinos. Looking outwards, a long-awaited discovery of galactic neutrinos was presented by IceCube.

The current FCC feasibility status was presented, along with that of other proposed colliders that could serve as Higgs factories. The overarching need to join forces between the circular- and linear-collider communities and to use all the gained knowledge for getting at least one accelerator approved was reflected during the discussions and many talks, as were the sustainability and energy consumption of detector and accelerator concepts. Intense discussions took place on novel and potentially game-changing accelerator concepts, such as energy recovery technologies or plasma acceleration. While not yet ready to be used on a large scale, they promise to have a big impact on the way accelerators are built in the future. Beyond colliders, the community also looked ahead to the DUNE and Hyper-Kamiokande experiments, and to proposed experiments such as the Einstein Telescope and those searching for axions.

A rich social programme included a public lecture by Andreas Hoecker (CERN) about particle physics at the highest energies, a concert with an introduction to the physics of the organ by Wolfgang Hillert (University of Hamburg), as well as an art exhibition called “High Energy” and a Ukrainian photo exhibition depicting science during times of war.

The next EPS-HEP conference will take place in 2025 in Marseille.

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A lack of uniqueness

For several decades, the hunt for the Higgs boson has been central to such a captivating narrative. Today, 11 years after its discovery, all other fundamental open questions remain open, and questions about the precise nature of the Higgs mechanism have become newly accessible to experimentation. What the field is facing today is not a lack of long-term challenges and opportunities, but a lack of uniqueness of one scientific hypothesis behind which a broad and intrinsically heterogeneous international research community could be assembled most easily.

We need to learn how to communicate this reality more effectively. Particle physics, even if no longer driven by the hypothesis of a particular particle within guaranteed experimental reach, continues to have a well-defined aim in understanding the fundamental composition of the universe. From discussions, however, I sense that many of my colleagues find it harder to develop long-term motivation in this more versatile situation. As a theorist I know that nature does not care about the words I attach to its equations. And yet, our research community is not immune to the motivational power of snappy formulations.

The exploration of the Higgs sector provides a two-decade-long perspective for future experimentation at the LHC and its high-luminosity upgrade (HL-LHC). However, any thorough exploration of the Brout–Englert–Higgs mechanism exceeds the capabilities of the HL-LHC and motivates a new machine. Why is it then challenging to communicate to the greater public that collecting 3 ab^–1 of data by the end of the HL-LHC is more than filling-in details on a discovery made in 2012? How can our narrative better reflect the evolving emphasis of our research? Should we talk, for example, about the Higgs’ self-interaction as a “fifth force”? Or would this be misleading cheerleader language, given that the Higgs self-coupling, unlike the other forces in the Standard Model Lagrangian, is not gauged? Whatever the best pitch is, it deserves to be sharpened within our community and more homogeneously disseminated.

Another compelling narrative for a future collider is the growing synergy with other fields. In recent decades, space-based astrophysical observatories have started to reach a complexity and cost comparable to the LHC. In addition, there is a multitude of smaller astrophysical observatories. We should welcome the important complementarities between lab-based experimental and space-based observational approaches. In the case of dark matter, for example, there are strong generic reasons to expect that collider experiments can constrain (and finally, establish) the microscopic nature of dark matter and that the solution lies in experimentally unchartered territory, such as either very massive or very feebly interacting particles.

What makes the physics of the infinitesimally small exciting for the public is also what makes it difficult to communicate

What makes the physics of the infinitesimally small exciting for the public is also what makes it difficult to communicate, starting with subtle differences in the use of everyday language. For a lay audience, for instance, a “search for something” is easy to picture, and not finding the something is a failure. In physics, however, particles can reveal themselves in quantum fluctuations even if the energy needed to produce them can’t be reached. Far from being a failure, not-finding with increased precision becomes an intrinsic mark of progress. When talking to non-scientists, should we try to bring to the forefront such unique and subtle features of our search logic? Could this be a safeguard against the foes of our science who misrepresent the perspectives and consequences of our research by naively equating any unconfirmed hypothesis with failure? Or is this simply too subtle and intellectual to be heard?

Clearly, in our everyday work at CERN, getting the numbers out is the focus. But going beyond this operational attitude and fighting for the most adequate words and pictures that give meaning to what we are doing is crucial to keep the community focused and motivated for the long march ahead.

• Adapted from text originally published in the CERN Staff Association newsletter.

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About 90 physicists attended the sixth plenary workshop of the Muon g-2 Theory Initiative, held in Bern from 4 to 8 September, to discuss the status and strategies for future improvements of the Standard Model (SM) prediction for the anomalous magnetic moment of the muon. The meeting was particularly timely given the recent announcement of the results from runs two and three of the Fermilab g-2 experiment (Muon g-2 update sets up showdown with theory), which reduced the uncertainty of the world average to 0.19 ppm, in dire need of a SM prediction at commensurate precision. The main topics of the workshop were the two hadronic contributions to g-2, hadronic vacuum polarisation (HVP) and hadronic light-by-light scattering (HLbL), evaluated either with a lattice–QCD or data-driven approach.

Hadronic vacuum polarisation

The first one-and-a-half days were devoted to the evaluation of HVP – the largest QCD contribution to g-2, whereby a virtual photon briefly transforms into a hadronic “blob” before being reabsorbed – from e⁺e^– data. The session started with a talk from the CMD-3 collaboration at the VEPP-2000 collider, whose recent measurement of the e⁺e^– → π⁺π^– cross section generated shock waves earlier this year by disagreeing (at the level of 2.5–5σ) with all previous measurements used in the Theory Initiative’s 2020 white paper. The programme also featured a comparison with results from the earlier CMD-2 experiment, and a report from seminars and panel discussions organised by the Theory Initiative in March and July on the details of the CMD-3 result. While concerns remain regarding the estimate of certain systematic effects, no major shortcomings could be identified.

Further presentations from BaBar, Belle II, BESIII, KLOE and SND detailed their plans for new measurements of the 2π channel, which in the case of BaBar and KLOE involve large data samples never analysed before for this measurement. Emphasis was put on the role of radiative corrections, including a recent paper by BaBar on additional radiation in initial-state-radiation events and, in general, the development of higher-order Monte Carlo generators. Intensive discussions reflected a broad programme to clarify the extent to which tensions among the experiments can be due to higher-order radiative effects and structure-dependent corrections. Finally, updated combined fits were presented for the 2π and 3π channels, for the former assessing the level of discrepancy among datasets, and for the latter showing improved determinations of isospin-breaking contributions.

CMD-3 generated shock waves by disagreeing with all previous measurements at the level of 2.5-5σ

Six lattice collaborations (BMW, ETMC, Fermilab/HPQCD/MILC, Mainz, RBC/UKQCD, RC^*) presented updates on the status of their respective HVP programmes. For the intermediate-window quantity (the contribution of the region of Euclidean time between about 0.4–1.0 fm, making up about one third of the total), a consensus has emerged that differs from e⁺e^–-based evaluations (prior to CMD-3) by about 4σ, while the short-distance window comes out in agreement. Plans for improved evaluations of the long-distance window and isospin-breaking corrections were presented, leading to the expectation of new, full computations for the total HVP contribution in addition to the BMW result in 2024. Several talks addressed detailed comparisons between lattice-QCD and data-driven evaluations, which will allow physicists to better isolate the origin of the differences once more results from each method become available. A presentation on possible beyond-SM effects in the context of the HVP contribution showed that it seems quite unlikely that new physics can be invoked to solve the puzzles.

Light-by-light scattering

The fourth day of the workshop was devoted to the HLbL contribution, whereby the interaction of the muon with the magnetic field is mediated by a hadronic blob connected to three virtual photons. In contrast to HVP, here the data-driven and lattice-QCD evaluations agree. However, reducing the uncertainty by a further factor of two is required in view of the final precision expected from the Fermilab experiment. A number of talks discussed the various contributions that feed into improved phenomenological evaluations, including sub-leading contributions such as axial-vector intermediate states as well as short-distance constraints and their implementation. Updates on HLbL from lattice QCD were presented by the Mainz and RBC/UKQCD groups, as were results on the pseudoscalar transition form factor by ETMC and BMW. The latter in particular allow cross checks of the numerically dominant pseudoscalar- pole contributions between lattice QCD and data-driven evaluations.

It is critical that the Theory Initiative work continues beyond the lifespan of the Fermilab experiment

On the final day, the status of alternative methods to determine the HVP contribution were discussed, first from the MUonE experiment at CERN, then from τ data (by Belle, CLEOc, ALEPH and other LEP experiments). First MUonE results could become available at few-percent precision with data taken in 2025, while a competitive measurement would proceed after Long Shutdown 3. For the τ data, new input is expected from the Belle II experiment, but the critical concern continues to be control over isospin-breaking corrections. Progress in this direction from lattice QCD was presented by the RBC/UKQCD collaboration, together with a roadmap showing how, potentially in combination with data-driven methods, τ data could lead to a robust, complementary determination of the HVP contribution.

The workshop concluded with a discussion on how to converge on a recommendation for the SM prediction in time for the final Fermilab result, expected in 2025, including new information expected from lattice QCD, the BaBar 2π analysis and radiative corrections. A final decision for the procedure for an update of the 2020 white paper is planned to be taken at the next plenary meeting in Japan in September 2024. In view of the long-term developments discussed at the workshop – not least the J-PARC Muon g-2/EDM experiment, due to start taking data in 2028 – it is critical that the work by the Theory Initiative continues beyond the lifespan of the Fermilab experiment, to maximise the amount of information on physics beyond the SM that can be inferred from precision measurements of the anomalous magnetic moment of the muon.

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The Forward Physics Facility (FPF) is a proposed new facility to operate concurrently with the High-Luminosity LHC, housing several new experiments on the ATLAS collision axis. The FPF offers a broad, far-reaching physics programme ranging from neutrino, QCD and hadron-structure studies to beyond-the-Standard Model (BSM) searches. The project, which is being studied within the Physics Beyond Colliders initiative, would exploit the pre-existing HL-LHC beams and thus have minimal energy-consumption requirements.

On 8 and 9 June, the 6th workshop on the Forward Physics Facility was held at CERN and online. Attracting about 160 participants, the workshop was organised in sessions focusing on the facility design, the proposed experiments and physics studies, leaving plenty of time for discussion about the next steps.

Groundbreaking

Regarding the facility itself, CERN civil-engineering experts presented its overall design: a 65 m-long, 10 m-high/wide cavern connected to the surface via an 88 m-deep shaft. The facility is located 600 m from the ATLAS collision point, in the SM18 area of CERN. A workshop highlight was the first results from a site investigation study, whereby a 20 cm-diameter core was taken at the proposed location of the FPF shaft to a depth of 100 m. The initial analysis of the core showed that the geological conditions are positive for work in this area. Other encouraging studies towards confirming the FPF feasibility were FLUKA simulations of the expected muon flux in the cavern (the main background for the experiments), the expected radiation level (shown to allow people to enter the cavern during LHC operations with various restrictions), and the possible effect on beam operations of the excavation works. One area where more work is required concerns the possible need to install a sweeper magnet in the LHC tunnel between ATLAS and the FPF to reduce the muon backgrounds.

Currently there are five proposed experiments to be installed in the FPF: FASER2 (to search for decaying long-lived particles); FASERν2 and AdvSND (dedicated neutrino detectors covering complementary rapidity regions); FLArE (a liquid-argon time projection chamber for neutrino physics and light dark-matter searches); and FORMOSA (a scintillator-based detector to search for milli-charged particles). The three neutrino detectors offer complementary designs to exploit the huge number of TeV energy neutrinos of all flavours that would be produced in such a forward-physics configuration. Four of these have smaller pathfinder detectors, FASER(ν), SND@LHC and milliQan that are already operating during LHC Run 3. First results from these pathfinder experiments were presented at the CERN workshop, including the first ever direct observation of collider neutrinos by FASER and SND@LHC, which provide a key proof of principle for the FPF. The latest conceptual design and expected performance of the FPF experiments were presented. Furthermore, first ideas on models to fund these experiments are in place and were discussed at the workshop.

In the past year, much progress has been made in quantifying the physics case of the FPF. It effectively extends the LHC with a “neutrino–ion collider’’ with complementary reach to the Electron–Ion Collider under construction in the US. The large number of high-energy neutrino interactions that will be observed at the FPF allows detailed studies of deep inelastic scattering to constrain proton and nuclear parton distribution functions (PDFs). Dedicated projections of the FPF reveal that uncertainties in light-quark PDFs could be reduced by up to a factor of two or even more compared to current models, leading to improved HL-LHC predictions for key measurements such as the W-boson mass.

In the past year, much progress has been made in quantifying the physics case of the FPF

High-energy electrons and tau neutrinos at the FPF predominantly arise from forward charm production. This is initiated by gluon–gluon scattering involving very low and high momentum fractions, with the former reaching down to Bjorken-x values of 10^–7 – beyond the range of any other experiment. The same FPF measurements of forward charm production are relevant for testing different models of QCD at small-x, which would be instrumental for Higgs production at the proposed Future Circular Collider (FCC-hh). This improved modeling of forward charm production is also essential for understanding the backgrounds to diffuse astrophysics neutrinos at telescopes such as IceCube and KM3NeT. In addition, measurements of the ratio of electron-to-muon neutrinos at the FPF probe forward kaon-to-pion production ratios that could explain the so-called muon puzzle (a deficit in muons in simulations compared to measurements), affecting cosmic-ray experiments.

The FPF experiments would also be able to probe a host of BSM scenarios in uncharted regions of parameter space, such as dark-matter portals, dark Higgs bosons and heavy neutral leptons. Furthermore, experiments at the FPF will be sensitive to the scattering of light dark-matter particles produced in LHC collisions, and the large centre-of-mass energy enables probes of models, such as quirks (long-lived particles that are charged under a hidden-sector gauge interaction), and some inelastic dark-matter candidates, which are inaccessible at fixed-target experiments. On top of that, the FPF experiments will significantly improve the sensitivity of the LHC to probe millicharged particles.

The June workshop confirmed both the unique physics motivation for the FPF and the excellent progress in technical and feasibility studies towards realising it. Motivated by these exciting prospects, the FPF community is now working on a Letter of Intent to submit to the LHC experiments committee as the next step.

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Despite its exceptional success, we know that the standard model (SM) is incomplete. To date, the LHC has not yet found clear indications of physics beyond the SM (BSM), which might mean that the BSM energy scale is above what can be directly probed at the LHC. An alternative way to probe BSM physics is through searches of off-shell effects, which can be done using the effective field theory framework (EFT). By treating the SM Lagrangian as the lowest order term in a perturbative expansion, EFT allows us to include higher-dimension operators in the Lagrangian, while respecting the experimentally verified SM symmetries.

Operators

The CMS collaboration recently performed a search for BSM physics using EFT, analysing data containing top quarks with additional final-state leptons. The top quark is of particular interest because of its large mass, resulting in a Higgs–Yukawa coupling of order unity. Many BSM models connect the top-quark mass to large couplings to new physics. In the context of top quark EFT, there are 59 total operators at dimension six, controlled by the so-called Wilson coefficients, 26 of which produce final-state leptons. These coefficients enter the model as corrections to the SM matrix element, with a first term corresponding to the interference between the SM and BSM contributions, and a second term reflecting pure BSM effects. 

The analysis was performed on the Run 2 proton–proton collisions sample, corresponding to an integrated luminosity of 138 fb^–1. It obtained limits on those 26 dimension-six coefficients, simulated at detector level with leading order precision (plus an additional parton when possible), exploiting six final-state signals, with different numbers of top quarks and leptons: ttH, ttℓν, ttℓℓ, tℓℓq, tHq and tttt. The analysis splits the data into 43 discrete categories, based primarily on lepton multiplicity, total lepton charge, and total jet or b-quark jet multiplicities. The events are analysed as differential distributions in the kinematics of the final-state leptons and jets. 

A statistical analysis is performed using a profiled likelihood to extract the 68% and 95% confidence intervals for all 26 Wilson coefficients by varying one of them while profiling the other 25. All the coefficients are compatible with zero (i.e. in agreement with the SM) at the 95% confidence level. For many of them, these results are the most competitive to date, even when compared to analyses that fit only one or two coefficients. Figure 1 shows how the 95% confidence intervals (2σ limit) translate into upper limits on the energy scale of the probed BSM interaction. 

The CMS collaboration will continue to refine these measurements by expanding upon the final-state observables and leveraging the Run 3 data sample. With the HL-LHC quickly approaching, the future of BSM physics searches is full of potential.

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On 10 August, the Muon g-2 collaboration at Fermilab presented its latest measurement of the anomalous magnetic moment of the muon a_μ. Combining data from Run 1 to Run 3, the collaboration found a_μ = 116 592 055 (24) × 10^–11, representing a factor-of-two improvement on the precision of its initial 2021 result. The experimental world average for a_μ now stands more than 5σ above the Standard Model (SM) prediction published by the Muon g-2 Theory Initiative in 2020. However, calculations based on a different theoretical approach (lattice QCD) and a recent analysis of e⁺e^– data that feeds into the prediction are in tension with the 2020 calculation, and more work is needed before the discrepancy is understood.

The anomalous magnetic moment of the muon a_μ = (g-2)/2 (where g is the muon’s gyromagnetic ratio) is the difference between the observed value of the muon’s magnetic moment and the Dirac prediction (g = 2) due to contributions of virtual particles. This makes measurements of a_μ, which is one of the most precisely calculated and measured quantities in physics, an ideal testbed for physics beyond the SM. To measure it, a muon beam is sent into a superconducting storage ring reused from the former g-2 experiment at Brookhaven National Laboratory. Initially aligned, the muon spin axes precess as they interact with the magnetic field. Detectors located along the ring’s inner circumference allow the precession rate and thus a_μ to be determined. Many improvements to the setup have been made since the first run, including better running conditions, more stable beams and an improved knowledge of the magnetic field.

The new result is based on data taken from 2019 and 2020, and has four times the statistics compared to the 2021 result. The collaboration also decreased the systematic uncertainty to levels beyond its initial goals. Currently, about 25% of the total data (Run 1–Run 6) has been analysed. The collaboration plans to publish its final results in 2025, targeting a precision of 0.14 ppm compared to the current 0.2 ppm. “We have moved the accuracy bar of this experiment one step further and now we are waiting for the theory to complete the calculations and cross-checks necessary to match the experimental accuracy,” explains collaboration co-spokesperson Graziano Venanzoni of INFN Pisa and the University of Liverpool. “A huge experimental and theoretical effort is going on, which makes us confident that theory prediction will be in time for the final experimental result from FNAL in a few years from now.”

The theoretical picture is foggy. The SM prediction for the anomalous magnetic moment receives contributions from the electromagnetic, electroweak and strong interactions. While the former two can be computed to high precision in perturbation theory, it is only possible to compute the latter analytically in certain kinematic regimes. Contributions from hadronic vacuum polarisation and hadronic light-by-light scattering dominate the overall theoretical uncertainty on a_μ at 83% and 17%, respectively.

To date, the experimental results are confronted with two theory predictions: one by the Muon g-2 Theory Initiative based on the data-driven “R-ratio” method, which relies on hadronic cross-section measurements, and one by the Budapest–Marseille–Wuppertal (BMW) collaboration based on simulations of lattice QCD and QED. The latter significantly reduces the discrepancy between the theoretical and measured values. Adding a further puzzle, a recently published value of hadronic cross-section measurements by the CMD-3 collaboration that contrasts with all other experiments narrows the gap between the Muon g-2 Theory Initiative and the BMW predictions (see p19).

“This new result by the Fermilab Muon g-2 experiment is a true milestone in the precision study of the Standard Model,” says lattice gauge theorist Andreas Jüttner of CERN and the University of Southampton. “This is really exciting – we are now faced with getting to the roots of various tensions between experimental and theoretical findings.”

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New physics may come at us in unexpected ways that may be completely hidden to conventional search methods. One unique example of this is the narrowly spaced, semi-periodic spectra of heavy gravitons predicted by the clockwork gravity model. Similar to models with extra dimensions, the clockwork model addresses the hierarchy problem between the weak and Planck scales, not by stabilising the weak scale (as in supersymmetry, for example), but by bringing the fundamental higher dimensional Planck scale down to accessible energies. The mass spectrum of the resulting graviton tower in the clockwork model is described by two parameters: k, a mass parameter that determines the onset of the tower, and M₅, the five-dimensional reduced Planck mass that controls the overall cross-section of the tower’s spectrum.

At the LHC, these gravitons would be observed via their decay into two light Standard Model particles. However, conventional bump/tail hunts are largely insensitive to this type of signal, particularly when its cross section is small. A recent ATLAS analysis approaches the problem from a completely new angle by exploiting the underlying approximate periodicity feature of the two-particle invariant mass spectrum.

Graviton decays with dielectron or diphoton final states are an ideal testbed for this search due to the excellent energy resolution of the ATLAS detector. After convolving the mass spectrum of the graviton tower with the ATLAS detector resolution corresponding to these final states, it resembles a wave-packet (like the representation of a free particle propagating in space as a pulse of plane-wave superposition with a finite momenta range). This implies that a transformation exploiting the periodic nature of the signal may be helpful.

Figure 1 shows how a particularly faint clockwork signal would emerge in ATLAS for the diphoton final state. It is compared with the data and the background-only fit obtained from an earlier (full Run 2) ATLAS search for resonances with the same final state. As an illustration, the signal shape is given without realistic statistical fluctuations. The tiny “bumps” or the shape’s integral over the falling background cannot be detected with conventional bump/tail-hunting methods. Instead, for the first time, a continuous wavelet transformation is applied to the mass distribution. The problem is therefore transformed to the “scalogram” space, i.e. the mass versus scale (or inverse frequency) space, as shown in figure 2 (left). The large red area at high scales (low frequencies) represents the falling shape of the background, while the signal from figure 1 now appears as a clear, distinct local “blob” above m_γγ = k and at low scales (high frequencies).

The strongest exclusion contours to date are placed in the clockwork parameter space

With realistic statistical fluctuations and uncertainties, these distinct “blobs” may partially wash out, as shown in figure 2 (right). To counteract this effect, the analysis uses multiple background-only and background-plus-signal scalograms to train a binary convolutional neural-network classifier. This network is very powerful in distinguishing between scalograms belonging to the two classes, but it is also model-specific. Therefore, another search for possible periodic signals is performed independently from the clockwork model hypothesis. This is done in an “anomaly detection” mode using an autoencoder neural-network. Since the autoencoder is trained on multiple background-only scalograms (unlabelled data) to learn the features of the background (unsupervised learning), it can predict the compatibility of a given scalogram with the background-only hypothesis. A statistical test based on the two networks’ scores is derived to check the data compatibility with the background-only or the background+signal hypotheses.

Applying these novel procedures to the dielectron and diphoton full Run 2 data, ATLAS sees no significant deviation from the background-only hypothesis in either the clockwork-model search or in the model-independent one. The strongest exclusion contours to date are placed in the clockwork parameter space, pushing the sensitivity to beyond 11 TeV in M₅. Despite the large systematic uncertainties in the background model, these do not exhibit any periodic structure in the mass space and their impact is naturally reduced when transforming to the scalogram space. The sensitivity of this analysis is therefore mostly limited by statistics and is expected to improve with the full Run 3 dataset.

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The Future Circular Collider (FCC) is the most powerful post-LHC experimental infrastructure proposed to address key open questions in particle physics. Under study for almost a decade, it envisions an electron–positron collider phase, FCC-ee, followed by a proton–proton collider in the same 91 km-circumference tunnel at CERN. The hadron collider, FCC-hh, would operate at a centre-of-mass energy of 100 TeV, extending the energy frontier by almost an order of magnitude compared to the LHC, and provide an integrated luminosity a factor of 5–10 larger. The mass reach for direct discovery at FCC-hh will reach several tens of TeV and allow, for example, the production of new particles whose existence could be indirectly exposed by precision measurements at FCC-ee. 

The potential of FCC-hh offers an unprecedented opportunity to address fundamental unknowns about our universe

At the time of the kickoff meeting for the FCC study in 2014, the physics potential and the requirements for detectors at a 100 TeV collider were already heavily debated. These discussions were eventually channelled into a working group that provided the input to the 2020 update of the European strategy for particle physics and recently concluded with a detailed writeup in a 300-page CERN Yellow Report. To focus the effort, it was decided to study one reference detector that is capable of fully exploiting the FCC-hh physics potential. At first glance it resembles a super CMS detector with two LHCb detectors attached (see “Grand designs” image). A detailed detector performance study followed, allowing a very efficient study of the key physics capabilities. 

The first detector challenge at FCC-hh is related to the luminosity, which is expected to reach 3 × 10³⁵ cm^–2s^–1. This is six times larger than the HL-LHC luminosity and 30 times larger than the nominal LHC luminosity. Because the FCC will operate beams with a 25 ns bunch spacing, the so-called pile-up (the number of pp collisions per bunch crossing) scales by approximately the same factor. This results in almost 1000 simultaneous pp collisions, requiring a highly granular detector. Evidently, the assignment of tracks to their respective vertices in this environment is a formidable task. 

The plan to collect an integrated pp luminosity of 30 ab^–1 brings the radiation hardness requirements for the first layers of the tracking detector close to 10¹⁸ hadrons/cm², which is around 100 times more than the requirement for the HL-LHC. Still, the tracker volume with such high radiation load is not excessively large. From a radial distance of around 30 cm outwards, radiation levels are already close to those expected for the HL-LHC, thus the silicon technology for these detector regions is already available.

The high radiation levels also need very radiation-hard calorimetry, making a liquid-argon calorimeter the first choice for the electromagnetic calorimeter and forward regions of the hadron calorimeter. The energy deposit in the very forward regions will be 4 kW per unit of rapidity and it will be an interesting task to keep cryogenic liquids cold in such an environment. Thanks to the large shielding effect of the calorimeters, which have to be quite thick to contain the highest energy particles, the radiation levels in the muon system are not too different from those at the HL-LHC. So the technology needed for this system is available. 

Looking forward 

At an energy of 100 TeV, important SM particles such as the Higgs boson are abundantly produced in the very forward region. The forward acceptance of FCC-hh detectors therefore has to be much larger than at the LHC detectors. ATLAS and CMS enable momentum measurements up to pseudorapidities (a measure of the angle between the track and beamline) of around η = 2.5, whereas at FCC-hh this will have to be extended to η = 4 (see “Far reaching” figure). Since this is not achievable with a central solenoid alone, a forward magnet system is assumed on either side of the detector. Whether the optimum forward magnets are solenoids or dipoles still has to be studied and will depend on the requirements for momentum resolution in the very forward region. Forward solenoids have been considered that extend the precision of momentum measurements by one additional unit of rapidity. 

A silicon tracking system with a radius of 1.6 m and a total length of 30 m provides a momentum resolution of around 0.6% for low-momentum particles, 2% at 1 TeV and 20% at 10 TeV (see “Forward momentum” figure). To detect at least 90% of the very forward jets that accompany a Higgs boson in vector-boson-fusion production, the tracker acceptance has to be extended up to η = 6. At the LHC such an acceptance is already achieved up to η = 4. The total tracker surface of around 400 m² at FCC-hh is “just” a factor two larger than the HL-LHC trackers, and the total number of channels (16.5 billion) is around eight times larger.

It is evident that the FCC-hh reference detector is more challenging than the LHC detectors, but not at all out of reach. The diameter and length are similar to those of the ATLAS detector. The tracker and calorimeters are housed inside a large superconducting solenoid 10 m in diameter, providing a magnetic field of 4 T. For comparison, CMS uses a solenoid with the same field and an inner diameter of 6 m. This difference does not seem large at first sight, but of course the stored energy (13 GJ) is about five times larger than the CMS coil, which needs very careful design of the quench protection system.

For the FCC-hh calorimeters, the major challenge, besides the high radiation dose, is the required energy resolution and particle identification in the high pile-up environment. The key to achieve the required performance is therefore a highly segmented calorimeter. The need for longitudinal segmentation calls for a solution different from the “accordion” geometry employed by ATLAS. Flat lead/steel absorbers that are inclined by 50 degrees with respect to the radial direction are interleaved with liquid-argon gaps and straight electrodes with high-voltage and signal pads (see “Liquid argon” figure). The readout of these pads on the back of the calorimeter is then possible thanks to the use of multi-layer electrodes fabricated as straight printed circuit boards. This idea has already been successfully prototyped within the CERN EP detector R&D programme.

The considerations for a muon system for the reference detector are quite different compared to the LHC experiments. When the detectors for the LHC were originally conceived in the late 1980s, it was not clear whether precise tracking in the vicinity of the collision point was possible in this unprecedented radiation environment. Silicon detectors were excessively expensive and gas detectors were at the limit of applicability. For the LHC detectors, a very large emphasis was therefore put on muon systems with good stand-alone performance, specifically for the ATLAS detector, which is able to provide a robust measurement of, for example, the decay of a Higgs particle into four muons, with the muon system alone. 

Thanks to the formidable advancement of silicon-sensor technology, which has led to full silicon trackers capable of dealing with around 140 simultaneous pp collisions every 25 ns at the HL-LHC, standalone performance is no longer a stringent requirement. The muon systems for FCC-hh can therefore fully rely on the silicon trackers, assuming just two muon stations outside the coil that measure the exit point and the angle of the muons. The muon track provides muon identification, the muon angle provides a coarse momentum measurement for triggering and the track position provides improved muon momentum measurement when combined with the inner tracker. 

The major difference between an FCC-hh detector and CMS is that there is no yoke for the return flux of the solenoid, as the cost would be excessive and its only purpose to shield the magnetic field towards the cavern. The baseline design assumes the cavern infrastructure can be built to be compatible with this stray field. Infrastructure that is sensitive to the magnetic field will be placed in the service cavern 50 m from the solenoid, where the stray field is sufficiently low.

The high granularity and acceptance of the FCC-hh reference detector will result in about 250 TB/s of data for calorimetry and the muon system, about 10 times more than the ATLAS and CMS HL-LHC scenarios. There is no doubt that it will be possible to digitise and read this data volume at the full bunch-crossing rate for these detector systems. The question remains whether the data rate of almost 2500 TB/s from the tracker can also be read out at the full bunch-crossing rate or whether calorimeter, muon and possible coarse tracker information need to be used for a first-level trigger decision, reducing the tracker readout rate to the few MHz level, without the loss of important physics. Even if the optical link technology for full tracker readout were available and affordable, sufficient radiation hardness of devices and infrastructure constraints from power and cooling services are prohibitive with current technology, calling for R&D on low-power radiation-hard optical links. 

Benchmarks physics

The potential of FCC-hh in the realms of precision Higgs and electroweak physics, high mass reach and dark-matter searches offers an unprecedented opportunity to address fundamental unknowns about our universe. The performance requirements for the FCC-hh baseline detector have been defined through a set of benchmark physics processes, selected among the key ingredients of the physics programme. The detector’s increased acceptance compared to the LHC detectors, and the higher energy of FCC-hh collisions, will allow physicists to uniquely improve the precision of measurements of Higgs-boson properties for a whole spectrum of production and decay processes complementary to those accessible at the FCC-ee. This includes measurements of rare processes such as Higgs pair-production, which provides a direct measure of the Higgs self-coupling – a crucial parameter for understanding the stability of the vacuum and the nature of the electroweak phase transition in the early universe – with a precision of 3 to 7% (see “Higgs self-coupling” figure).

Moreover, thanks to the extremely large Higgs-production rates, FCC-hh offers the potential to measure rare decay modes in a novel boosted kinematic regime well beyond what is currently studied at the LHC. These include the decay to second-generation fermions, muons, which can be measured to a precision of 1%. The Higgs branching fraction to invisible states can be probed to a value of 10^–4, allowing the parameter space for dark matter to be further constrained. The much higher centre-of-mass energy of FCC-hh, meanwhile, significantly extends the mass reach for discovering new particles. The potential for detecting heavy resonances decaying into di-muons and di-electrons extends to 40 TeV, while for coloured resonances like excited quarks the reach extends to 45 TeV, thus extending the current limit by almost an order of magnitude. In the context of supersymmetry, FCC-hh will be capable of probing stop squarks with masses up to 10 TeV, also well beyond the reach of the LHC.

In terms of dark-matter searches, FCC-hh has immense potential – particularly for probing scenarios of weakly interacting massive particles such as higgsinos and winos (see “Dark matters” figure). Electroweak multiplets are typically elusive, especially in hadron collisions, due to their weak interactions and large masses (needed to explain the relic abundance of dark matter in our universe). Their nearly degenerate mass spectrum produces an elusive final state in the form of so-called “disappearing tracks”. Thanks to the dense coverage of the FCC-hh detector tracking system, a general-purpose FCC-hh experiment could detect these particle decays directly, covering the full mass range expected for this type of dark matter. 

A detector at a 100 TeV hadron collider is clearly a challenging project. But detailed studies have shown that it should be possible to build a detector that can fully exploit the physics potential of such a machine, provided we invest in the necessary detector R&D. Experience with the Phase-II upgrades of the LHC detectors for the HL-LHC, developments for further exploitation of the LHC and detector R&D for future Higgs factories will be important stepping stones in this endeavour.

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On 13 and 14 March CERN hosted an international workshop on atom interferometry and the prospects for future large-scale experiments employing this quantum-sensing technique. The workshop had some 300 registered participants, of whom about half participated in person. As outlined in a keynote introductory colloquium by Mark Kasevich (Stanford), one of the pioneers of the field, this quantum sensing technology holds great promise for making ultra-sensitive measurements in fundamental physics. Like light interferometry, atom interferometry involves measuring interference patterns, but between atomic wave packets rather than light waves. Interactions between coherent waves of ultralight bosonic dark matter and Standard Model particles could induce an observable shift in the interference phase, as could the passage of gravitational waves.

Atom interferometry is a well-established concept that can provide exceptionally high sensitivity, e.g., to inertial/gravitational effects. Experimental designs take advantage of features used by state-of-the-art atomic clocks in combination with established techniques for building inertial sensors. This makes atom interferometry an ideal candidate to hunt for physics beyond the Standard Model such as waves of ultralight bosonic dark matter, or to measure gravitational waves in a frequency range around 1 Hz that is inaccessible to laser interference experiments on Earth, such as LIGO, Virgo and KAGRA, or the upcoming space-borne experiment LISA. As discussed during the workshop, measurements of gravitational waves in this frequency range could reveal mergers of black holes with masses intermediate between those accessible to laser interferometers, casting light on the formation of the supermassive black holes known to inhabit the centres of galaxies. Atom interferometer experiments can also explore the limits of quantum mechanics and its interface with gravity, for example by measuring a gravitational analogue of the Aharonov-Bohm effect.

A deep shaft at Point 4 of the LHC is a promising location for an atom interferometer with a vertical baseline of over 100 m

Although the potential of atom interferometers for fundamental scientific measurements was the principal focus of the meeting, it was also emphasised that technologies based on the same principles also have wide-ranging practical applications. These include gravimetry, geodesy, navigation, time-keeping and Earth observation from space, providing, for example, a novel and sensitive technique for monitoring the effects of climate change through measurements of the Earth’s gravitational field.

Several large atom interferometers with a length of 10m already exist, for example at Stanford University, or are planned, for example in Hanover (VLBAI), Wuhan and at Oxford University (AION). However, many of the proposed physics measurements require next-generation setups with a length of 100m, and such experiments are under construction at Fermilab (MAGIS), in France (MIGA) and in China (ZAIGA). The Atomic Interferometric Observatory and Network (AION) collaboration is evaluating possible sites in the UK and at CERN. In this context, a recent conceptual feasibility study supported by the CERN Physics Beyond Colliders study group concluded that a deep shaft at Point 4 of the LHC is a promising location for an atom interferometer with a vertical baseline of over 100 m. The March workshop provided a forum for discussing such projects, their current status, future plans and prospective sensitivities.

Looking further ahead, participants discussed the prospects for one or more km-scale atom interferometers, which would provide the maximal sensitivity possible with a terrestrial experiment to search for ultralight dark matter and gravitational waves. It was agreed that the global community interested in such experiments would work together towards establishing an informal proto-collaboration that could develop the science case for such facilities, provide a forum for exchanging ideas how to develop the necessary technological advances and develop a roadmap for their realisation.

A highlight of the workshop was a poster session that provided an opportunity for 30 early-career researchers to present their ideas and current work on projects exploiting the quantum properties of cold atoms and related topics. The liveliness of this session showed how this interdisciplinary field at the boundaries between atomic physics, particle physics, astrophysics and cosmology is inspiring the next generation of researchers. These researchers may form the core of the team that will lead atom interferometers to their full potential.

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Faced with the no-show of phenomena beyond the Standard Model at the high mass and energy scales explored so far by the LHC, it has recently become a much considered possibility that new physics hides “in plain sight”, namely at mass scales that can be very easily accessed but at very small coupling strengths. If this were the case, then high-intensity experiments have an advantage: thanks to the large number of events that can be generated, even the most feeble couplings corresponding to the rarest processes can be accessible.

Such a high-intensity experiment is NA62 at CERN’s North Area. Designed to measure the ultra-rare kaon decay K → πνν, it has also released several results probing the existence of weakly coupled processes that could become visible in its apparatus, a prominent example being the decay of a kaon into a pion and an axion. But there is also an unusual way in which NA62 can probe this kind of physics using a configuration that was not foreseen when the experiment was planned, for which the first result was recently reported. 

During normal NA62 operations, bunches of 400 GeV protons from the SPS are fired onto a beryllium target to generate secondary mesons from which, using an achromat, only particles with a fixed momentum and charge are selected. These particles (among them kaons) are then propagated along a series of magnets and finally arrive at the detector 100 m downstream. In a series of studies starting in 2015, however, NA62 collaborators with the help of phenomenologists began to explore physics models that could be tested if the target was removed and protons were fired directly into a “dump” that can be arranged by moving the achromat collimators. They concluded that various processes exist in which new MeV-scale particles such as dark photons could be produced and detected from their decays into di-lepton final states. The challenge is to keep the muon-induced background under control, which cannot be easily understood from simulations alone. 

A breakthrough came in 2018 when beam physicists in the North Area understood how the beamline magnets could be operated in such a way as to vastly reduce the background of both muons and hadrons. Instead of using the two pairs of dipoles as a beam achromat for momentum selection, the currents in the second pair are set to induce additional muon sweeping. The scheme was verified during a 2021 run lasting 10 days, during which 1.4 × 10¹⁷ protons were collected on the beam dump. The first analysis of this rapidly collected dataset – a search for dark photons decaying to a di-muon final state – has now been performed.

Hypothesised to mediate a new gauge force, dark photons, A′, could couple to the Standard Model via mixing with ordinary photons. In the modified NA62 set-up, dark photons could be produced either via bremsstrahlung or decays of secondary mesons, the mechanisms differing in their cross-sections and distributions of the momenta and angles of the A′. No sign of A′ → μ⁺μ^– was found, excluding a region of parameter space for dark-photon masses between 215 and 550 MeV at 90% confidence. A preliminary result for a search for A′ → e⁺e^– was also presented at the Rencontres de Moriond in March.

“This result is a milestone,” explains analysis leader Tommaso Spadaro of LNF Frascati. “It proves the capability of NA62 for studying physics in the beam-dump configuration and paves the way for upcoming analyses checking other final states.” 

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The CMS collaboration has been relentlessly searching for physics beyond the Standard Model (SM) since the start of the LHC. One of the most appealing new theories is supersymmetry or SUSY – a novel fermion-boson symmetry that gives rise to new particles, “naturally” leads to a Higgs boson almost as light as the W and Z bosons, and provides candidate particles for dark matter (DM).

By the end of LHC Run 2, in 2018, CMS had accumulated a high-quality data sample of proton–proton (pp) collisions at an energy of 13 TeV, corresponding to an integrated luminosity of 137 fb^–1. With such a large data set, it was possible to search for the production of strongly interacting SUSY particles, i.e. the partners of gluons (gluinos) and quarks (squarks), as well as for SUSY partners of the W and Z bosons (electroweakinos: winos and binos), of the Higgs boson (higgsinos), and of the leptons (sleptons). The cross sections for the direct production of SUSY electroweak particles are several orders of magnitude lower than those for gluino and squark pair production. However, if the partners of gluons and quarks are heavier than a few TeV, it could be that the SUSY electro­weak sector is the only one accessible at the LHC. In the minimal SUSY extension of the SM, electroweakinos and higgsinos mix to form six mass eigenstates: two charged (charginos) and four neutral (neutralinos). The lightest neutralino is often considered to be the lightest SUSY particle (LSP) and a DM candidate.

CMS has recently reported results, based on the full Run 2 dataset, from searches for the electroweak production of sleptons, charginos and neutralinos. Decays of these particles to the LSP are expected to produce leptons, or Z, W and Higgs bosons. The Z and W bosons subsequently decay to leptons or quarks, while the Higgs boson primarily decays to b quarks. All final states have been explored with complementary channels to enhance the sensitivity to a wide range of electroweak SUSY mass hypotheses. These cover very compressed mass spectra, where the mass difference between the LSP and its parent particles is small (leading to low-momentum particles in the final state) as well as uncompressed scenarios that would instead produce highly boosted Z, W and Higgs bosons. None of the searches showed event counts that significantly deviate from the SM predictions.

CMS maximised the output of the Run 2 dataset, providing its legacy reference on electroweak SUSY searches

The next step was to statistically combine the results of mutually exclusive search channels to set the strongest possible constraints with the Run 2 dataset and interpret the results of searches in different final states under unique SUSY-model hypotheses. For the first time, fully leptonic, semi-leptonic and fully hadronic final states from six different CMS searches were combined to explore models that differ depending on whether the next-to-lightest supersymmetric partner (NLSP) is “wino-like” or “higgsino-like”, as shown in the left and right panels of figure 1, respectively. The former are now excluded up to NLSP masses of 875 GeV, extending the constraints obtained from individual searches by up to 100 GeV, while the latter are excluded up to NLSP masses of 810 GeV.

With this effort, CMS maximised the output of the Run 2 dataset, providing its legacy reference on electroweak SUSY searches. While the same data are still being used to search for new physics in yet uncovered corners of the accessible phase-space, CMS is planning to extend its reach in the upcoming years, profiting from the extension of the data set collected during LHC Run 3 at an unprecedented centre-of-mass energy of 13.6 TeV.

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Imagine now the vast network of paths opened by ideas, such as emission theory, that led to no fruition despite their originality. Was pursuing these useful, or a waste of resources? Scientists would answer that the spirit of basic research is precisely to follow those paths with unknown destinations; it’s how humanity reached the level of knowledge that sustains modern life. As particle physicists, as long as the aim is to answer nature’s outstanding mysteries, the path is worth following. The Higgs-boson discovery is the latest triumph of this approach and, as for the quantum revolution, we are still working hard to make sense of it. 

Particle discoveries are milestones in the history of our field, but they signify something more profound: the realisation of a new principle in nature. Naively, it may seem that the Higgs discovery marked the end of our quest to understand the TeV scale. The opposite is true. The behaviour of the Higgs boson, in the form it was initially proposed, does not make sense at a quantum level. As a fundamental scalar, it experiences quantum effects that grow with their energy, doggedly pushing its mass towards the Planck scale. The Higgs discovery solidified the idea that gauge symmetries could be hidden, spontaneously broken by the vacuum. But it did not provide an explanation of how this mechanism makes sense with a fundamental scalar sensitive to mysterious phenomena such as quantum gravity. 

Now comes the hard part. From the plethora of ideas proposed during the past decades to make sense of the Higgs boson – supersymmetry being the most prominent – most physicists predicted that it would have an entourage of companion particles with electroweak or even strong couplings. Arguments of naturalness, that these companions should be close-by to prevent troublesome fine-tunings of nature, led to the expectation that discoveries would follow or even precede that of the Higgs. Ten years on, this wish has not been fulfilled. Instead, we are faced with a cold reality that can lead us to sway between attitudes of nihilism and hubris, especially when it comes to the question of whether particle physics has a future beyond the Higgs. Although these extremes do not apply to everyone, they are understandable reactions to viewing our field next to those with more immediate applications, or to the personal disappointment of a lifelong career devoted to ideas that were not chosen by nature. 

Such despondence is not useful. Remember that the no-lose theorem we enjoyed when planning the LHC, i.e. the certainty that we would find something new, Higgs boson or not, at the TeV scale, was an exception to the rules of basic research. Currently, there is no no-lose theorem for the LHC, or for any future collider. But this is precisely the inherent premise of any exploration worth doing. After the incredible success we have had, we need to refocus and unify our discourse. We face the uncertainty of searching in the dark, with the hope that we will initiate the path to a breakthrough, still aware of the small likelihood that this actually happens. 

The no-lose theorem we enjoyed when planning the LHC was an exception to the rules of basic research

Those hopes are shared by wider society, which understands the importance of exploring big questions. From searching for exoplanets that may support life to understanding the human mind, few people assume these paths will lead to immediate results. The challenge for our field is to work out a coherent message that can enthuse people. Without straying far from collider physics, we could notice that there is a different type of conversation going on in the search for dark matter. Here, there is no no-lose theorem either, and despite the current exclusion of most vanilla scenarios, there is excitement and cohesion, which are effectively communicated. As for our critics, they should be openly confronted and viewed as an opportunity to build stronger arguments.

We have powerful arguments to keep delving into the smallest scales, with the unknown nature of dark matter, neutrinos and the matter–antimatter asymmetry the most well-known examples. As a field, we need to renew the excitement that led us where we are, from the shock of watching alpha particles bounce back from a thin gold sheet, to building a colossus like the LHC. We should be outspoken about our ambition to know the true face of nature and the profound ideas we explore, and embrace the new path that the Higgs discovery has opened. 

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The triennial workshop “Physics of fundamental Symmetries and Interactions – PSI2022” took place for the sixth time at the Paul Scherrer Institut (PSI) in Switzerland from 17 to 22 October, bringing the worldwide fundamental symmetries community together. More than 190 participants including some 70 young scientists welcomed the close communication of an in-person meeting built around 35 invited and 25 contributed talks.

A central goal of the meeting series is to deepen relations between disciplines and scientists. This year, exceptionally, participants connected with the FIPs workshop at CERN on the second day of the conference, due to the common topics discussed.

With PSI’s leading high-intensity muon and pion beams, many topics in muon physics and lepton-flavour violation were highlighted. These covered rare muon decays (μ → e + γ, μ → 3e) and muon conversion (μ → e), muonic atoms and proton structure, and muon capture. Presentations covered complementary experimental efforts at J-PARC, Fermilab and PSI. The status of the muon g-2 measurement was reviewed from an experimental and theoretical perspective, where lattice-QCD calculations from 2021 and 2022 have intensified discussions around the tension with Standard Model expectations.

Fundamental physics using cold and ultracold neutrons was a second cornerstone of the programme. Searches for a neutron electric dipole moment (EDM) were discussed in contributions by collaborations from TRIUMF, LANL, SNS, ILL and PSI, complemented by presentations on searches for EDMs in atomic and molecular systems. Along with new results from neutron-beta-decay measurements, the puzzle of the neutron lifetime keeps the community busy, with improving “bottle” and “beam” measurements presently differing by more than 5 standard deviations. Several talks highlighted possible explanations via neutron oscillations into sterile or mirror states.

The current status of direct neutrino-mass measurements and future outlook down into the meV range was covered together with updates on searches for neutrinoless double-beta decay. An overview of the hunt for the unknown at the dark-matter frontier was presented together with new limits and plans from various searches. Ultraprecise atomic clocks were discussed allowing checks of general relativity and the Standard Model, and for searches beyond established theories. The final session covered the latest results from antiproton and antihydrogen experiments at CERN, demonstrating the outstanding precision achieved in CPT tests with these probes. The workshop was a great success and participants look forward to reconvening at PSI2025.

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So far, the experimental effort has been driven by theoretical arguments that favoured the existence of new particles with relatively large couplings to the Standard Model (SM) and masses commensurate the mass of the Higgs boson. Searching for these particles has been one of the main goals of the physics programme of the LHC. However, several beyond-the-SM theories predict the existence of light (sub-GeV) particles, which interact very weakly with the SM fields. Such feebly interacting particles (FIPs) can provide elegant explanations to several unresolved problems in modern physics. Furthermore, searching for them requires specific and distinct techniques, creating new experimental challenges along with innovative theoretical efforts.

FIPs are currently one of the most debated and discussed topics in fundamental physics and were recommended by the 2020 update of the European strategy for particle physics as a compelling field to explore in the next decade. The FIPs 2022 workshop held at CERN from 17 to 21 October was the second in a series dedicated to the physics of FIPs, attracted 320 experts from collider, beam-dump and fixed-target experiments, as well as from the astroparticle, cosmology, axion and dark-matter communities gathered to discuss the progress in experimental searches and new developments in underlying theoretical models.

The main goal of the workshop was to create a base for a multi-disciplinary and interconnected approach. The breadth of open questions in particle physics and their deep interconnection requires a diversified research programme with different experimental approaches and techniques, together with a strong and focused theoretical involvement. In particular, FIPs 2022, which is strongly linked with the Physics Beyond Colliders initiative at CERN, aimed at shaping the FIPs programme in Europe. Topics under discussion include the impact that FIPs might have in stellar evolution, Λ_CDM cosmological-model parameters, indirect dark-matter detection, neutrino physics, gravitational-wave physics and AMO (atoms-molecular-optical) physics. This is in addition to searches currently performed at colliders and extracted beam lines worldwide.

The main sessions were organised around three main themes: light dark matter in particle and astroparticle physics and cosmology; ultra-light FIPs and their connection with cosmology and astrophysics; and heavy neutral leptons and their connection with neutrino physics. In addition, young researchers in the field presented and discussed their work in the “new ideas” sessions.

FIPs 2022 aimed not only to explore new answers to the unresolved questions in fundamental physics, but to analyse the technical challenges and necessary infrastructure and collaborative networks required to answer them. Indeed, no single experiment or laboratory would be able by itself to cover the large parameter space in terms of masses and couplings that FIPs models suggest. Synergy and complementarity among a great variety of experimental facilities are therefore paramount, calling for a deep collaboration across many laboratories and cross-fertilisation among different communities and experimental techniques. We believe that a network of interconnected laboratories can become a sustainable, flexible and efficient way of addressing the particle physics questions in the next millennium.

The next appointment for the community is the retreat/school “FIPs in the ALPs” to be held in Les Houches from 15 to 19 May 2023, to be followed by the next edition of the FIPs workshop at CERN in autumn 2024.

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The Physics Beyond Colliders (PBC) study was launched in 2016 to explore the opportunities offered by CERN’s unique accelerator and experimental-area complex to address some of the outstanding questions in particle physics through experiments that are complementary to the high-energy frontier. Following the recommendations of the 2020 update of the European strategy for particle physics, the CERN directorate renewed the mandate of the PBC study, continuing it as a long-term activity.

The fourth PBC annual workshop took place at CERN from 7 to 9 November 2022. The aim was to review the status of the studies, with a focus on the programmes under consideration for the start of operations after Long Shutdown 3 (LS3), scheduled for 2026–2029.

The North Area (NA) at CERN, where experiments are driven by beams from the Super Proton Synchrotron (SPS), is at the heart of many present and proposed explorations for physics beyond the Standard Model. The NA includes an underground cavern (ECN3), which can host unique high-energy/high-intensity proton beams. Several proposals for experiments have been made, all of which require higher intensity proton beams than are currently available. It is therefore timely to identify the synergies and implications of a future ECN3 high-intensity programme on the otherwise ongoing NA technical consolidation programme. 

The following proposals are being considered within the PBC study group:

• HIKE (High Intensity Kaon Experiment) is a proposed expansion of the current NA62 programme to study extremely rare decays of charged kaons and, in a second phase, those of neutral kaons. This would be complemented by searches for visible decays of feebly interacting particles (FIPs) that could emerge on-axis from the dump of an intense proton beam within a thick absorber that would contain all other known particles, except muons and neutrinos;

• SHADOWS (Search for Hidden And Dark Objects With the SPS) would search for visible FIP decays off-axis and could run in parallel to HIKE when operated in beam-dump mode. The proposed detector is compact and employs existing technologies to meet the challenges of reducing the muon background;

• SHiP (Search for Hidden Particles) would allow a full investigation of hidden sectors in the GeV mass range. Comprehensive design studies for SHiP and the Beam Dump Facility (BDF) in a dedicated experimental area were published in preparation for the European strategy update. During 2021, an analysis of alternative locations using existing infrastructure at CERN revealed ECN3 to be the most promising option;

• Finally, TauFV (Tau Flavour Violation) would conduct searches for lepton-flavour violating tau-lepton decays.

The HIKE, SHADOWS and BDF/SHiP collaborations have recently submitted letters of intent describing their proposals for experiments in ECN3. The technical feasibility of the experiments, their physics potential and implications for the NA consolidation are being evaluated in view of a possible decision by the beginning of 2023. A review of the experimental programme in the proposed high-intensity  facility will take place during 2023, in parallel with a detailed comparison of the sensitivity to FIPs in a worldwide context.

A vibrant programme

The NA could also host a vibrant ion-physics programme after LS3, with NA60++ aiming to measure the caloric curve of the strong-force phase transition with lead–ion beams, and NA61++ proposing to explore the onset of the deconfined nuclear medium, extending the scan in the momentum/ion space with collisions of lighter ion beams. The conceptual implementation of such schemes in the accelerators and experimental area is being studied and the results, together with the analysis of the physics potential, are expected during 2023.

The search for long-lived particles with dedicated experiments and the exploration of fixed-target physics is also open at the LHC. The proposed forward-physics facility, located in a cavern that could be built at a distance of 600 m along the beam direction from LHC Interaction Point 1, would take advantage of the large flux of high-energy particles produced in the very forward direction in LHC collisions. It is proposed to host a comprehensive set of detectors (FASER2, FASERν2, AdvSND, FORMOSA, FLArE) to explore a broad range of new physics and to study the highest energy neutrinos produced by accelerators. A conceptual design report of the facility, including detector design, background analysis and mitigation measures, civil engineering and integration studies is in preparation. Small prototypes of the MATHUSLA, ANUBIS and CODEX-b detectors aiming at the search for long-lived particles at large angles from LHC collisions are also being built for installation during the current LHC run.

The North Area at CERN is at the heart of many present and proposed explorations for physics beyond the Standard Model

A gas-storage cell (SMOG2) was installed in front of the LHCb experiment during the last LHC long shutdown, opening the way to high-precision fixed-target measurements at the LHC. The storage cell enhances the density of the gas and therefore the rate of the collisions by up to two orders of magnitude as compared to the previous internal gas target. SMOG2 has been successfully commissioned with neon gas, demonstrating that it can be operated in parallel to LHCb. Future developments include the injection of different types of gases and a polarised gas target to explore nucleon spin-physics at the LHC.

Crystal clear

Fixed-target experiments are also being developed that would extract protons from LHC beams by channelling the beam halo with a bent crystal.  The extracted protons would impinge on a target and be used for measurements of proton structure functions (“single crystal setup”) or estimation of the magnetic and electric dipole moments of short-lived heavy baryons (“double crystal setup”). In the latter case, the measurement would be based on the baryon spin precession in the strong electric field of a second bent crystal installed immediately downstream from the baryon-production proton target. A proof-of-principle experiment of the double-crystal setup is being designed for installation in the LHC to determine the channelling efficiency for long crystals at TeV energies, as well as to demonstrate the control and management of the secondary halo and validate the estimate of the achievable luminosity.

The technology know-how at CERN can also benefit non-accelerator experiments

The technology know-how and experience available at CERN can also benefit non-accelerator experiments such as the Atom Interferometer Observatory and Network (AION), proposed to be installed in one of the shafts at Point 4 of the LHC for mid-frequency gravitational-wave detection and ultra-light dark-matter searches, as well as the development of superconducting cavities for the Relic Axion Detector Experimental Setup (RADES) and for the heterodyne detection of axion-like particles.

During the workshop, progress on the possible applications of a gamma factory at CERN, as well as the status of the design of a Charged-Particle EDM Prototype Ring and of the R&D for novel monitored or tagged neutrino beamlines, were also presented.

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In the Standard Model (SM) of particle physics, the only way the Higgs boson can decay without leaving any traces in the LHC detectors is through the four-neutrino decay, H → ZZ → 4ν, which has an expected branching fraction of only 0.1%. This very small value can be seen as a difficulty but is also an exciting opportunity. Indeed, several theories of physics beyond the SM predict considerably enhanced values for the branching fraction of invisible Higgs-boson decays. In one of the most interesting scenarios, the Higgs boson acts as a portal to the dark sector by decaying to a pair of dark matter (DM) particles. Measurements of the “Higgs to invisible” branching fraction are clearly among the most important tools available to the LHC experiments in their searches for direct evidence of DM particles.

The CMS collaboration recently reported the combined results of different searches for invisible Higgs-boson decays, using data collected at 7, 8 and 13 TeV centre-of-mass energies. To find such a rare signal among the overwhelming background produced by SM processes, the study considers events in most Higgs-boson production modes: via vector boson (W or Z) fusion, via gluon fusion and in association with a top quark–antiquark pair or a vector boson. In particular, the analysis looked at hadronically decaying vector bosons or top quark–antiquark pairs. A typical signature for invisible Higgs-boson decays is a large missing energy in the detector, so that the missing transverse energy plays a crucial role in the analysis. No significant signal has been seen, so a new and stricter upper limit is set on the probability that the Higgs boson decays to invisible particles: 15% at 95% confidence level.

This result has been interpreted in the context of Higgs-portal models, which introduce a dark Higgs sector and consider several dark Higgs-boson masses. The extracted upper limits on the spin-independent DM-nucleon scattering cross section, shown in figure 1 for a range of DM mass points, have better sensitivities than those of direct searches over the 1–100 GeV range of DM masses. Once the Run 3 data will be added to the analysis, much stricter limits will be reached or, if we are lucky, evidence for DM production at the LHC will be seen.

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The conference programme began with a warm welcome from Eberhard Widmann (Austrian Academy of Sciences) who was delighted to resume the SSP series, the last one held in Aachen in spring 2018. As proposed by the International Advisory Committee, the scientific programme this year focused more on fundamental symmetries and interactions in theory and laboratory experiments compared to previous editions and included topics such as dark matter and cosmology.  51 invited and contributed talks, as well as 17 posters were presented, highlighting scientific achievements worldwide.

These included topics on searches for lepton-flavour violation and symmetries in heavy quark decays at BELLE in Japan, BESIII in Beijing, muon-decay experiments at the Paul Scherrer Institute, and the first direct test of T and CPT symmetries in Φ decays at DAΦNE in Frascati. Prospects to discover physics beyond the Standard Model, such as the g-2 measurement at Fermilab, or at high-energy colliders were also presented, as well as searches for the electric dipole moments (EDM) of the neutron, deuteron, muon and in atoms and molecules. Double β-decay experiments, sterile-neutrino searches and flavour oscillations were also discussed. Results and upper limits on CPT tests with antihydrogen, muonium and positronium were reported.

The meeting ended with presentations on advanced instrumentation and on upcoming future facilities at PSI, DESY, Mainz university and J-PARC. Many participants from regions such as China attended the conference online. Discussions on various subjects followed during the poster session, where master and PhD students presented their work and results. Stefan Paul (TU Munich) gave a public lecture in the picturesque Festsaal of the Austrian Academy of Sciences about the shortest length scales that humankind has explored so far and how laboratory experiments test theoretical models describing the beginning of the universe.

SSP2022 was a successful and enjoyable conference, which created many fruitful and at times lively discussions in the field of symmetries in subatomic physics. The many contributions together with the social events around the conference programme provided an inspiring environment for animated discussions. SSP2022 benefited from being a relatively small-scale conference and the natural lightness it brings when meeting new colleagues and carrying out in-depth conversations on physics topics that we are passionate about.

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Involving around 1500 participants, 17 parallel sessions, 900 talks and 250 posters, ICHEP2022 (which took place in Bologna from 6 to 13 July) was a remarkable week of physics, technology and praxis. The energy and enthusiasm among the more than 1200 delegates who were able to attend in person was palpable. As the largest gathering of the community since the beginning of the pandemic – buoyed by the start of LHC Run 3 and the 10th anniversary of the Higgs-boson discovery – ICHEP2022 served as a powerful reminder of the importance of non-digital interactions.

Roberto Tenchini’s (INFN Pisa) heroic conference summary began with a reminder: it is 10 years since ICHEP included a session titled “Standard Model”, the theory being so successful that it now permeates most sessions. As an example, he highlighted cross-section predictions tested over 14 orders of magnitude at the LHC. Building on the Higgs@10 symposium at CERN on 4 July, the immense progress in understanding the properties and interactions of the Higgs boson (including legacy results with full Run 2 statistics in two papers by ATLAS and CMS published in Nature on 4 July) was centre stage. CERN Director-General Fabiola Gianotti gave a sweeping tour of the path to discovery and emphasised the connections between the Higgs boson and profound structural problems in the SM. Many speakers highlighted the concomitant role of the Higgs boson in exploring new physics, dashing notions that future precision measurements are “business as usual”. Chiara Mariotti (INFN Torino) pointed out that only 3% of the total Higgs data expected at the LHC has been analysed so far.

Hot topics

Another hot electroweak topic was CDF’s recent measurement of the mass of the W boson, as physicists try to understand what could cause it to lie so far from its prediction and from previous measurements. Andrea Rizzi (Pisa) confirmed that CMS is working hard on a W-mass analysis that will bring crucial information, on a time-scale to be decided. Patience is king with such a complex analysis, he said: “we are really trying to do the measurement the way we want to do it.”

CMS presented a total of 85 parallel talks and 28 posters, including new searches related to b-anomalies with taus, and the most precise measurement of B_s → μ⁺μ^–. Among new results presented by ATLAS in 71 parallel talks and 59 posters were the observation of a four charm–quark state consistent with one seen by LHCb, joint-polarisation measurements of the W and Z bosons, and measurements of the total proton–proton cross section and the ratio of the real vs imaginary parts of the elastic-scattering amplitude. ATLAS and CMS also updated participants on many searches for new particles, in particular leptoquarks. Among highlights were searches by ATLAS for events with displaced vertices, which could be caused by long-lived particles, and by CMS for resonances decaying to Higgs bosons and pairs of either photons or b quarks, which show interesting excesses. “Se son rose fioriranno!” said Tenchini. 

The sigmas are rather higher for exotic hadrons. LHCb presented the discovery of a new strange pentaquark (with a minimum quark content ccuds) and two tetraquarks (one corresponding to the first doubly charged open-charm tetraquark with csud), taking the number of hadrons discovered at the LHC so far to well over 60, and introducing a new exotic-hadron naming scheme for “particle zoo 2.0” (Exotic hadrons brought into order by LHCb). LHCb also reported the first evidence for direct CP violation in the charm system (LHCb digs deeper in CP-violating charm decays) and a new precise measurement of the CKM angle γ. Vladimir Gligorov (LPNHE) described how, in addition to the flavour factories LHCb and Belle II, experiments including ATLAS, CMS, BESIII, NA62 and KOTO will be crucial to enable the next level of understanding in quark mixing. Despite no significant new results having been presented, the status of tests of lepton flavour universality (LFU) in B decays by LHCb generated lively discussions, while Toshinori Mori (Tokyo) described exciting prospects for LFU tests in charged-lepton flavour experiments, in particular MEG-II, which has just started operations at PSI, and the upcoming Mu2e and MUonE experiments.

ICHEP2022 served as a powerful reminder of the importance of non-digital interactions

Moving to leptons that are known to mix, neutrinos continue to play very important roles in understanding the smallest and largest scales, said Takaaki Kajita (Tokyo) via a link from the IUPAP Centennial Symposium taking place in parallel at ICTP Trieste. Status reports on DUNE, Hyper-K, JUNO, KM3NeT and SNB showed how these detectors will help constrain the still poorly-known PNMS matrix that describes leptonic mixing, while new results from NOvA and STEREO further reveal anomalous behaviour. Among the major open questions in neutrino physics summed-up by theorist Joachim Kopp (Mainz and CERN) were: how do neutrinos interact? What explains the oscillation anomalies? And how do supernova neutrinos oscillate?

Several plenary presentations showcased the increasing complementarity with astroparticle physics and cosmology, with the release of the first-science images from the James Webb Space Telescope on 12 July adding spice (Webb opens new era in observational astrophysics). Multiband gravitational-wave astronomy across 12 or more orders of magnitude in frequency will bloom in the next decade, predicted Giovanni Andrea Prodi (Trento), while larger datasets and synchronisation of experiments offer a bright future in all messengers, said Gwenhael De Wasseige (Louvain): “We are just at the beginning of the story.” The first results from the Lux–Zeplin experiment were presented, setting the tightest limits on spin-independent WIMP–nucleon cross-sections for WIMP masses above 9 GeV (CERN Courier September/October 2022 p13), while the increasingly crowded plot showing limits from direct searches for axions illustrate the vibrancy and shifting focus of dark-matter research. Indeed, among several sessions devoted to the exploration of high-energy QCD in heavy-ion, proton–lead and proton–proton collisions, Andrea Dainese (INFN Padova) described how the LHC is not only a collider of nuclei but an (anti-)nuclei factory relevant for dark-matter searches.

The unique ability of theorists to put numerous results and experiments in perspective was on full display. We should all renew the enthusiasm that built the LHC, and be a lot more outspoken about the profound ideas we explore, urged Veronica Sanz (Sussex); after all, she said, “we are searching for something that we know should be somewhere.” A timely talk by Gavin Salam (Oxford) summarised the latest understanding of QCD effects relevant to the muon g-2 and W-mass anomalies and also to future Higgs-boson measurements, concluding that, as we approach high precision, we should expect to be confronted by conceptual problems that we could, so far, ignore.

The unique ability of theorists to put numerous results and experiments in perspective was on full display

Accelerators (including a fast-paced summary of the HL-LHC niobium-tin magnet programme from Lucio Rossi), detectors (68 talks and posters revealing an increasingly holistic approach to detector design), computing (highlighting a period of rapid evolution thanks to optimisation, modernisation, machine-learning algorithms and increasing hardware diversity), industry, diversity and outreach were addressed in detail. A highly acclaimed outreach event in Bologna’s Piazza Maggiore on the evening of 12 July saw thousands of people listen to Fabiola Gianotti, Guido Tonelli, Gian Giudice and Antonio Zoccoli discuss the implications of the Higgs-boson discovery.

Only the narrowest snapshot of proceedings is possible in such a short report. What was abundantly clear from ICHEP2022 is that, following the discovery of the Higgs boson and as-yet no new particles beyond the SM, the field is in a fascinating and challenging period where confusion is more than matched by confidence that new physics must exist. The strategic direction of the field was addressed in two wide-ranging round-table discussions where laboratory directors and senior physicists answered questions submitted by participants. Much discussion concerned future colliders, and addressed a perceived worry in some quarters that the field is entering a period of decline. For anyone following the presentations at ICHEP2022, nothing could be further from the truth.

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To explain the large matter–antimatter asymmetry in the universe, the laws of nature need to be asymmetric under a combination of charge-conjugation (C) and parity (P) transformations. The Standard Model (SM) provides a mechanism for CP violation, but it is insufficient to explain the observed baryon asymmetry in the universe. Thus, searching for new sources of CP violation is important.

The non-invariance of the fundamental forces under CP can lead to different rates between a particle and an antiparticle decay. The CP violation in the decay of a particle is quantified through the parameter A_CP, equal to the relative difference between the decay rate of the process and the decay rate of the CP-conjugated process. Three years ago, the LHCb collaboration reported the first observation of CP violation in the decay of charmed hadrons by measuring the difference between the time-integrated A_CP in D⁰ → K^–K⁺ and D⁰ → π^– π⁺ decays, ΔA_CP. This difference was found to lie at the upper end of the SM expectation, prompting renewed interest in the charm-physics community. There is now an ongoing effort to understand whether this signal is consistent with the SM or a sign of new physics.

At the 41^st ICHEP conference in Bologna on 7 July, the LHCb collaboration announced a new measurement of the individual time-integrated CP asymmetry in the D⁰ → K^–K⁺ decay using the data sample collected during LHC Run 2. The measured value, A_CP(K^–K⁺) = [6.8 ± 5.4 (stat) ± 1.6 (syst)] × 10^–4, is almost three times more precise than the previous LHCb determination obtained with Run 1 data. This was thanks not only to a larger data sample but also the inclusion of additional control channels D_s⁺ → K^– K⁺ π⁺ and D_s⁺ → K_s⁰ K⁺. Together with the previous control channels, D⁺ → K^– π⁺ π⁺ and D⁺ → K_s⁰ π⁺, these decays allow the separation between tiny signals of CP asymmetries from the much larger bias due to the asymmetric meson production and instrumental effects.

The combination of the measured values with the previously obtained ones of A_CP(K^–K⁺) and ΔA_CP by LHCb allowed the determination of the direct CP asymmetries in the D⁰ → π^– π⁺ and D⁰ → K^– K⁺ decays: [23.2 ± 6.1] × 10^–4 and [7.7 ± 5.7] × 10^–4, respectively, with correlated uncertainties (ρ = 0.88). This is the first evidence of direct CP violation in an individual charm–hadron decay (D⁰ → π^– π⁺), with a significance of 3.8σ.

The sum of the two direct asymmetries, which is expected to be equal to 0 in the limit of s–d quark symmetry (called U-spin symmetry), is equal to [30.8 ± 11.4] × 10^–4. This corresponds to a departure from U-spin symmetry of 2.7σ. In addition, this result is essential to the theory community in the quest to clarify the theoretical picture of CP-violation in the charm system. Since the measurement is statistically limited, its precision will improve with the larger dataset collected during Run 3.

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Aside from the discovery of the Higgs boson, the absence of additional elementary-particle discoveries is the LHC’s main result so far. For many physicists, it is also the more surprising one. Such further discoveries are suggested by the properties of the Higgs boson, which are now established experimentally to a large extent. The Higgs boson’s low mass, despite its susceptibility to quantum corrections from heavy particles that should push it orders-of-magnitude higher, and its hierarchy of coupling strengths to fermions present extreme, “unnatural” values that so far lack an explanation. Therefore, searches for new physics at the TeV energy scale remain strongly motivated, irrespective of the no-show so far. 

Naturalness has triggered the development of many new-physics models, but the large extent of their parameter space allows them to evade exclusion again and again. Whereas the discoveries of the past decades, including that of the Higgs boson, were driven by precise quantitative predictions, the search for physics beyond the Standard Model (SM) simply requires more perseverance.

LHC Run 3 will bring long-awaited new insights to the question of naturalness with respect to Higgs physics, as well as to many other SM puzzles such as the nature of dark matter or the cosmological matter–antimatter asymmetry. With considerably more data and a slightly higher centre-of-mass energy than at Run 2, in addition to new triggers and improved event reconstruction and physics-analysis techniques, a significant increase in sensitivity compared to the current results will be achieved. Searches for new phenomena with Run 3 data will also benefit from a much improved definition of the physics targets, thanks to information gathered during Run 2 and the various anomalies observed at lower energies.

The story so far

During the past 12 years, a broad search programme has emerged at the LHC in parallel with precision measurements (see “Pushing the precision frontier”). Initially, the most favoured new-physics scenario was supersymmetry (SUSY), a new fermion–boson symmetry that gives rise to supersymmetric partners of SM particles and naturally leads to a light Higgs boson close to the masses of the W and Z bosons. SUSY is expected to produce events containing jets and missing transverse energy (MET), the study of which at Run 2 placed exclusion limits on gluino masses as high as 2.3 TeV. More challenging searches for stop quarks, with background processes up to a million times more frequent than the predicted signal, were also performed thanks to the excellent performance of the ATLAS and CMS detectors. Yet, no signs of stops have been found up to a mass of 1.3 TeV, excluding a sizeable fraction of the SUSY parameter space suggested by naturalness arguments. Further SUSY searches were performed, including those for only weakly interacting SUSY particles (“electroweakinos”), where the Run 2 data allowed the experiments to surpass the sensitivity achieved by LEP in some scenarios. Half a century since SUSY was first proposed, ATLAS and CMS have demonstrated that the simplest models containing TeV-scale sparticle masses are not realised in nature (see “Stop quarks and electroweakinos” figure).

In fact, a large number of new-physics searches during LHC Run 1 and Run 2 targeted models other than SUSY, many of which also address the question of naturalness. Signs of extra spatial dimensions have been searched for in “mono-jet” events containing a single energetic jet and large MET, which could be caused by excited gravitons propagating in a higher dimensional space. Searches for vector-like quarks, as suggested by models with a composite Higgs boson, covered numerous complex final states with decays into all of the heavier known elementary particles. In these and other searches, the Higgs boson has entered the experimental toolkit, for example via the identification of high-momentum Higgs-boson decays reconstructed as large-radius jets.

The Higgs sector itself has been the subject of new-physics searches. These target additional Higgs bosons that would arise from an extended Higgs sector and exotic decays of the known Higgs boson, for instance into weakly interacting massive particles (WIMPs), which are candidates for dark matter. Improvements in both theoretical and data-driven background determinations have also allowed searches for Higgs-boson decays into invisible particles, with the Run 2 dataset setting an upper limit of 10% on their rate.

Searches for dark matter also continued to be performed in traditional channels, for example via the mono-jet signature. To increase the accuracy of this search using the full Run 2 statistics, theorists contributed differential background predictions that go beyond the next-to-leading order in perturbation theory to achieve an unprecedented background uncertainty of only 3% at MET values above 1 TeV. The resulting constraints on WIMP dark matter are complementary to those achieved with ultrasensitive detectors deep underground as well as astroparticle experiments. The absence of dark-matter signals in such established search channels led to the development of new models that predict a number of relevant but previously unexplored signatures.

LHC Run 3 will allow searches to go significantly beyond the sensitivity achieved with the Run 2 data 

In several respects, searches for new physics at the LHC experiments have gone well beyond what was foreseen at the time of their design. “Scouting” data streams were introduced to store small-size event records suitable for di-jet and di-muon resonance searches such that recording rates could be increased by up to two orders of magnitude within the available bandwidth. Consequently, the mass reach of these searches was extended to lower values whereas previously this was impossible due to the high background rates at low masses. Long-lived particle searches also opened a new frontier, motivating proposals for new LHC detectors.

Overall, LHC Run 1 and Run 2 led to an enormous diversification of new-physics searches at the energy frontier by ATLAS and CMS, with complementary searches conducted by LHCb targeting lower invariant masses. The absence of new-physics signals despite the exploration of a multitude of signatures with unforeseen precision is a strong experimental result that feeds back to the phenomenology community to shape this programme further. While the analysis of Run 2 data is still ongoing, the experience gained so far in terms of experimental techniques and investigated signatures puts the experimental collaborations in a better position to search for new physics at Run 3.

Experimental improvements

LHC Run 3 will allow searches to go significantly beyond the sensitivity achieved with the Run 2 data. ATLAS and CMS are expected to collect datasets with an integrated luminosity of up to 300 fb^–1, adding to the 140 fb^–1 collected in Run 2. Taking into account the additional, smaller benefit provided by the increase in the centre-of-mass energy from 13 to 13.6 TeV, new-physics search sensitivities will generally increase by a factor of two in terms of cross sections. Additional gains in sensitivity will result from the exploration of new territory in several respects.

Already at the level of data acquisition, significant improvements will increase the sensitivity of searches. The CMS higher level trigger system has been reinforced using graphics processing units to increase the recording rate in the data scouting stream from 9 to 30 kHz. ATLAS has extended this technique to encompass more final states, including photons and b-jets. These techniques extend the sensitivity to hadronic resonances with low masses and weak coupling strengths to a domain that has never been probed before.

The particularly challenging searches for new long-lived particles will also benefit from experimental advances. ATLAS has improved the reconstruction of displaced tracks, reducing the amount of fake tracks by a factor of 20 at similar efficiencies compared to the current data analysis. New, dedicated triggers have been developed by ATLAS and CMS to identify electrons, muons and tau-leptons displaced from the primary interaction vertex. These trigger developments will allow the collection of signal candidate events at unprecedented rates, for example to test exotic Higgs-boson decays into long-lived particles with branching ratios far below the current experimental limits. 

Likewise, ongoing developments in machine learning will contribute to the Run 3 search programme. While Run 1 physics analyses used generic, simple algorithms to distinguish between hypotheses, in Run 2 more powerful approaches of deep learning were introduced. For Run 3 their development continues, using a multitude of different algorithms tailored to the needs of event reconstruction and physics analysis to increase the reach of new-physics searches further.

New signatures

The Run 3 data will also be scrutinised in view of final states that either have been proposed more recently or that require a particularly large dataset. Examples of the latter are searches for electroweakinos, which have a production cross-section at the LHC at least two orders of magnitude smaller than strongly interacting SUSY particles. First results based on Run 2 data surpassed the sensitivity of the LEP experiments, including tests of unconventional “R-parity violating” scenarios in which electroweakinos can decay into only SM particles. This results in complicated final states containing electrons, muons and many jets but relatively low MET. Here, the challenging background determination could only be achieved thanks to machine-learning techniques, which lay the ground for further searches for particularly rare and challenging SUSY signals at Run 3.

If R-parity is not a symmetry, SUSY does not provide a WIMP dark-matter candidate. Among alternative explanations of the nature of this substance, models with bound-state dark matter are gaining increasing attention. In this new approach, strong interactions similar to quantum chromodynamics determine the particle spectrum in a dark sector that includes stable dark-matter candidate particles such as dark pions. At the LHC, coupling between such dark-sector particles and known ones would result in “semi-visible” jets comprising both types of particle (traditional dark-matter searches at the LHC have avoided such events to reduce background contributions). With the Run 2 data, CMS has already provided the very first collider constraints on these dark sectors, and more results from both ATLAS and CMS will follow in this and other proposed dark-sector scenarios.

Multiple deviations from the SM observed at lower energies are starting to shape the search programme at the energy frontier. The long-standing anomaly in the magnetic moment of the muon has recently reached a significance of 4.2σ, motivating increased efforts in searching for possible causes. One is the pair-production of a supersymmetric partner of the muon, for which models fit the low-energy data if the mass of this “smuon” is below 1 TeV and hence within the reach of the LHC. Another is to look for vector-like leptons, which are suggested by consistent extensions of the SM apart from SUSY, using final states containing a large number of leptons.

Multiple deviations from the SM observed at lower energies are starting to shape the search programme at the energy frontier

Moreover, the anomalies in B-meson decays consistently reported by BaBar, Belle and LHCb (see “A flavour of Run 3 physics”) have a strong and growing impact on the Run 3 search programme. Explanations for these anomalies require new particles with TeV-scale masses to fit the size of the observed effects and a hierarchy of fermion couplings to fit the deviations from lepton-flavour universality. Intriguingly these two requirements happen to coincide with the two peculiarities of the Higgs boson. Particular attention is now given to leptoquark searches investigating several production and decay modes. ATLAS and CMS have already started to probe leptoquark models suggested by the B-meson anomalies using Run 2 data (see “Leptoquarks” figure). While the analysis of key channels is ongoing, Run 3 will allow the experiments to probe a large fraction of the relevant parameter space. Furthermore, consistent models of leptoquarks include more new particles, namely colour-charged and colour-neutral bosons, vector-like quarks and vector-like leptons. These predict a variety of new-physics signatures that will further shape the Run 3 search programme.

In summary, searches for new physics at Run 3 will bring significant gains in sensitivity beyond the benefit provided by the increased amount of data. In particular, potential explanations of the anomalies observed at lower energies will be tested. Assuming that these anomalies point to new physics, the relevant searches with Run 3 data have a good chance of finding the first deviations from the SM at the TeV energy scale. Such an outcome would be of the utmost importance for particle physics, strengthening the case for the proposed Future Circular Collider at CERN.

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Confronted with multiple questions about how nature works at the smallest scales, we exploit precise measurements of the Standard Model (SM) to seek possible answers. Those answers could further confirm the SM or give hints of new phenomena. As a hadron collider, the LHC was primarily built as a discovery machine. After more than a decade of operation, however, it has surpassed expectations. Alongside the discovery of the Higgs boson and a broad programme of direct searches for new phenomena, ultra-precise measurements on a wide range of parameters have been carried out. These include particle masses, the width of the Z boson and the production cross-sections of various SM processes ranging over 10 orders of magnitude (see “Cross sections” figure); the latter are connected to a multitude of measurements including differential distributions and particle properties.

An example that is unique to the LHC is the measurement of the Higgs-boson mass, which was determined to a precision of 0.12% by CMS in 2019. Also of vital importance are the strengths of the Higgs-boson couplings to other known particles (see “Coupling strengths” figure). According to the SM, these couplings must be proportional to a particle’s mass. Nicely following the SM expectation, every coupling in this plot is extracted using various measurements of the Higgs-boson production and decay channels. Besides the remarkable agreement with the SM, the plot shows the result of the Higgs-boson decay to muons, which is challenging to measure because of the muon’s small mass. 

The LHC-experiment collaborations are currently concluding their Run 2 measurements using proton-collision data recorded at 13 TeV while getting ready for the Run 3 startup. From several notable achievements with the Run 2 data, one can point to the measurement of a fundamental parameter of the SM, the mass of the W boson with a precision of 0.02% by ATLAS and of 0.04% in the forward region by LHCb (see “W mass” figure). Precision measurements of the W-boson mass are crucial for testing the consistency of the SM, as radiative corrections connect it with the masses of the top quark and the Higgs boson. A future combination of the LHCb result with similar measurements from ATLAS and CMS can reduce the significant uncertainty of parton distribution functions on this parameter. Although the particle masses are crucial elements of the SM, it is not always possible to determine them directly. In the case of quarks, except for the heaviest top quark, their immediate hadronisation makes the properties of a bare quark inaccessible. Observed for the first time by ALICE, the QCD “dead cone” (an angular region of suppressed gluon emissions surrounding a heavy quark that is proportional to the quark’s mass) in charmed jets may be a possible way to ultimately access the heavy-quark mass directly. 

The coupling structure of the SM, especially between heavy particles, is another key aspect that is being pinned down by ATLAS and CMS. In 2017 the experiments marked an important milestone in this regard with the observation of WW scattering – a first step in a diverse programme of measurements of vector boson scattering (VBS), in which vector bosons emitted from each of the incoming quarks interact with one other (see “Critical physics” image). As VBS processes are sensitive to the self-interaction of four gauge bosons as well as to the exchange of a virtual Higgs boson, they remain a central part of the LHC physics programme during Run 3 and beyond, where the additional data will become a decisive factor.

Run 3 preparations 

The LHC is about to start a new endeavour at an unprecedented energy (13.6 TeV as opposed to 13 TeV) and with an instantaneous luminosity on average 1.5 times higher than in Run 2. In addition to higher statistics, the larger energy reach of Run 3 provides a unique opportunity to study unexplored territories in the kinematic phase space of particles. Prime targets are regions where the discovery of possible new phenomena is mainly awaiting additional data, and those where the insufficient size of the data sample is the main limiting factor on the precision.

A major challenge ahead is the increased number of additional interactions within the same or nearby bunch crossings, called pileup. The large rate of interactions puts strain on different parts of the detectors as well as their trigger systems. Relying on cutting-edge technologies, experiments at the LHC have performed extensive upgrades in several subsystems, hardware and software to cope with the associated complexities and exploit the full potential of the data. In some cases, this has involved the installation of new detectors or an entire renewal, or extension, of existing subdetectors. Examples are the New Small Wheel (NSW) muon detector in ATLAS and the muon gas electron multiplier (GEM) detectors in CMS. These gas-based detectors, which are designed in view of the High-Luminosity LHC (HL-LHC) and will be partially operational during Run 3, are installed in the endcap area of the experiments where a significant increase is expected in the particle flux. The improved muon momentum resolution they bring also plays a critical role in the trigger systems by keeping the rate low. 

It is now proven that with advanced analysis strategies we can surpass the expectations from projection studies

In the ALICE experiment, among other important upgrades, the inner tracker system has faced a complete renewal of the silicon-based detectors for enhanced low-momentum vertexing and tracking capabilities. At LHCb, in addition to new front-end electronics for higher-rate triggering and readout, the ring-imaging Cherenkov detector has been upgraded to deal with the large-pileup environment, while a brand new vertex locator and tracking system will allow the reconstruction of charged particles. In parallel to the hardware, the LHC experiments have accomplished a substantial upgrade in software and computing, including the implementation of fast readout systems and the use of state-of-the-art graphics processing units.

Physics ahead 

The series of upgrades undertaken during Long Shutdown 2 will enable the experiments to pursue a rich physics programme during Run 3 and to get ready for Run 4 at the HL-LHC. The preparation also involves Monte Carlo event generation at the new centre-of-mass energy, full simulation of collision events in the new detectors, and designing new methods with modern tools to identify particles and analyse the data. The additional data of Run 3, together with innovative analysis techniques, will result in reduced uncertainties and therefore push the precision frontier forward. The experience from Run 2 is of great value in this regard. 

It is now proven that with advanced analysis strategies which make maximal use of the available data, we can surpass the expectations from projection studies. An example is the Higgs-boson decay to muons. Whereas early Run 3 projections suggested an uncertainty of about 20% with 300 fb^–1 of LHC data, in 2020 the CMS experiment achieved such precision using Run 2 data alone. In the latest projections, a further improvement of 30–35% is expected thanks to the advanced analysis strategies developed during Run 2. The projected uncertainties in Higgs-boson couplings to other SM particles, including vector bosons and third-generation leptons, are also expected to be reduced. The Higgs-boson interaction with the heaviest known particle, the top quark, is of particular interest as it may give insights into the existence and energy scale of new physics above 100 GeV. Besides the famous ttH process, simultaneous production of four top quarks is also very sensitive to the top quark’s Yukawa interaction with the Higgs boson. Exhibiting the heaviest SM final state, “four-top” is one of the rarest but most important processes. Following evidence reported by ATLAS in 2021, Run 3 data may fully establish its observation. 

Among rare processes that may shed light on electroweak symmetry breaking, one can point to the VBS production of longitudinally polarised W bosons. The longitudinal polarisation is a result of electroweak symmetry breaking through which vector bosons acquire mass from their interaction with the Brout–Englert–Higgs field. Given that the analysis of Run 2 data has reached the expected significance (about 1σ) of the HL-LHC with the same luminosity, we look forward to Run 3 to test the SM with more data and further channels.

Run 3 excitement

The excitement about LHC Run 3 is not restricted to rare phenomena and new discoveries. Well-established processes such as top-quark, W- and Z-boson production are pivotal for a firm understanding of the SM. The upcoming data will provide us with gigantic statistics that translates to a significantly higher precision on the measured properties of these particles in addition to various fundamental parameters of the SM. The latter include the mass of the top quark, the precise determination of which is a critical factor in the stability of vacuum. Early Run 3 projection studies predicted an uncertainty of 1.5 GeV on the top-quark mass. This has already been achieved in Run 2 using tt differential cross-section measurements, and will be further reduced with the upcoming Run 3 data.

The upcoming data will provide us with gigantic statistics that translate to significantly higher precision

Such levels of precision also provide invaluable feedback to the theory community, whose tremendous efforts in modelling and state-of-the-art calculations and simulations are the basis of our measurements. Thanks to the increasing sophistication and precision of SM calculations, any statistically significant deviation from theory can be an unambiguous sign of new physics. Therefore, precision measurements in Run 3 can act as a gateway to new discoveries. These include measurements of properties such as vector-boson polarisation, which are sensitive to new physics by construction, inclusive cross sections of VBS and other rare processes, and differential distributions where new phenomena can appear in the tails.

In October 2021, stable proton beams were circulated and collided at a centre-of-mass energy of 900 GeV in the LHC for the first time since 2018. While preparing for the start up in May this year, the experiments made use of these data for a special period of commissioning to ensure their readiness to collect data in Run 3. The successful outcome of the commissioning brought further enthusiasm and motivation to the LHC-experiment collaborations, who very much look forward to executing their far-reaching Run 3 physics plans.

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A powerful way to discover new particles expected from physics beyond the SM is to search for high-mass dijet or multi-jet resonances, as these are expected to have large production cross-sections at hadron colliders. These searches look for a pair of jets originating from a pair of quarks or gluons, coming from the decay of a new particle “X” and appearing as a narrow bump in the invariant dijet-mass distribution. Since the energy scale of new physics is most likely high, it is natural to expect these new particles to be massive.

CMS and ATLAS have performed a suite of single-dijet-resonance searches. The next step is to look for new identical-mass particles “X” that are produced in pairs, with (resonant mode) or without (non-resonant mode) a new intermediate heavier particle “Y” being produced and decaying to pairs of X. Such processes would yield two dijet resonances and four jets in the final state: the dijet mass would correspond to particle X and the four-jet mass to particle Y.

The CMS experiment was also motivated to search for Y→ XX → 4-jets by a candidate event recorded in 2017, which was presented by a previous CMS search for dijet resonances (figure 1). This spectacular event has four high transverse-momentum jets, forming two dijet pairs each with an invariant mass of 1.9 TeV and a four-jet invariant mass of 8 TeV.

Presented on 14 March at Rencontres de Moriond, the CMS collaboration has found another very similar event in a new search optimised for this specific Y→ XX → 4-jets topology. These events could originate from quantum-chromodynamics processes, but those are expected to be extremely rare (figure 2). The two candidate events are clearly visible at high masses, distinct from all the rest. Also shown (magenta) is a simulation of a possible new-physics signal – a diquark decaying to vector-like quarks – with a four-jet mass of 8.4 TeV and a dijet mass of 2.1 TeV, which very nicely describes these two candidates.

The hypothesis that these events originate from the SM at the observed X and Y masses is disfavoured with a local significance of 3.9σ. Taking into account the full range of possible X and Y mass values, the compatibility of the observation with the SM expectation leads to a global significance of 1.6σ.

The upcoming LHC Run 3 and future High-Luminosity LHC runs will be crucial in telling us whether these events are statistical fluctuations of the SM expectation, or the first signs of yet another groundbreaking discovery at LHC.

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In the 1960s, the creators of the Standard Model made a smart choice: while all charged fermions came in pairs, with left-handed and right-handed components, neutrinos were only left-handed. This “handicap” of neutrinos allowed physicists to accommodate in the most economical way important features of the experimental data at that time. First, such left-handed-only neutrinos are naturally massless, and second, individual leptonic flavours (electron, muon and tau) are automatically conserved.

It is now well established that neutrinos have masses and that the neutrino flavours mix with each other, in similarity with quarks. If this were known 55 years ago, Weinberg’s seminal 1967 work “A Model of Leptons” would be different: in addition to the left-handed neutrinos, it would very likely also contain their right-handed counterparts. The structure of the Standard Model (SM) dictates that these new states, if they exist, are the only singlets with respect to weak-isospin and hyper-charge gauge symmetry and thus do not participate directly in electroweak interactions (see “On the other hand” figure). This makes right-handed neutrinos (also referred to as sterile neutrinos, singlet fermions or heavy neutral leptons) very special: unlike charged quarks and leptons, which get their masses from the Yukawa interaction with the Brout–Englert–Higgs field, the masses of right-handed neutrinos depend on an additional parameter – the Majorana mass – which is not related to the vacuum expectation value and which results in the violation of lepton-number conservation. As such, right-handed neutrinos are also sometimes referred to as Majorana leptons or Majorana fermions.

Leaving aside the possible signals of eV-scale neutrino states reported in recent years, all established experimental signatures of neutrino oscillations can be explained by the SM with the addition of two heavy-neutral leptons (HNLs). If there were only one HNL, then two out of three SM neutrinos would be massless; with two HNLs, only one of the SM neutrinos is massless – this is not excluded experimentally. Any larger number of HNLs is also possible.

The simplest way to extend the SM in the neutrino sector is to add several HNLs and no other new particles. Already this class of theories is very rich (different numbers of HNLs and different values of their masses and couplings imply very different phenomenology), and contains several different scenarios explaining not only the observed masses and flavour oscillations of the SM neutrinos but also other phenomena that are not accommodated by the SM. The scenario in which the Majorana masses of right-handed neutrinos are much higher than the electroweak scale is known as the “type I see-saw model”, first put forward in the late 1970s. The theory with three right-handed neutrinos (the same as the number of generations in the SM) with their masses below the electroweak scale is called the neutrino minimal standard model (νMSM), and was proposed in the mid-2000s.

Would these new particles be useful for anything else besides neutrino physics? The answer is yes. The first, lightest HNL N₁ may serve as a dark-matter particle, whereas the other two HNLs N_2,3 not only “give” masses to active neutrinos but can also lead to the matter–antimatter asymmetry of the universe. In other words, the SM extended by just three HNLs could solve the key outstanding observational problems of the SM, provided the masses and couplings of the HNLs are chosen in a specific domain. 

The leptonic extension of the SM by right-handed neutrinos is quite similar to the gradual adaptation of electroweak theory to experimental data during the past 50 years. While the bosonic sector of the electroweak model remains intact from 1967, with the discoveries of the W and Z bosons in 1983 and the Higgs boson in 2012, the fermionic sector evolved from one to two to three generations, revealing the remarkable symmetry between quarks and leptons. It took about 20 years to find all the quarks and leptons of the third generation. How much time it will take to discover HNLs, if they indeed exist, depends crucially on their masses.

The value of the Majorana mass, and therefore the physical mass of an HNL, is arbitrary from a theoretical point of view and cannot be found from neutrino-oscillation experiments. The famous see-saw formula that relates the observed masses of the active neutrinos to the Majorana masses of HNLs has a degeneracy: change the Yukawa couplings of HNLs to neutrinos by a factor x and the HNL masses by a factor x², and the active neutrino masses and the physics of their oscillations remain intact. The scale of HNL masses thus can be any number from a fraction of an eV to 10¹⁵ GeV (see “Options abound” figure). Moreover, there could be several HNLs with very different masses. Indeed, even in the SM the masses of charged fermions, though they share a similar origin, differ by almost six orders of magnitude. 

Motivated by the value of the active neutrino masses, the HNL could be light, with masses of the order of 1 eV. Alternatively, similar to the known quarks and charged leptons, they could be somewhere around the GeV or Fermi scale. Or they could be close to the grand unification scale, 10¹⁵ GeV, where the strong and electromagnetic interactions are thought to be unified. These possibilities have different theoretical and experimental consequences. 

The case of the light sterile neutrino

The see-saw formula tells us that if the mass of HNLs is around 1 eV, their Yukawa couplings should be of the order of 10^–12. Such light sterile neutrinos can be potentially observed in neutrino experiments, as they can be involved in the oscillations together with the three active neutrino species. Several experiments – including LSND, GALLEX, SAGE, MiniBooNE and BEST – have reported anomalies in neutrino-oscillation data (the so-called short-baseline, gallium and reactor anomalies) that could be interpreted as a signal for the existence of light sterile neutrinos. However, it looks difficult, if not impossible, to reconcile the existence of these states with recent negative results of other experiments such as MINOS+, MicroBooNE and IceCUBE, accounting for additional constraints coming from β-decay, neutrinoless double-β decay and cosmology.

The parameters of light sterile neutrinos required to explain the experimental anomalies are in strong tension with the cosmological bounds (see “Cosmological bounds” figure). For example, their mixing angle with the ordinary neutrinos should be sufficiently large that these states would have been produced abundantly in the early universe, affecting its expansion rate during Big Bang nucleosynthesis and thus changing the abundances of the light elements. In addition, light sterile neutrinos would affect the formation of structure. Having been created in the hot early universe with relativistic velocities, they would have escaped from forming structures until they cooled down in much later epochs. This so-called “hot dark matter” scenario would mean that the smallest structures, which form first, and the larger ones, which require much more time to develop, would experience different amounts of dark matter. Moreover, the presence of such particles would affect baryon acoustic oscillations and therefore impact the value of the Hubble constant deduced from them.

Besides tensions between the experiments and cosmological bounds, light sterile neutrinos do not provide any solution to the outstanding problems of the SM. They cannot be dark-matter particles because they are too light, nor can they produce the baryon asymmetry of the universe as their Yukawa couplings are too small to give any substantial contribution to lepton-number violation at the temperatures (> 160 GeV) at which the anomalous electroweak processes with baryon non-conservation have a chance to convert a lepton asymmetry into a baryon asymmetry. 

Three Fermi-scale heavy neutral leptons

Another possible scale for HNL masses is around a GeV, plus or minus a few orders of magnitude. Right-handed neutrinos with such masses do not interfere with active-neutrino oscillations because the corresponding length over which these oscillations may occur is far too small. As only two active-neutrino mass differences are fixed by neutrino-oscillation experiments, it is sufficient to have two HNLs N_2,3 with appropriate Yukawa couplings to active neutrinos: to get the correct neutrino masses, they should not be smaller than ~10^–8 (compared to the electron Yukawa coupling of ~10^–6). These two HNLs may produce the baryon asymmetry of the universe, as we explain later, whereas the lightest singlet fermion, N₁, may interact with neutrinos much more weakly and thus can be a dark-matter particle (although unstable, its lifetime can greatly exceed the age of the universe). 

Three main considerations determine the possible range of masses and couplings of the dark-matter sterile neutrino (see “Dark-matter constraints” figure). The first is cosmological production. If N₁ interact too strongly, they would be overproduced in ℓ⁺ℓ^– → N₁ν reactions and make the abundance of dark matter larger than what is inferred by observations, providing an upper limit on their interaction strength. Conversely, the requirement to produce enough dark matter results in a lower bound on the mixing angle that depends on the conditions in the early universe during the epoch of N₁ production. Moreover, the lower bound completely disappears if N₁ can also be produced at very high temperatures by interactions related to gravity or at the end of cosmological inflation. The second consideration is X-ray data. Radiative N₁ → γν decays produce a narrow line that can be detected by X-ray telescopes such as XMM–Newton or Chandra, resulting in an upper limit on the mixing angle between sterile and active neutrinos. While this upper limit depends on the uncertainties in the distribution of dark matter in the Milky Way and other nearby galaxies and clusters, as well as on the modelling of the diffuse X-ray background, it is possible to marginalise these to obtain very robust constraints. 

The third consideration for the sterile neutrino’s properties is structure formation. If N₁ is too light, a very large number-density of such particles is required to make an observed halo of a small galaxy. As HNLs are fermions, however, their number density cannot exceed that of a completely degenerate Fermi gas, placing a very robust lower bound on the N₁ mass. This bound can be further improved by taking into account that light dark-matter particles remain relativistic until late epochs and therefore suppress or erase density perturbations on small scales. As a result, they would affect the inner structure of the halos of the Milky Way and other galaxies, as well as the matter distribution in the intergalactic medium, in ways that can be observed via gravitational-lensed galaxies, gaps in the stellar streams in galaxies and the spectra of distant quasars. 

Neutrino experiments and robust conclusions from observational cosmology call for extensions of the SM

The upper limits on the interaction strength of sterile neutrinos fixes the overall scale of active neutrino masses in the νMSM. The dark-matter sterile neutrino effectively decouples from the see-saw formula, making the mass of one of the active neutrinos much smaller than the observed solar and atmospheric neutrino-mass differences and fixing the masses of the two other active neutrinos to approximately 0.009 eV and 0.05 eV (for the normal ordering) and to the near-degenerate value 0.05 eV for the inverted ordering.

HNLs at the GeV scale and beyond 

Our universe is baryon-asymmetric – it does not contain antimatter in amounts comparable with the matter. Though the SM satisfies all three “Sakharov conditions” necessary for baryon-asymmetry generation (baryon number non-conservation, C and CP-violation, and departure from thermal equilibrium), it cannot explain the observed baryon asymmetry. The Kobayashi–Maskawa CP-violation is too small to produce any substantial effects, and departures from thermal equilibrium are tiny at the temperatures at which the anomalous fermion-number non-conserving processes are active. This is not the case with two GeV-scale HNLs: these particles are not in thermal equilibrium for temperatures above a few tens of GeV, and CP violation in their interactions with leptons can be large. As a result, a lepton asymmetry is produced, which is converted into baryon asymmetry by the baryon-number violating reactions of the SM.

The requirement to get baryon asymmetry in the νMSM puts stringent constraints on the masses and coupling of HNLs (see “Baryon-asymmetry constraints” figure). The mixing angle of these particles cannot be too large, otherwise they equilibrate and erase the baryon asymmetry, and it cannot be below a certain value because it would make the active neutrino masses too small. We know that their mass should be larger than that of the pion, otherwise their decays in the early universe would break the success of Big Bang nucleosynthesis. In addition, the masses of two HNLs should be close to each other so as to enhance CP-violating effects. Interestingly, the HNLs with these properties are within the experimental reach of existing and future accelerators, as we shall see.

The final possible choice of HNL masses is associated with the grand unification scale, ~10¹⁵ GeV. To get the correct neutrino masses, the Yukawa couplings of a pair of these superheavy particles should be of the order of one, in which case the baryon asymmetry of the universe can be produced via thermal leptogenesis and anomalous baryon- and lepton-number non-conservation at high temperatures. The third HNL, if interacting extremely weakly, may play the role of a dark-matter particle, as described previously. Another possibility is that there are three superheavy HNLs and one light one, to play the role of dark matter. This model, as well as that with HNL masses of the order of the electroweak scale, may therefore solve the most pressing problems of the SM. The only trouble is that we will never be able to test it experimentally, since the masses of N_2,3 are beyond the reach of any current or future experiment.

Experimental opportunities

It is very difficult to detect HNLs experimentally. Indeed, if the masses of these particles are within the reach of current and planned accelerators, they must interact orders of magnitude more weakly than the ordinary weak interactions. As for the dark-matter sterile neutrino, the most promising route is indirect detection with X-ray space telescopes. The new X-ray spectrometer XRISM, which is planned to be launched this year, has great potential to unambiguously detect a signal from dark-matter decay. Like many astrophysical observatories, however, it will not be able to determine the particle origin of this signal. Thus, complementary laboratory searches are needed. One experimental proposal that claims a sufficient sensitivity to enter into the cosmologically relevant region is HUNTER, based on radio­active atom trapping and high-resolution decay-product spectrometry. Sterile neutrinos with masses of around a keV can also show up as a kink in the β-decay spectrum of radioactive nuclei, as discussed by the ambitious PTOLEMY proposal. The current generation of experiments that study β-decay spectra – KATRIN and Troitsk nu-mass – also perform searches for keV HNLs, but they are sensitive to significantly larger mixing angles than required for a dark-matter particle. Extending the KATRIN experiment with a multi-pixel silicon drift detector, TRISTAN, will significantly improve the sensitivity here.

The most promising perspectives to find N_2,3 responsible for neutrino masses and baryogenesis are experiments at the intensity frontier. For HNL masses below 5 GeV (the beauty threshold) the best strategy is to direct proton beams at a target to create K, D or B mesons that decay producing HNLs, and then to search for HNL decays through “nothing → leptons and hadrons” processes in a near detector. This strategy was used in the previous PS191 experiment at CERN’s Proton Synchrotron (PS), NOMAD, BEBC and CHARM at the Super Proton Synchrotron (SPS) and NuTeV at Fermilab. There are several proposals for future experiments along these lines. The proposed SHiP experiment at the SPS Beam Dump Facility has the best potential as it can potentially cover almost all parameter space down to the lowest bound on coupling constants coming from neutrino masses. The SHiP collaboration has already performed detailed studies and beam tests, and the experiment is under consideration by the SPS and PS experiments committee. A smaller-scale proposal, SHADOWS, covers part of the interesting parameter space.

The search for HNLs can be carried out at the near detectors of DUNE at Fermilab and T2K/T2HK in Japan, which are due to come online later this decade. The LHC experiments ATLAS, CMS, LHCb, FASER and SND, as well as the proposed CODEX-b facility, can also be used, albeit with fewer chances to enter deeply into the cosmologically interesting part of the HNL parameter space. The decays of HNLs can also be searched for at future huge detectors such as MATHUSLA. And, going to larger HNL masses, breakthroughs can be made at the proposed Future Circular Collider FCC-ee, studying the processes Z → νN with a displaced vertex (DV) corresponding to the subsequent decay of N to available channels (see “Electron coupling” figure).

Conclusions

Neutrino experiments and robust conclusions from observational cosmology call for extensions of the SM. But the situation is very different from that in the period preceding the discovery of the Higgs boson, where the consistency of the SM together with other experimental results allowed us to firmly conclude that either the Higgs boson had to be discovered at the LHC, or new physics beyond the SM must show up. Although we know for sure that the SM is incomplete, we do not have a firm prediction about where to search for new particles nor what their masses, spins, interaction types and strengths are.

Experimental guidance and historical experience suggest that the SM should be extended in the fermion sector, and the completion of the SM with three Majorana fermions solves the main observational problems of the SM at once. If this extension of the SM is correct, the only new particles to be discovered in the future are three Majorana fermions. They have remained undetected so far because of their extremely weak interactions with the rest of the world.

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The successful restart of Linac4 on 9 February marked the start of the final countdown to LHC Run 3. Inaugurated in May 2017 after two decades of design and construction, Linac4 was connected to the next link in the accelerator chain, the Proton Synchrotron Booster (PSB), in 2019 at the beginning of Long Shutdown 2 and operated for physics last year. The 86 m-long accelerator now replaces the long-serving Linac2 as the source of all proton beams for CERN experiments.

On 14 February, H^– ions accelerated to 160 MeV in Linac4 were sent to the PSB, with beam commissioning and physics to start in ISOLDE on 7 and 28 March. Beams will be sent to the PS on 28 February, to serve, after set-up, experiments in the East Area, the Antiproton Decelerator and n_TOF. The SPS will be commissioned with beam during the week beginning 7 March, after which beams will be supplied to the AWAKE facility and to the North Area experiments, where physics operations are due to begin on 25 April.

Meanwhile, preparations for some of the protons’ final destination, the LHC, are under way. Powering tests and magnet training in the last of the LHC’s eight sectors are scheduled to start in the week of 28 February and to last for four weeks, after which the TI12 and TI18 transfer tunnels and the LHC experiments will be closed and machine checkout will begin. LHC beam commissioning with 450 GeV protons is scheduled to start on 11 April, with collisions at 450 GeV per beam expected around 10 May. Stable beams with collisions at 6.8 TeV per beam and nominal bunch population are scheduled for 15 June. An intensity ramp-up will follow, producing collisions with 1200 bunches per beam in the week beginning 18 July on the way to over double this number of bunches. High-energy proton-proton operations will continue for 3–4 months, before the start of a month-long run with heavy ions on 14 November. All dates are subject to change as the teams grapple with LHC operations at higher luminosities and energies than those during Run 2, following significant upgrade and consolidation work completed during LS2.

Among the highlights of Run 3 are the first runs of the neutrino experiments FASERν and SND@LHC

Among the highlights of Run 3 are the first runs of the neutrino experiments FASERν and SND@LHC, as well as the greater integrated luminosities and physics capabilities resulting from upgrades of the four main LHC experiments. A special request was made by LHCb for a SMOG2 proton-helium run in 2023 to measure the antiproton production rate and thus improve understanding of the cosmic antiproton excess reported by AMS-02. Ion runs with oxygen, including proton-oxygen and oxygen-oxygen, will commence in 2023 or 2024. The former is also long-awaited by the cosmic-ray community, to help improve models of high-energy air showers, while high-energy oxygen-oxygen collisions allow studies of the emergence of collective effects in small systems. High β* runs to maximise the interaction rate will be available for the forward experiments TOTEM and LHCf in late 2022 and early 2023.

On 28 January, CERN announced a change to the LHC schedule to allow necessary work for the High-Luminosity LHC (HL-LHC) both in the machine and in the ATLAS and CMS experiments. The new schedule foresees Long Shutdown 3 to start in 2026, one year later than in the previous schedule, and to last for three instead of 2.5 years. “Although the HL-LHC upgrade is not yet completed, a gradual intensity increase from 1.2 × 10¹¹ to 1.8 × 10¹¹ protons per bunch is foreseen for 2023,” says Rende Steerenberg, head of the operations group. “This promises exciting times and a huge amount of data for the experiments.”

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The 30^th International Symposium on Lepton Photon Interactions at High Energies, hosted online by the University of Manchester from 10 to 14 January, saw more than 500 physicists from around the world engaged in a broad science programme. The Lepton Photon series dates to the 1960s and takes place every two years. This was the first time the conference was meant to return to the UK in over 50 years, with its original August time slot moved to January due to Covid-19 restrictions. The agenda was stretched to improve accessibility in different time zones. Posters were presented via pre-recorded videos and three prizes were awarded following a public vote.

With 2022 marking the ten-year anniversary of the Higgs-boson discovery, it was appropriate that the conference kicked-off with an experimental Higgs-summary talk. Both the ATLAS and CMS collaborations showcased their latest high-precision measurements of Higgs-boson properties and searches for physics beyond the Standard Model using the Higgs boson as a portal. ATLAS presented a new combination of the Higgs total and differential cross-section measurements in the two-photon and four-lepton channels, while CMS shared the first full Run-2 search for resonant di-Higgs production in several multi-lepton final states.

The LHC experiments continue to demonstrate the power of hadron colliders to test the electroweak sector. Notable new results included the first observation of opposite-charge WWjj production at CMS, the first tri-boson (WWW) observation at ATLAS, and LHCb entering the game of W-boson mass measurements. A highlight of the talks covering QCD topics was a combined fit of the parton distribution function of the proton to differential cross-section measurements from ATLAS and HERA data. A wide range of new-physics searches were presented, including a dark-photon search from ATLAS with the full Run-2 data, and a CMS search for new scalars decaying into final states with Higgs-bosons.

In flavour physics, the pattern of anomalies in rare leptonic and semi-leptonic processes continues to intrigue. Highlights in this area included new tests of lepton universality from LHCb in Λ_b⁰ → Λ_c⁺ℓ^–? decays (ℓ=e, μ, τ) , where the decay involving a τ lepton was observed for the first time, and from Belle in Ω_?⁰→Ω⁻ℓ⁺? decays, where the ratio of the e-μ final-state branching ratios was found to be in agreement with the expectation of unity and where the μ decay had been measured for the first time. Similar studies of rare leptonic decays are now also taking place in the charm sector. The BESIII collaboration tested in one study the e-μ universality in a second decay mode and confirmed its agreement with the Standard Model. Participants also heard about the latest searches for the ultra-rare decay K→π?? from KOTO, searching for the neutral kaon decay mode, and from NA62, which now has a 3.4σ evidence for the charged kaon decay mode.

With the 2021 update on muon g-2 from Fermilab, and with the MEG-II, DeeMe and Mu3e experiments getting ready to search for muon-to-electron transitions, there is much excitement about charged-lepton physics. CP violation in beauty and charm remains a hot topic, with updates from LHCb, Belle and BES-III on D⁰ and B_s oscillations and the CKM angle γ. In all these areas, the theoretical community continues to push the boundaries to make improved predictions. Among other things, theorists presented the latest global fits of Wilson coefficients, and several welcome developments in lattice QCD. 

The highlights from the neutrino sector included the low-energy excess search by MicroBooNE and the observation of the CNO cycle of solar neutrinos by Borexino. The latest results from the long-baseline experiments – T2K and recently NovA– are starting to hint at large CP violating effects in neutrino oscillations.

A series of talks on dark-matter searches spanned collider experiments, direct detection and astrophysical signatures. Some interesting anomalies persist, such as the DAMA annual modulation and the XENON1T low-energy excess. These will be challenged by a suite of next-generation detectors, such as PANDAX-4T, XENONnT, LZ and DarkSide-20k.

The conference also included a rich programme of talks covering astrophysics with an emphasis on gravitational waves and multi-messenger astronomy. Hot-off-the-press was a combined search for spatial correlations between neutrinos and ultra-high energy cosmic rays, using data from ANTARES, IceCube, Auger and TA collaborations, with no sign yet of a connection.

As well as many new results from experiments in operation, the conference included sessions devoted to R&D in accelerators, detectors, software and computing, covering both collider and non-collider experiments. With many new facilities proposed in the medium and long terms, technological challenges, which include power consumption, data rates and radiation tolerance, are immense and demand significant efforts in harnessing promising avenues such as high-temperature superconductors, quantum sensors or specialised computer accelerators. Common to all areas is the need to train and retain highly skilled people to lead these efforts in future.

A firm part of the Lepton Photon plenary programme are discussions around diversity, inclusion and outreach. A lively panel discussion covered many aspects of the former two topics and ended with a key message to the whole community: be an ally and take an active stance in support of minorities. The conference ended with traditional reports from the IUPAP commission on particles and fields and from ICFA, followed by strategy updates from Snowmass and the African Strategy for Fundamental and Applied Physics. While Snowmass is an established process for regular updates of the US strategy for the field based on wide-spread community input both from the US and internationally, the African strategy is the first of its kind and is testament to the continent’s ambition and growing importance in physics research. The next conference will take place in Melbourne in July 2023.

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Back in the late 1970s and early 1980s when the LEP/LHC programme was first proposed, the W and Z bosons mediating the weak interactions had not yet been observed, the top quark was considered a possible discovery, and the Higgs boson was regarded as a distant speculation. Precise studies of the W and Z, which were discovered in 1983 at the SPS proton–antiproton collider at CERN, were key items in LEP’s physics programme along with direct searches for the top quark, the Higgs boson and possible unknown particles. Even though the LEP experiments did not reveal any new particles beyond the W and Z, the unprecedented precision of its measurements revealed indirect effects (via quantum fluctuations) of the top and the Higgs, thereby providing indirect evidence for the SM mechanism of electroweak symmetry breaking. When the top quark was discovered at the Tevatron proton–antiproton collider at Fermilab in 1995, and the Higgs boson at the LHC in 2012, their masses were within the ranges indicated by precision measurements made at lepton colliders. 

Nowadays, the hope is that the proposed FCC programme – comprising an electron–positron collider followed by a high-energy proton-proton collider in the same ~100 km tunnel – will repeat the LEP/LHC success story at an even higher level of precision and energy. The e⁺e^– FCC stage would reproduce the entire LEP sample of Z bosons within a couple of minutes, yielding around 5 × 10¹² Z bosons after four years of operation. In addition to allowing an incredibly accurate determination of the Z-boson’s properties, Z decays would also provide unprecedented samples of bottom quarks (1.5 × 10¹²) and tau leptons (3 × 10¹¹). Potential increases in the FCC-ee centre-of-mass-energy would also produce unparalleled numbers of W⁺W^– and top–antitop pairs, which are important for the global electroweak fit, close to their respective thresholds, as well as more Higgs bosons than promised by other proposed e⁺e^– Higgs factories.

Probing beyond the Standard Model

Analyses of FCC-ee data, combined with results from previous experiments at the LHC and elsewhere, would not only push our understanding of the SM to the next level but would also provide powerful indirect probes of possible physics beyond the SM, with sensitivities to masses an order of magnitude greater than those of the LHC. A possible subsequent proton–proton FCC stage (FCC-hh) operating at a centre-of-mass energy of at least 100 TeV would then provide unequalled opportunities to discover this new physics directly, just as the LHC made possible the discovery of the Higgs boson following the indirect hints from high-precision LEP data. Whereas the combination of LEP and the LHC explore the TeV scale both indirectly and directly, the combination of FCC-ee and FCC-hh will carry the search for new physics to 30 TeV and beyond. 

The e⁺e^– stage of FCC would reproduce the entire LEP sample of Z bosons within a couple of minutes

However, for this dream scenario to play out, at least one beyond-the-SM particle must exist within FCC’s discovery reach. While the existence of dark matter and neutrino masses already prove that the SM cannot be complete (and there is no shortage of theoretical ideas as to what extensions of the SM could account for them), these observations can be explained by new particles within a very wide mass range – possibly well beyond the reach of FCC-hh. Fortunately, intriguing hints for new physics in the flavour sector have accumulated in recent years that point towards beyond-the-SM physics that should be accessible to FCC.

B-decay anomalies

Within the SM, the charged leptons – electrons, muons and taus – all have very similar properties. They interact with the photon as well as the W and Z bosons in the same way, and differ only in their masses, which in the SM are represented as Yukawa couplings to the Higgs boson. It is therefore said that the SM (approximately) respects lepton-flavour universality (LFU), despite the seemingly large differences in charged-lepton lifetimes originating from phase-space effects. 

Flavour observables (i.e. processes resulting from rare transitions among the different generations of quarks and leptons), and observables measuring LFU in particular, are especially promising to test the SM because they are strongly suppressed in the SM and thus very sensitive to new physics. In recent years, a coherent pattern of anomalies, all pointing towards the violation of LFU, have emerged. Two classes of fundamental processes giving rise to decays of B mesons – b → sℓ⁺ℓ^– and b → cτν – show deviations from the SM predictions. 

In the flavour-changing neutral-current process b → sℓ⁺ℓ^–, a heavy bottom quark undergoes a transition to a strange quark and a pair of oppositely-charged leptons, which could be either electrons or muons. The ratios R_K = Br(B → Kμ⁺μ^–)/Br(B → Ke⁺e^–) and R_K* = Br(B → K^*μ⁺μ^–)/Br(B → K^*e⁺e^–), measured most precisely by the LHCb collaboration, are particularly interesting because their SM predictions are very clean. Since the muon and electron masses are negligible compared to the B-meson mass, the ratio of muon to electron decays should be close to unity according to the SM. However, intriguingly, LHCb has observed values significantly lower than one, and recently reported first evidence for LFU violation in R_K . These hints of new physics are supported by measurements of the angular observable P₅′ in B⁰ → K^*0μ⁺μ^– decays and the rate of B_s → φμ⁺μ^– decays. Importantly, all these observations can potentially be explained by the same new-physics interactions and are consistent with all other available measurements of processes involving b → sℓ⁺ℓ^– transitions. In fact, global fits of all available b → sℓ⁺ℓ^–  data find a preference for new physics compared to the SM hypothesis which reeks of a possible discovery.

The second class of anomalies involves the charged-current process b → cτν, which is already mediated at tree level in the SM. The corresponding B-meson decays therefore have much higher probabilities to occur and thus larger branching ratios. However, the non-negligible tau mass leads to imperfect cancellations of the form factors in the ratio to electron or muon final states, and thus the resulting SM prediction is not as precise as those for R_K and R_K*. The most prominent examples of observables involving b → cτν transitions are the ratios R_D = Br(B → Dτν_τ)/Br(B → Dℓν_ℓ) and R_D* = Br(B → D*τ ν_τ)/Br(B → D*τν_ℓ). Here, the measurements of Belle, BaBar and LHCb consistently point above the SM predictions, resulting in a combined tension of 3σ. Importantly, as these processes happen quite frequently in the SM, a significant new-physics effect would be required to account for the corresponding anomaly. 

With the FCC-ee capable of producing 1.5 × 10¹² b quarks, clearly the b anomalies could be further verified within a short period of running, assuming that LHCb, Belle II and possibly other experiments do confirm them. The large data sample would also allow physicists to study complementary modes that bear upon LFU but are more difficult for LHCb to measure, such as other “R” measurements involving neutral kaons. These measurements would be invaluable for pinning down the mechanism responsible for any violation of lepton universality.

Other possible anomalies

The B anomalies are just one exciting avenue that a “Tera-Z factory” like FCC-ee could explore further. The anomalous magnetic moment of the muon, a_μ, can also be viewed as an exciting hint for new physics in the lepton sector. Predicted by the Dirac equation to have a value exactly equal to two, the physical value of the magnetic moment of the muon is slightly higher due to fluctuations at the quantum level. The very high precision of both the calculation and measurement therefore make it a powerful observable with which to search for new physics. A tension between the measured and predicted value of a_μ has persisted since Brookhaven published its final result in 2006, and was recently strengthened by the muon g-2 experiment at Fermilab, yielding an overall significance of 4.2σ when combined with the earlier Brookhaven data. 

Various models have been proposed to explain the g-2 anomaly. They include leptoquarks (scalar or vector particles that carry colour and couple directly to a quark and a lepton that arise in models with extended gauge groups) and supersymmetry. Such leptoquarks could have masses anywhere between the lower LHC limit of 1.5 TeV and about 10 TeV, thus being within the reach of FCC-hh, whereas a supersymmetric explanation would require a couple of new particles with masses of a few hundred GeV, possibly even within reach of FCC-ee. Importantly, any explanation involving heavy new particles would also lead to effects in Z → μ⁺μ^–, as both observables are sensitive to interactions with sizeable coupling strength to muons. FCC-ee’s large Z-boson sample could therefore reveal deviations from the SM predictions at the suggested level. Leptoquarks could also modify the SM prediction for H → μ⁺μ^– decay, which will be measured very accurately at FCC-hh (see “Anomalous correlations” figure).

CKM under scrutiny

As the Cabibbo–Kobayashi–Maskawa (CKM) matrix, which describes flavour violation in the quark sector, is unitary, the sum of the squares of the elements in each row and in each column must add up to unity. This unitarity relation can be used to check the consistency of different determinations of CKM elements (within the SM) and thus also to search for new physics. Interestingly, a deficit in the first-row unitarity relation exists at the 3σ level. This can be traced back to the fact that the value of the element V_ud, extracted from super-allowed beta decays, is not compatible with the value of V_us, determined from kaon and tau decays, given CKM unitarity. Interestingly, this deviation can also be interpreted as a sign of LFU violation, since beta decays involve electrons while the most precise determination of V_us comes from decays with final-state muons. 

Here, a new-physics effect at a relative sub-per-mille level compared to the SM would suffice to explain the anomaly. This could be achieved by a heavy new lepton or a massive gauge boson affecting the determination of the Fermi constant that parametrises the strength of the weak interactions. As the Fermi constant can also be determined from the global electroweak fit, for which Z decays are crucial inputs, FCC-ee would again be the perfect machine to investigate this anomaly, as it could improve the precision by a large factor (see “High precision” figure). Indeed, the Fermi constant may be determined directly to one part in 10⁵ from the enormous sample (> 10¹¹) of Z decays to tau leptons. 

For this dream scenario to play out, at least one beyond-the-SM particle must exist within FCC’s discovery reach

FCC-ee’s extraordinarily large dataset will also enable scrutiny of a long-standing anomaly in the forward-backward asymmetry of Z → bb– decays. The LEP measurement of ΔA_FB, which arises from the difference between the Z boson couplings to left- and right-handed chiral states with different strengths, lies 2–3σ below the SM prediction. Although not significant, this anomaly may also be linked to new physics entering in b → s transitions.

Finally, a possible difference in the decay asymmetries of B → D^*μν vs B → D^*eν was recently reported by an analy­sis of Belle data. As in the case of R_K, the SM prediction that the difference between the muon and the electron asymmetries should be zero is very clean and, like R_D and R_D*, this observable points towards new physics in b → c transitions and could be related via leptoquarks to g-2 of the muon. Once more, the great number of b quarks to be produced at FCC-ee, together with the clean environment of a lepton collider, would allow this observable to be determined with unprecedented accuracy.

Since all these anomalies point, to varying degrees, towards the existence of LFU-violating new physics, it raises the question of whether a common explanation exists? There are several particularly interesting possibilities, including leptoquarks, new scalars and fermions (as arise in supersymmetric extensions of the SM), new vector bosons (W′ and Z′) and new heavy fermions. In the overwhelming majority of such scenarios, a direct discovery of a new particle is possible at FCC-hh. For example, it could discover leptoquarks with masses up to 10 TeV and Z′ bosons with masses up to 40 TeV, covering most of the mass ranges expected in such models.

A return to the Z pole and beyond

The LEP programme was extremely successful in determining the mechanism of electroweak symmetry breaking, in particular by measuring the properties and decays of the Z boson very precisely from a 17 million-strong sample. This allowed for a prediction of a range for the Higgs mass within which it was later discovered at the LHC. The flavour anomalies could lead to a similar situation in the near future. In this case, the roughly 5 × 10¹² Z bosons that the FCC-ee is designed to collect would not only be able to test the effects of new particles in precision electroweak observables, but also, via Z decays into bottom quarks and tau leptons, provide a unique testing ground for flavour physics. As noted earlier, FCC-ee’s Z-pole run is also envisaged to be the first step in a broader electroweak programme encompassing large statistics at the WW and tt– thresholds, in addition to its key role as a precision Higgs factory. 

Looking much further ahead to the energy frontier, FCC-hh would be able, in the overwhelming number of scenarios motivated by the flavour anomalies, to directly discover a new particle. Furthermore, FCC-hh would allow for a precise determination of rare Higgs decays and the Higgs potential, probing new-physics effects related to this sector, such as leptoquark explanations of the anomalous magnetic moment of the muon.

Pending the outcome of the FCC feasibility study recommended by the 2020 update of the European strategy for particle physics, the hope that the LEP/LHC success story could be repeated by FCC-ee/FCC-hh is well justified. While FCC-ee could be used to indirectly pin down the parameters of the model(s) of new physics explaining the flavour anomalies via precision electroweak and flavour measurements, FCC-hh would be capable of searching for the predicted particles directly. 

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The neutron lifetime is key to a range of fields, not least astrophysics and cosmology, where it is used in the modeling of the synthesis of helium and heavier elements in the early universe. Its value, however, is uncertain. In recent years, discrepancies of up to 4σ between measurements of the neutron lifetime using different methods present a puzzle that particle physicists, nuclear physicists and cosmologists are increasingly eager to solve. 

A recent experiment with the UCNτ experiment at the Los Alamos Neutron Science Center, which resulted in the most constraining measurement of the lifetime to date, further strengthens the discrepancy. The latest result, achieved using the so called “bottle” method, results in a neutron lifetime of 877.75 ± 0.28 (stat) ^+0.22 _–0.16 (syst) s, whereas measurements using the “beam” method have consistently resulted in longer lifetimes (see figure). While the beam method determines the lifetime by measuring the decay products of the neutron, the bottle method instead stores cold, or thermalised, neutrons for a certain time before counting the remaining ones by direct detection. If not the result of some unknown systematic error, the discrepancy could be a sign of exotic physics whereby the longer lifetime in the beam method stems from an unmeasured second decay channel. 

Escape detection

Astrophysics brings a third, independent measurement into play based on the bombardment of galactic cosmic rays on planetary surfaces. This continual process liberates large numbers of high-energy neutrons, some of which escape into space while others approach thermal equilibrium with surface and atmospheric material, a proportion subsequently escaping into space where at some point they will decay. The neutron lifetime can therefore be inferred by counting the neutrons remaining at different distances from their production location, using detectors positioned hundreds to thousands of kilometres above the surface. As the escaped neutron flux depends on a planet’s particular elemental composition at depths corresponding to the neutron mean-free path (typically around 10 cm), neutron spectrometers have already been installed on several missions to explore planetary surface compositions.

A dedicated instrument on a future lunar mission could bring a crucial third independent tool to tackle the neutron lifetime puzzle

In 2020, using neutrons produced through interactions of cosmic rays with Venus and Mercury, a team from the Johns Hopkins Applied Physics Laboratory and Durham University demonstrated the feasibility of such a neutron-lifetime measurement. Now, using data from a lunar mission, the same team has provided the first results with uncertainties approaching those coming from lab-based experiments. Importantly, since it also relies on direct detection, the result from space should produce the same lifetime as the bottle experiments.

For this latest study, the researchers used data from NASA’s Lunar Prospector taken during several elliptical orbits around the moon in 1998. The orbiter contained two neutron detectors, one with a cadmium shield making it insensitive to slow or thermal neutrons, and one containing a tin shield that allows it to measure thermal as well as higher- energy neutrons. The difference between the two count rates then provides the thermal neutron flux. Combining this with the spacecraft position, the group deduced the thermal neutron flux for different positions and distances towards the Moon and fitted the data against a model that includes the production and propagation of thermal neutrons originating from interactions of cosmic rays with the lunar surface.

Surface studies

The highly detailed models account for neutron production from cosmic-ray interactions with the different elements of the lunar surface, and also for the varying composition of the surface in different regions. For the lifetime measurement, thermal neutrons were used due to their lower velocities (a few km/s), which makes their flux as a function of the distance to the surface (typically several 100 km) more sensitive to their lifetimes. The higher sensitivity comes at the cost of greater model complexity, however. For example, thermal neutrons cannot simply be modeled as traveling in a straight line, but are affected by the lunar gravity, meaning that they not only come directly from the surface but also enter the detector from the back as they perform elliptical orbits. 

The study found a lifetime of 887 ± 14 (stat) ⁺⁷_–3 (syst) s. The systematic error stems mainly from uncertainties in the surface composition and its variations as well as a lack of modeling of the temperature variation of the Moon’s surface, which affects the thermalisation process, and from uncertainties in the ephermides (location) of the spacecraft. In future dedicated missions, the latter two issues can be mitigated, while knowledge of the surface composition can be improved with additional studies. Indeed, the large statistical error arises from this being a non-dedicated mission where the small data sample used was not even part of the science data of the original mission. The results are therefore highly promising, as they show that a dedicated instrument on a future lunar mission would bring a crucial third independent tool to tackle the neutron lifetime puzzle.

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How has the discovery of a Standard Model-like Higgs boson changed your view of nature? 

The discovery of a Standard Model-like Higgs boson was a great triumph for renormalisable field theory, and really for simplicity. By the time the LHC was operating, attempts to make the Standard Model (SM) work without an elementary Higgs field – using a dynamical mechanism instead – had become rather convoluted. It turned out that, as far as one can judge from what we have learned so far, the original idea of an elementary Higgs particle was correct. This also means that nature takes advantage of all the possible building blocks of renormalisable field theory – fields of spin 0, 1/2 and 1 – and the flexibility that that allows. 

The other key fact is that the Higgs particle has appeared by itself, and without any sign of a mechanism that would account for the smallness of the energy scale of weak interactions compared to the much larger presumed energy scales of gravity, grand unification and cosmic inflation. From the perspective that my generation of particle physicists grew up with (and not only my generation, I would say), this is quite a shock. Of course, we lived through a somewhat similar shock a little over 20 years ago with the discovery that the expansion of the universe is accelerating – something that is most simply interpreted in terms of a very small but positive cosmological constant, the energy density of the vacuum. It seems that the ideas of naturalness that we grew up with are failing us in at least these two cases.

What about new approaches to the fine-tuning problem such as the relaxion or “Nnaturalness”?

Unfortunately, it has been very hard to find a conventional natural explanation of the dark energy and hierarchy problems. Reluctantly, I think we have to take seriously the anthropic alternative, according to which we live in a universe that has a “landscape”of possibilities, which are realised in different regions of space or maybe in different portions of the quantum mechanical wavefunction, and we inevitably live where we can. I have no idea if this interpretation is correct, but it provides a yardstick against which to measure other proposals. Twenty years ago, I used to find the anthropic interpretation of the universe upsetting, in part because of the difficulty it might present in understanding physics. Over the years I have mellowed. I suppose I reluctantly came to accept that the universe was not created for our convenience in understanding it.

Which experimental paths should physicists prioritise at this time?

It is extremely important to probe the twin mysteries of the cosmic acceleration and the smallness of the electroweak scale as thoroughly as possible, in order to determine whether we are interpreting the facts correctly and possibly to discover a new layer of structure. In the case of the cosmic acceleration, this means measuring as precisely as we can the parameter w (the ratio of pressure and energy), which equals –1 if the acceleration of the expansion is governed by a simple cosmological constant, but would be greater than –1 in most alternative models. In particle physics, we would like to probe for further structure as precisely as we can both indirectly, for example with precision studies of the Higgs particle, and hopefully directly by going to higher energies than are available at the LHC.

What might be lurking at energies beyond the LHC?

If it is eventually possible to go to higher energies, I can imagine several possible outcomes. It might become rather clear that the traditional idea of naturalness is not the whole story and that we have on our hands a “bare” Higgs particle, without a mechanism that would account for its mass scale. Alternatively, we might find out that the apparent failure of naturalness was an illusion and that additional particles and forces that provide an explanation for the electroweak scale are just beyond our current experimental reach. There is also an intermediate possibility that I find fascinating. This is that the electroweak scale is not natural in the customary sense, but additional particles and forces that would help us understand what is going on exist at an energy not too much above LHC energies. A fascinating theory of this type is the “split supersymmetry” that has been proposed by Nima Arkani-Hamed and others.  

It seems that the ideas of naturalness that we grew up with are now failing us 

There is an obvious catch, however. It is easy enough to say “such-and-such will happen at an energy not too much above LHC energies”. But for practical purposes, it makes a world of difference whether this means three times LHC energies, six times LHC energies, 25 times LHC energies, or more. In theories such as split supersymmetry, the clues that we have are not sufficient to enable a real answer. A dream would be to get a concrete clue from experiment about what is the energy scale for new physics beyond the Higgs particle. 

Could the flavour anomalies be one such clue?

There are multiple places that new clues could come from. The possible anomalies in b physics observed at CERN are extremely significant if they hold up. The search for an electric dipole moment of the electron or neutron is also very important and could possibly give a signal of something new happening at energies close to those that we have already probed. Another possibility is the slight reported discrepancy between the magnetic moment of the muon and the SM prediction. Here, I think it is very important to improve the lattice gauge theory estimates of the hadronic contribution to the muon moment, in order to clarify whether the fantastically precise measurements that are now available are really in disagreement with the SM. Of course, there are multiple other places that experiment could pinpoint the next energy scale at which the SM needs to be revised, ranging from precision studies of the Higgs particle to searches for muon decay modes that are absent in the SM. 

Which current developments in theory are you most excited about?

The new ideas about gravity and quantum mechanics that go under the rough title “It from qubit” are really exciting. Black-hole thermodynamics was discovered in the 1970s through the work of Jacob Bekenstein, Stephen Hawking and others. These results were fascinating, but for several decades it seemed to me – rightly or wrongly – that this field was evolving only slowly compared to other areas of theoretical physics. In the past decade or so, that is clearly no longer the case. In large part the change has come from thinking about “entropy” as microscopic or fine-grained von Neumann entropy, as opposed to the thermodynamic entropy that Bekenstein and others considered. A formulation in terms of fine-grained entropy has made possible new statements and more general statements which reduce to the traditional ones when thermodynamics is valid. All this has been accelerated by the insights that come from holographic duality between gravity and gauge theory.

How different does the field look today compared to when you entered it?

It is really hard to exaggerate how the field has changed. I started graduate school at Princeton in September 1973. Asymptotic freedom of non-abelian gauge theory had just been discovered a few months earlier by David Gross, Frank Wilzcek and David Politzer. This was the last key ingredient that was needed to make possible the SM as we know it today. Since then there has been a revolution in our experimental knowledge of the SM. Several key ingredients (new quarks, leptons and the Higgs particle) were unknown in 1973. Jets in hadronic processes were still in the future, even as an idea, let alone an experimental reality, and almost nothing was known about CP violation or about scaling violations in high-energy hadronic processes, just to mention two areas that developed later in an impressive way. 

Not only is our experimental knowledge of the SM so much richer than it was in 1973, but the same is really true of our theoretical understanding as well. Quantum field theory is understood much better today than was the case in 1973. There really is no comparison.

Perhaps equally dramatic has been the change in our understanding of cosmology. In 1973, the state of cosmological knowledge could be summarised fairly well in a couple of numbers – notably the cosmic-microwave temperature and the Hubble constant – and of these only the first was measured with any reasonable precision. In the intervening years, cosmology became a precision science and also a much more ambitious science, as cosmologists have learned to grapple with the complex processes of the formation of structure in the universe. In the inhomogeneities of the microwave background, we have observed what appear to be the seeds of structure formation. And the theory of cosmic inflation, which developed starting around 1980, seems to be a real advance over the framework in which cosmology was understood in 1973, though it is certainly still incomplete.

Exploring the string-theory framework has led to a remarkable series of discoveries

Finally, 50 years ago the gulf between particle physics and gravity seemed unbridgeably wide. There is still a wide gap today. But the emergence in string theory of a sensible framework to study gravity unified with particle forces has changed the picture. This framework has turned out to be very powerful, even if one is not motivated by gravity and one is just searching for new understanding of ordinary quantum field theory. We do not understand today in detail how to unify the forces and obtain the particles and interactions that we see in the real world. But we certainly do have a general idea of how it can work, and this is quite a change from where we were in 1973. Exploring the string-theory framework has led to a remarkable series of discoveries. This well has not run dry, and that is one of the reasons that I am optimistic about the future.

Which of the numerous contributions you have made to particle and mathematical physics are you most proud of?

I am most satisfied with the work that I did in 1994 with Nathan Seiberg on electric-magnetic duality in quantum field theory, and also the work that I did the following year in helping to develop an analogous picture for string theory.

Who knows, maybe I will have the good fortune to do something equally significant again in the future.

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The status of theory improvements and phenomenological interpretations, such as those from effective field theory, were also presented. Highlights included the Higgs pair-production process, which is particularly challenging at the LHC due to its low rate. ATLAS and CMS showed greatly improved sensitivity in various final states, thanks to improvements in analysis techniques. Also shown were results on the scattering of weak vector bosons, a process that is strongly related to the Higgs sector, highlighting large improvements from both the larger datasets and the higher collision energy available in Run 2.

Several searches for phenomena beyond the Standard Model – in particular for additional Higgs bosons – were presented. No significant excesses have yet been found.

The historical talk “The LHC timeline: a personal recollection (1980-2012)” was given by Luciano Maiani, former CERN Director-General, and concluding talks were given by Laura Reina (Florida) and Paolo Meridiani (Rome). A further highlight was the theory talk from Nathaniel Craig, who discussed the progress being made in addressing six open questions. Does the Higgs boson have a size? Does it interact with itself? Does it mediate a Yukawa force? Does it fulfill the naturalness strategy? Does it preserve causality? And does it realise electroweak symmetry?

The next Higgs Hunting workshop will be held in Orsay and Paris from 12 to 14 September 2022.

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Cold atoms offer exciting prospects for high-precision measurements based on emerging quantum technologies. Terrestrial cold-atom experiments are already widespread, exploring both fundamental phenomena such as quantum phase transitions and applications such as ultra-precise timekeeping. The final quantum frontier is to deploy such systems in space, where the lack of environmental disturbances enables high levels of precision.

This was the subject of a workshop supported by the CERN Quantum Technology Initiative, which attracted more than 300 participants online from 23 to 24 September. Following a 2019 workshop triggered by the European Space Agency (ESA)’s Voyage 2050 call for ideas for future experiments in space, the main goal of this workshop was to begin drafting a roadmap for cold atoms in space.

The workshop opened with a presentation by Mike Cruise (University of Birmingham) on ESA’s vision for cold atom R&D for space: considerable efforts will be required to achieve the technical readiness level needed for space missions, but they hold great promise for both fundamental science and practical applications. Several of the cold-atom teams that contributed white papers to the Voyage 2050 call also presented their proposals.

Atomic clocks

Next came a session on atomic clocks, including descriptions of their potential for refining the definitions of SI units, such as the second, and distributing this new time-standard worldwide, and potential applications of atomic clocks to geodesy. Next-generation spacebased atomic-clock projects for these and other applications are ongoing in China, the US (Deep Space Atomic Clock) and Europe.

This was followed by a session on Earth observation, featuring the prospects for improved gravimetry using atom interferometry and talks on the programmes of ESA and the European Union. Quantum space gravimetry could contribute to studies of climate change, for example, by measuring the densities of water and ice very accurately and with improved geographical precision.

Cold-atom experiments in space offer great opportunities to probe the foundations of physics

For fundamental physics, prospects for space-borne cold-atom experiments include studies of wavefunction collapse and Bell correlations in quantum mechanics, probes of the equivalence principle by experiments like STEQUEST, and searches for dark matter.

The proposed AEDGE atom interferometer will search for ultralight dark matter and gravitational waves in the deci-Hertz range, where LIGO/Virgo/KAGRA and the future LISA space observatory are relatively insensitive, and will probe models of dark energy. AEDGE gravitational- wave measurements could be sensitive to first-order phase transitions in the early universe, as occur in many extensions of the Standard Model, as well as to cosmic strings, which could be relics of symmetries broken at higher energies than those accessible to colliders.

These examples show that cold-atom experiments in space offer great opportunities to probe the foundations of physics as well as make frontier measurements in astrophysics and cosmology.

Several pathfinder experiments are underway. These include projects for terrestrial atom interferometers on scales from 10 m to 1 km, such as the MAGIS project at Fermilab and the AION project in the UK, which both use strontium, and the MIGA project in France and proposed European infrastructure ELGAR, which both use rubidium. Meanwhile, a future stage of AION could be situated in an access shaft at CERN – a possibility that is currently under study, and which could help pave the way towards AEDGE. Pioneering experiments using Bose-Einstein condensates on research rockets and the International Space Station were also presented.

A strong feature of the workshop was a series of breakout sessions to enable discussions among members of the various participating communities (atomic clocks, Earth observation and fundamental science), as well as a group considering general perspectives, which were summarised in a final session. Reports from the breakout sessions will be integrated into a draft roadmap for the development and deployment of cold atoms in space. This will be set out in a white paper to appear by the end of the year and presented to ESA and other European space and funding agencies.

Space readiness

Achieving space readiness for cold-atom experiments will require significant research and development. Nevertheless, the scale of participation in the workshop and the high level of engagement testifies to the enthusiasm in the cold-atom community and prospective user communities for deploying cold atoms in space. The readiness of the different communities to collaborate in drafting a joint roadmap for the pursuit of common technological and scientific goals was striking.

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An LLP decaying in the endcap muon spectrometer volume should produce a particle shower when its decay products interact with the return yoke of the CMS solenoid. The secondary particles produced by the shower would traverse the gaseous regions of the cathode-strip chamber (CSC) detector and produce a large multiplicity of signals on the wire anodes and strip cathodes. Localised hits are reconstructed by combining these signals using a density-based clustering algorithm. This is the first time the CSC detectors have been used as a sampling calorimeter to try to detect and identify LLP decays. 

Searching for CSC clusters with a sufficiently large number of hits suppresses background processes while maintaining a high efficiency for detecting potential LLP decays. The large amount of steel in the CMS return yoke nearly eliminates “punch-through” hadrons that are not fully stopped by the calorimeter, potentially mimicking the signature of an LLP. The largest remaining source of backgrounds is known LLPs produced by SM processes such as the neutral kaon, K_L. These particles are copiously produced in LHC collisions and, on rare occasions, traverse the material without being stopped. Kaons are predominantly produced with much lower energies than the signal LLPs and therefore result in clusters with a smaller number of hits. Requiring clusters with more than 130 CSC hits suppresses these dominant background events to a negligible level (see figure 1).

This search improves on the previous best results by more than a factor of six

Using the full Run-2 dataset, the CMS collaboration detected no excess of particle-shower events above the expected backgrounds, setting constraints on a benchmark-simplified model of scalar LLP production mediated by the Higgs boson (a so-called Higgs portal model). This search improves on the previous best results by more than a factor of six (two) for an LLP mass of 7 GeV (≥ 15) GeV for a proper decay length (cτ) of the scalar larger than 100 m. It is the first to be sensitive to LLP decays with cτ up to 1000 m and masses between 40 and 55 GeV at branching ratios of the Higgs to a pair of LLPs below 20%.

This novel approach to identifying showers in muon detectors opens up an exciting new programme of searches for LLPs in a wide variety of theoretical models. Potential frameworks range from Higgs-portal models to other portals to a dark sector, including neutrinos, axions and dark photons. The on-going development of a dedicated Level-1 and High-Level Trigger focusing on particle showers detected in the CMS muon spectrometer promises an order of magnitude improvement in the discovery sensitivity for LLPs in the forthcoming run of the LHC.

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After a three-year hiatus, protons are once again circulating in the LHC, as physicists make final preparations for the start of Run 3. At the beginning of October, a beam of 450 GeV protons made its way from the Super Proton Synchrotron (SPS) down the TI2 beamline towards Point 2, where it struck a dump block and sprayed secondary particles into the ALICE experiment (see image). Beam was also successfully sent down the TI8 transfer line, which meets the LHC near to where the LHCb experiment is located.

Today, counter-rotating protons were finally injected into the LHC, marking the latest milestone in the reawakening of CERN’s accelerator complex, which closed down at the end of 2018 for Long Shutdown 2 (LS2). Two weeks of beam tests are planned, along with first low-energy collisions in the experiments, before the machine is shut down for a 3-4 month maintenance period. Meanwhile, the experiments are continuing to ready themselves for more luminous Run-3 operations.

Final countdown

Beams have been back at CERN since the spring. After a comprehensive two-year overhaul, the Proton Synchrotron (PS) accelerated its first beams on 4 March and has recently started supplying experiments in the newly refurbished East Area and at the new ELENA ring at the Antimatter Factory. Connecting the brand-new Linac4 to the upgraded PS Booster (which also serves ISOLDE) was a major step in the upgrade programme.  Together, they now provide the PS with a 2 GeV beam, 0.6 GeV up from before, for which the 60-year-old machine had to be fitted out with refurbished magnets, new beam-dump systems, instrumentation, and upgraded RF and cooling systems.

When the LHC comes back online for physics in May 2022, it will not only be more luminous, but it will also operate at higher energies

LS2 saw an even greater overhaul of the SPS, including the addition of a new beam-dump system, a refurbished RF system that now includes the use of solid-state amplifier technology, and a major overhaul of the control system. Combined with the LHC Injectors Upgrade project (the main focus of LS2), the accelerator complex is now primed for more intense beams, in particular for the High-Luminosity LHC (HL-LHC) later this decade.

The first bunch was injected from the PS into the SPS on 12 April, building up to “LHC-like” beams of up to 288 bunches a few weeks later. The SPS delivers beams to all of CERN’s North Area experiments, which include a new facility, NA65, approved in 2019 to investigate fast-neutron production for better understanding of the background in underground neutrino experiments. It also drives the AWAKE experiment, which performs R&D for plasma-wakefield acceleration and entered its second run in July with the goal of demonstrating acceleration gradients of 1 GV/m while preserving the beam quality. The restart of North Area experiments will also see pilot runs for new experiments such as AMBER (the successor of COMPASS) and NA64μ (NA64 running with muon beams).

Brighter and more powerful

When the LHC comes back online for physics in May 2022, it will not only be more luminous (with up to 1.8 × 10¹¹ protons per bunch compared to 1.3–1.4 × 10¹¹ during Run 2), but it will also operate at higher energies. This year, the majority of the LHC’s 1232 dipole magnets were trained to carry 6.8 TeV proton beams, compared to 6.5 TeV before, which involves operating with a current of 11.5 kA (with a margin of 0.1 kA). Following the beam tests this autumn, magnet training for the final two of the machine’s eight sectors will take place during a scheduled maintenance period from 1 November to 21 February. After that, the LHC tunnel and experiment areas will be closed for a two-week-long “cold checkout”, with beam commissioning commencing on 7 March and first stable beams expected during the first week of May.

Meanwhile, the LHC experiments are continuing to ready their detectors for the bumper Run-3 data harvest ahead: at least 160 fb^–1 (as for Run 2) to ATLAS and CMS; 25 fb^–1 to LHCb (compared to 6 fb^–1 in Run 2); and 7.5 nb^–1 of Pb–Pb collisions to ALICE (compared to 1.3 nb^–1 in Run 2). The higher integrated luminosities expected for ALICE and LHCb are largely possible thanks to the ability of their upgraded detectors to handle the Run-3 data rate, with LHCb teams currently working around the clock to ensure their brand-new sub-detectors are in place. New forward-experiments, FASER, FASERν and SND@LHC, which aim to make the first observations of collider neutrinos and open new searches for feebly interacting particles, are also gearing up to take first data when the LHC comes back to life.

“The injector performance reached in 2021 is just the start of squeezing out the potential they have been given during LS2, paving the way for the HL-LHC, but also benefiting the LHC’s performance during Run 3,” says Rende Steerenberg, head of the operations group. “Having beam back in the entire complex and routinely providing the experimental facilities with physics is testimony to the excellent and hard work of many people at CERN.”

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At a seminar at CERN today, the LHCb collaboration presented new tests of lepton universality in rare B-meson decays. While limited in statistical sensitivity, the results fit an intriguing pattern of recent results in the flavour sector, says the collaboration.

Since 2013, several measurements have hinted at deviations from lepton-flavour universality (LFU), a tenet of the Standard Model (SM) which treats charged leptons, ℓ, as identical apart from their masses. The measurements concern decay processes involving the transition between a bottom and a strange quark b→sℓ⁺ℓ^–, which are strongly suppressed by the SM because they involve quantum corrections at the one-loop level (leading to branching fractions of one part in 10⁶ or less). A powerful way to probe LFU is therefore to measure the ratio of B-meson decays to muons and electrons, for which the SM prediction, close-to-unity, is theoretically very clean.

In March this year, an LHCb measurement of R_K = BR(B⁺→K⁺μ⁺μ^–)/BR(B⁺→K⁺e⁺e^–) based on the full LHC Run 1 and 2 dataset showed a 3.1σ difference from the SM prediction. This followed departures at the level of 2.2—2.5σ in the ratio R_K*⁰ (which probes B⁰→K*⁰ℓ⁺ℓ^– decays) reported by LHCb in 2017. The collaboration has also seen slight deficits in the ratio R_pK, and departures from theory in measurements of the angular distribution of final-state particles and of branching fractions in neutral B-meson decays. None of the results is individually significant enough to constitute evidence of new physics. But taken together, say theorists, they point to a coherent pattern.

We are seeing a similar deficit of rare muon decays to rare electron decays that we have seen in other LFU tests

Harry Cliff

The latest LHCb analysis clocked the ratio of muons to electrons in the isospin-partner B-decays: B⁰→ K_S⁰ℓ⁺ℓ^– and B⁺→K*⁺ℓ⁺ℓ^–. As well as being a first at the LHC, it’s the first single-experiment observation of these decays, and the most precise measurement yet of their branching ratios. Being difficult to reconstruct due to the presence of a long-lived K_S⁰ in the final state, however, the sensitivity of the results is lower than for previous “R_K” analyses. LHCb found R(K_S⁰) = 0.66+0.2/-0.15 (stat) +0.02/-0.04 (syst) and R(K*⁺) = 0.70+0.18/-0.13 (stat) +0.03/-0.04 (syst), which are consistent with the SM at the level of 1.5 and 1.4σ, respectively.

“What is interesting is that we are seeing a similar deficit of rare muon decays to rare electron decays that we have seen in other LFU tests,” said Harry Cliff of the University of Cambridge, who presented the result on behalf of LHCb (in parallel with a presentation at Rencontres de Blois by Cambridge PhD student John Smeaton). “With many other LFU tests in progress using Run 1 and 2 data, there will be more to come on this puzzle soon. Then we have Run 3, where we expect to really zoom in on the measurements and obtain a detailed understanding.”

The experimental and theoretical status of the flavour anomalies in b→sℓ⁺ℓ and semi-leptonic B-decays will be the focus of the Flavour Anomaly Workshop at CERN on Wednesday 20 October, at which ATLAS and CMS activities will also be discussed, along with perspectives from theorists.

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In this year’s unusual Olympic summer, high-energy physicists pushed back the frontiers of knowledge and broke many records. The first one is surely the number of registrants to the EPS-HEP conference, hosted online from 26 to 30 July by the University of Hamburg and DESY: nearly 2000 participants scrutinised more than 600 talks and 280 posters. After 18 months of the COVID pandemic, the community showed a strong desire to meet and discuss physics with international colleagues. 

200 trillion b-quarks, 40 billion electroweak bosons, 300 million top quarks and 10 million Higgs bosons

The conference offered the opportunity to hear about analyses using the full LHC Run-2 data set, which is the richest hadron-collision data sample ever recorded. The results are breathtaking. As my CERN colleague Michelangelo Mangano explained recently to summer students, “The LHC works and is more powerful than expected, the experiments work and are more precise than expected, and the Standard Model works beautifully and is more reliable than expected.” About 3000 papers have been published by the LHC collaborations in the past decade. They have established the LHC as a truly multi-messenger endeavour, not so much because of the multitude of elementary particles produced – 200 trillion b-quarks, 40 billion electroweak bosons, 300 million top quarks and 10 million Higgs bosons – but because of the diversity of scientifically independent experiments that historically would have required different detectors and facilities, built and operated by different communities. “Data first” should always remain the leitmotif of the natural sciences. 

Paula Alvarez Cartelle (Cambridge) reminded us that the LHC has revealed new states of matter, with LHCb confirming that four or even five quarks can assemble themselves into new long-lived bound states, stabilised by the presence of two charm quarks. For theorists, these new quark-molecules provide valuable input data to tune their lattice simulations and to refine their understanding of the non-perturbative dynamics of strong interactions.

Theoretical tours de force

While Run 1 was a time for inclusive measurements, a multitude of differential measurements were performed during Run 2. Paolo Azzurri (INFN Pisa) reviewed the transverse momentum distribution of the jets produced in association with electroweak gauge bosons. These offer a way to test quantum chromodynamics and electroweak predictions at the highest achievable precision through higher-order computations, resummation and matching to parton showers. The work is fuelled by remarkable theoretical tours de force reported by Jonas Lindert (Sussex) and Lorenzo Tancredi (Oxford), which build on advanced mathematical techniques, including inspiring new mathematical developments in algebraic geometry and finite-field arithmetic. We experienced a historic moment: the LHC definitively became a precision machine, achieving measurements reaching and even surpassing LEP’s precision. This new situation also induced a shift more towards precision measurements, model-independent interpretations and Standard Model (SM) compatibility checks, and away from model-dependent searches for new physics. Effective-field-theory analyses are therefore gaining popularity, explained Veronica Sanz (Valencia and Sussex).

We know for certain that the SM is not the ultimate theory of nature. How and when the first cracks will be revealed is the big question that motivates future collider design studies. The enduring and compelling “B anomalies” reported by LHCb could well be the revolutionary surprise that challenges our current understanding of the structure of matter. The ratios of the decay widths of B mesons, either through charged or neutral currents, b→cℓν and b→sℓ⁺ℓ^–, could finally reveal that the electron, muon and tau lepton differ by more than just their masses.

The statistical significance of the lepton flavour anomalies is growing, reported Franz Muheim (Edinburgh and CERN), creating “cautious” excitement and stimulating the creativity of theorists like Ana Teixeira (Clermont-Ferrand), who builds new physics models with leptoquarks and heavy vectors with different couplings to the three families of leptons, to accommodate the apparent lepton-flavour-universality violations. Belle II should soon bring new additional input to the debate, said Carsten Niebuhr (DESY).

Long-awaited results

The other excitement of the year came from the long-awaited results from the muon g-2 experiment at Fermilab, presented by Alex Keshavarzi (Manchester). The spin precession frequency of a sample of 10 billion muons was measured with a precision of a few hundred parts per million, confirming the deviation from the SM prediction observed nearly 20 years ago by the E821 experiment at Brookhaven. With the current statistics, the deviation now amounts to 4.2σ. With an increase by a factor 20 of the dataset foreseen in the next run, the measurement will soon become systematics limited. Gilberto Colangelo (Bern) also discussed new and improved lattice computations of the hadronic vacuum polarisation, significantly reducing the discrepancy between the theoretical prediction and the experimental measurement. The jury is still out – and the final word might come from the g-2/EDM experiment at J-PARC.

Accelerator-based experiments might not be the place to prove the SM wrong. Astrophysical and cosmological observations have already taught us that SM matter only constitutes around 5% of the stuff that the universe is made of. The traditional idea that the gap in the energy budget of the universe is filled by new TeV-scale particles that stabilise the electroweak scale under radiative corrections is fading away. And a huge range of possible dark-matter scales opens up a rich and reinvigorated experimental programme that can profit from original techniques exploiting electron and nuclear recoils caused by the scattering of dark-matter particles. A front-runner in the new dark-matter landscape is the QCD axion originally introduced to explain why strong interactions do not distinguish matter from antimatter. Babette Döbrich (CERN) discussed the challenges inherent in capturing an axion, and described the many new experiments around the globe designed to overcome them.

Progress could also come directly from theory

Progress could also come directly from theory. Juan Maldacena (IAS Princeton) recalled the remarkable breakthroughs on the black-hole information problem. The Higgs discovery in 2012 established the non-trivial vacuum structure of space–time. We are now on our way to understanding the quantum mechanics of this space–time.

Like at the Olympics, where breaking records requires a lot of work and effort by the athletes, their teams and society, the quest to understand nature relies on the enthusiasm and the determination of physicists and their funding agencies. What we have learnt so far has allowed us to formulate precise and profound questions. We now need to create opportunities to answer them and to move ahead.

One cannot underestimate how quickly the landscape of physics can change, whether the B-anomalies will be confirmed or whether a dark-matter particle will be discovered. Let’s see what will be awaiting us at the next EPS-HEP conference in 2023 in Hamburg – in person this time!

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Ever since its discovery in 1995 at the Tevatron, the top quark has been considered to be a highly effective probe of new physics. A key reason is that the last fundamental fermion predicted by the Standard Model (SM) has a remarkably high mass, just a sliver under the Higgs vacuum expectation value divided by the square root of two, implying a Yukawa coupling close to unity. This has far-reaching implications: the top quark impacts the electroweak sector significantly through loop corrections, and may couple preferentially to new massive states. But while the top quark may represent a window into new physics, we cannot know a priori whether new massive particles could ever be produced at the LHC, and direct searches have so far been inconclusive. Model-inde­pendent measurements carried out within the framework of effective field theory (EFT) are therefore becoming increasingly important as a means to make the most of the wealth of precision measurements at the LHC. This approach makes it possible to systematically correlate sparse deviations observed in different measurements, in order to pinpoint any anomalies in top-quark couplings that might arise from unknown massive particles.

The top quark impacts the electroweak sector significantly through loop corrections

A new CMS analysis searches for anomalies in top-quark interactions with the Z boson using an EFT framework. The cross-section measurements of the rare associated production of either one (tZ) or two (ttZ) top quarks with a Z boson were statistically limited until recently. These interactions are among the least constrained by the available data in the top-quark sector, despite being modified in numerous beyond-SM models, such as composite Higgs models and minimal supersymmetry. Using the full LHC Run-2 data set, this study targets high-purity final states with multiple electrons and muons. It sets some of the tightest constraints to date on five generic types of EFT interactions that could substantially modify the characteristics of associated top-Z production, while having negligible or no effect on background processes.

Machine learning

In contrast to the more usual reinterpretations of SM measurements that require assumptions on the nature of new physics, this analysis considers EFT effects on observables at the detector level and constrains them directly from the data using a strategy that combines observables specifically selected for their sensitivity to EFT. The key feature of this work is its heavy use of multivariate-analysis techniques based on machine learning, which improve its sensitivity to new interactions. First, to define regions enriched in the processes of interest, a multiclass neural network is trained to discriminate between different SM processes. Subsequently, several binary neural networks learn to separate events generated according to the SM from events that include EFT effects arising from one or more types of anomalous interactions. For the first time in an analysis using LHC data, these classifiers were trained on the full physical amplitudes, including the interference between SM and EFT components.

The binary classifiers are used to construct powerful discriminant variables out of high-dimensional input data. Their distributions are fitted to data to constrain up to five types of EFT couplings simultaneously. The widths of the corresponding confidence intervals are significantly reduced thanks to the combination of the available kinematic information that was specifically chosen to be sensitive to EFT in the top quark sector. All results are consistent with the SM, which indicates either the absence of new effects in the targeted interactions or that the mass scale of new physics is too high to be probed with the current sensitivity. This result is an important step towards the more widespread use of machine learning to target EFT effects, to efficiently explore the enormous volume of LHC data more globally and comprehensively.

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Particle physics is at its heart a reductionistic endeavour that tries to reduce reality to its most basic building blocks. This view of nature is most evident in the search for a theory of everything – an idea that is nowadays more common in popularisations of physics than among physicists themselves. If discovered, all physical phenomena would follow from the application of its fundamental laws.

A complementary perspective to reductionism is that of emergence. Emergence says that new and different kinds of phenomena arise in large and complex systems, and that these phenomena may be impossible, or at least very hard, to derive from the laws that govern their basic constituents. It deals with properties of a macroscopic system that have no meaning at the level of its microscopic building blocks. Good examples are the wetness of water and the superconductivity of an alloy. These concepts don’t exist at the level of individual atoms or molecules, and are very difficult to derive from the microscopic laws. 

As physicists continue to search for cracks in the Standard Model (SM) and Einstein’s general theory of relativity, could these natural laws in fact be emergent from a deeper reality? And emergence is not limited to the world of the very small, but by its very nature skips across orders of magnitude in scale. It is even evident, often mesmerisingly so, at scales much larger than atoms or elementary particles, for example in the murmurations of a flock of birds – a phenomenon that is impossible to describe by following the motion of an individual bird. Another striking example may be intelligence. The mechanism by which artificial intelligence is beginning to emerge from the complexity of underlying computing codes shows similarities with emergent phenomena in physics. One can argue that intelligence, whether it occurs naturally, as in humans, or artificially, should also be viewed as an emergent phenomenon. 

Data compression

Renormalisable quantum field theory, the foundation of the SM, works extraordinarily well. The same is true of general relativity. How can our best theories of nature be so successful, while at the same time being merely emergent? Perhaps these theories are so successful precisely because they are emergent. 

As a warm up, let’s consider the laws of thermodynamics, which emerge from the microscopic motion of many molecules. These laws are not fundamental but are derived by statistical averaging – a huge data compression in which the individual motions of the microscopic particles are compressed into just a few macroscopic quantities such as temperature. As a result, the laws of thermodynamics are universal and independent of the details of the microscopic theory. This is true of all the most successful emergent theories; they describe universal macroscopic phenomena whose underlying microscopic descriptions may be very different. For instance, two physical systems that undergo a second-order phase transition, while being very different microscopically, often obey exactly the same scaling laws, and are at the critical point described by the same emergent theory. In other words, an emergent theory can often be derived from a large universality class of many underlying microscopic theories. 

Successful emergent theories describe universal macroscopic phenomena whose underlying microscopic descriptions may be very different

Entropy is a key concept here. Suppose that you try to store the microscopic data associated with the motion of some particles on a computer. If we need N bits to store all that information, we have 2^N possible microscopic states. The entropy equals the logarithm of this number, and essentially counts the number of bits of information. Entropy is therefore a measure of the total amount of data that has been compressed. In deriving the laws of thermodynamics, you throw away a large amount of microscopic data, but you at least keep count of how much information has been removed in the data-compression procedure.

Emergent quantum field theory

One of the great theoretical-physics paradigm shifts of the 20th century occurred when Kenneth Wilson explained the emergence of quantum field theory through the application of the renormalisation group. As with thermodynamics, renormalisation compresses microscopic data into a few relevant parameters – in this case, the fields and interactions of the emergent quantum field theory. Wilson demonstrated that quantum field theories appear naturally as an effective long-distance and low-energy description of systems whose microscopic definition is given in terms of a quantum system living on a discretised spacetime. As a concrete example, consider quantum spins on a lattice. Here, renormalisation amounts to replacing the lattice by a coarser lattice with fewer points, and redefining the spins to be the average of the original spins. One then rescales the coarser lattice so that the distance between lattice points takes the old value, and repeats this step many times. A key insight was that, for quantum statistical systems that are close to a phase transition, you can take a continuum limit in which the expectation values of the spins turn into the local quantum fields on the continuum spacetime.

This procedure is analogous to the compression algorithms used in machine learning. Each renormalisation step creates a new layer, and the algorithm that is applied between two layers amounts to a form of data compression. The goal is similar: you only keep the information that is required to describe the long-distance and low-energy behaviour of the system in the most efficient way.

So quantum field theory can be seen as an effective emergent description of one of a large universality class of many possible underlying microscopic theories. But what about the SM specifically, and its possible supersymmetric extensions? Gauge fields are central ingredients of the SM and its extensions. Could gauge symmetries and their associated forces emerge from a microscopic description in which there are no gauge fields? Similar questions can also be asked about the gravitational force. Could the curvature of spacetime be explained from an emergent perspective?

String theory seems to indicate that this is indeed possible, at least theoretically. While initially formulated in terms of vibrating strings moving in space and time, it became clear in the 1990s that string theory also contains many more extended objects, known as “branes”. By studying the interplay between branes and strings, an even more microscopic theoretical description was found in which the coordinates of space and time themselves start to dissolve: instead of being described by real numbers, our familiar (x, y, z) coordinates are replaced by non-commuting matrices. At low energies, these matrices begin to commute, and give rise to the normal spacetime with which we are familiar. In these theoretical models it was found that both gauge forces and gravitational forces appear at low energies, while not existing at the microscopic level.

While these models show that it is theoretically possible for gauge forces to emerge, there is at present no emergent theory of the SM. Such a theory seems to be well beyond us. Gravity, however, being universal, has been more amenable to emergence.

Emergent gravity

In the early 1970s, a group of physicists became interested in the question: what happens to the entropy of a thermodynamic system that is dropped into a black hole? The surprising conclusion was that black holes have a temperature and an entropy, and behave exactly like thermodynamic systems. In particular, they obey the first law of thermodynamics: when the mass of a black hole increases, its (Bekenstein–Hawking) entropy also increases.

The correspondence between the gravitational laws and the laws of thermodynamics does not only hold near black holes. You can artificially create a gravitational field by accelerating. For an observer who continues to accelerate, even empty space develops a horizon, from behind which light rays will not be able to catch up. These horizons also carry a temperature and entropy, and obey the same thermodynamic laws as black-hole horizons. 

It was shown by Stephen Hawking that the thermal radiation emitted from a black hole originates from pair creation near the black-hole horizon. The properties of the pair of particles, such as spin and charge, are undetermined due to quantum uncertainty, but if one particle has spin up (or positive charge), then the other particle must have spin down (or negative charge). This means that the particles are quantum entangled. Quantum entangled pairs can also be found in flat space by considering accelerated observers. 

Crucially, even the vacuum can be entangled. By separating spacetime into two parts, you can ask how much entanglement there is between the two sides. The answer to this was found in the last decade, through the work of many theorists, and turns out to be rather surprising. If you consider two regions of space that are separated by a two-dimensional surface, the amount of quantum entanglement between the two sides turns out to be precisely given by the Bekenstein–Hawking entropy formula: it is equal to a quarter of the area of the surface measured in Planck units. 

Holographic renormalisation

The AdS/CFT correspondence incorporates a principle called “holography”: the gravitational physics inside a region of space emerges from a microscopic description that, just like a hologram, lives on a space with one less dimension and thus can be viewed as living on the boundary of the spacetime region. The extra dimension of space emerges together with the gravitational force through a process called “holographic renormalisation”. One successively adds new layers of spacetime. Each layer is obtained from the previous layer through “coarse-graining”, in a similar way to both renormalisation in quantum field theory and data-compression algorithms in machine learning.

Unfortunately, our universe is not described by a negatively curved spacetime. It is much closer to a so-called de Sitter spacetime, which has a positive curvature. The main difference between de Sitter space and the negatively curved anti-de Sitter space is that de Sitter space does not have a boundary. Instead, it has a cosmological horizon whose size is determined by the rate of the Hubble expansion. One proposed explanation for this qualitative difference is that, unlike for negatively curved spacetimes, the microscopic quantum state of our universe is not unique, but secretly carries a lot of quantum information. The amount of this quantum information can once again be counted by an entropy: the Bekenstein–Hawking entropy associated with the cosmological horizon. 

This raises an interesting prospect: if the microscopic quantum data of our universe may be thought of as many entangled qubits, could our current theories of spacetime, particles and forces emerge via data compression? Space, for example, could emerge by forgetting the precise way in which all the individual qubits are entangled, but only preserving the information about the amount of quantum entanglement present in the microscopic quantum state. This compressed information would then be stored in the form of the areas of certain surfaces inside the emergent curved spacetime. 

In this description, gravity would follow for free, expressed in the curvature of this emergent spacetime. What is not immediately clear is why the curved spacetime would obey the Einstein equations. As Einstein showed, the amount of curvature in spacetime is determined by the amount of energy (or mass) that is present. It can be shown that his equations are precisely equivalent to an application of the first law of thermodynamics. The presence of mass or energy changes the amount of entanglement, and hence the area of the surfaces in spacetime. This change in area can be computed and precisely leads to the same spacetime curvature that follows from the Einstein equations. 

The idea that gravity emerges from quantum entanglement goes back to the 1990s, and was first proposed by Ted Jacobson. Not long afterwards, Juan Maldacena discovered that general relativity can be derived from an underlying microscopic quantum theory without a gravitational force. His description only works for infinite spacetimes with negative curvature called anti-de Sitter (or AdS–) space, as opposed to the positive curvature we measure. The microscopic description then takes the form of a scale-invariant quantum field theory – a so-called conformal field theory (CFT) – that lives on the boundary of the AdS–space (see “Holographic renormalisation” panel). It is in this context that the connection between vacuum entanglement and the Bekenstein–Hawking entropy, and the derivation of the Einstein equations from entanglement, are best understood. I have also contributed to these developments in a paper in 2010 that emphasised the role of entropy and information for the emergence of the gravitational force. Over the last decade a lot of progress has been made in our understanding of these connections, in particular the deep connection between gravity and quantum entanglement. Quantum information has taken centre stage in the most recent theoretical developments.

Emergent intelligence

But what about viewing the even more complex problem of human intelligence as an emergent phenomenon? Since scientific knowledge is condensed and stored in our current theories of nature, the process of theory formation can itself be viewed as a very efficient form of data compression: it only keeps the information needed to make predictions about reproducible events. Our theories provide us with a way to make predictions with the fewest possible number of free parameters. 

The same principles apply in machine learning. The way an artificial-intelligence machine is able to predict whether an image represents a dog or a cat is by compressing the microscopic data stored in individual pixels in the most efficient way. This decision cannot be made at the level of individual pixels. Only after the data has been compressed and reduced to its essence does it becomes clear what the picture represents. In this sense, the dog/cat-ness of a picture is an emergent property. This is even true for the way humans process the data collected by our senses. It seems easy to tell whether we are seeing or hearing a dog or a cat, but underneath, and hidden from our conscious mind, our brains perform a very complicated task that turns all the neural data that come from our eyes and ears into a signal that is compressed into a single outcome: it is a dog or a cat. 

Emergence is often summarised with the slogan “the whole is more than the sum of its parts”

Can intelligence, whether artificial or human, be explained from a reductionist point of view? Or is it an emergent concept that only appears when we consider a complex system built out of many basic constituents? There are arguments in favour of both sides. As human beings, our brains are hard-wired to observe, learn, analyse and solve problems. To achieve these goals the brain takes the large amount of complex data received via our senses and reduces it to a very small set of information that is most relevant for our purposes. This capacity for efficient data compression may indeed be a good definition for intelligence, when it is linked to making decisions towards reaching a certain goal. Intelligence defined in this way is exhibited in humans, but can also be achieved artificially.

Artificially intelligent computers beat us at problem solving, pattern recognition and sometimes even in what appears to be “generating new ideas”. A striking example is DeepMind’s AlphaZero, whose chess rating far exceeds that of any human player. Just four hours after learning the rules of chess, AlphaZero was able to beat the strongest conventional “brute force” chess program by coming up with smarter ideas and showing a deeper understanding of the game. Top grandmasters use its ideas in their own games at the highest level. 

In its basic material design, an artificial-intelligence machine looks like an ordinary computer. On the other hand, it is practically impossible to explain all aspects of human intelligence by starting at the microscopic level of the neurons in our brain, let alone in terms of the elementary particles that make up those neurons. Furthermore, the intellectual capability of humans is closely connected to the sense of consciousness, which most scientists would agree does not allow for a simple reductionist explanation.

Emergence is often summarised with the slogan “the whole is more than the sum of its parts” – or as condensed-matter theorist Phil Anderson put it, “more is different”. It counters the reductionist point of view, reminding us that the laws that we think to be fundamental today may in fact emerge from a deeper underlying reality. While this deeper layer may remain inaccessible to experiment, it is an essential tool for theorists of the mind and the laws of physics alike.

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CERN surveyors have performed the first geodetic measurements for a possible Future Circular Collider (FCC), a prerequisite for high-precision alignment of the accelerator’s components. The millimetre-precision measurements are one of the first activities undertaken by the FCC feasibility study, which was launched last year following the recommendation of the 2020 update of the European strategy for particle physics. During the next three years, the study will explore the technical and financial viability of a 100 km collider at CERN, for which the tunnel is a top priority. Geology, topography and surface infrastructure are the key constraints on the FCC tunnel’s position, around which civil engineers will design the optimal route, should the project be approved.

The FCC would cover an area about 10 times larger than the LHC, in which every geographical reference must be pinpointed with unprecedented precision. To provide a reference coordinate system, in May the CERN surveyors, in conjunction with ETH Zürich, the Federal Office of Topography Swisstopo, and the School of Engineering and Management Vaud, performed geodetic levelling measurements along an 8 km profile across the Swiss–French border south of Geneva.

Such measurements have two main purposes. The first is to determine a high-precision surface model, or “geoid”, to map the height above sea level in the FCC region. The second purpose is to improve the present reference system, whose measurements date back to the 1980s when the tunnel housing the LHC was built.

“The results will help to evaluate if an extrapolation of the current LHC geodetic reference systems and infrastructure is precise enough, or if a new design is needed over the whole FCC area,” says Hélène Mainaud Durand, group leader of CERN’s geodetic metrology group.

The FCC feasibility study, which involves more than 140 universities and research institutions from 34 countries, also comprises technological, environmental, engineering, political and economic considerations. It is due to be completed by the time the next strategy update gets under way in the middle of the decade. Should the outcome be positive, and the project receive the approval of CERN’s member states, civil-engineering works could start as early as the 2030s.

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Can we trust physics decisions made by machines? In recent applications of artificial intelligence (AI) to particle physics, we have partially sidestepped this question by using machine learning to augment analyses, rather than replace them. We have gained trust in AI decisions through careful studies of “control regions” and painstaking numerical simulations. As our physics ambitions grow, however, we are using “deeper” networks with more layers and more complicated architectures, which are difficult to validate in the traditional way. And to mitigate 10 to 100-fold increases in computing costs, we are planning to fully integrate AI into data collection, simulation and analysis at the high-luminosity LHC.

To build trust in AI, I believe we need to teach it to think like a physicist.

I am the director of the US National Science Foundation’s new Institute for Artificial Intelligence and Fundamental Interactions, which was founded last year. Our goal is to fuse advances in deep learning with time-tested strategies for “deep thinking” in the physical sciences. Many promising opportunities are open to us. Core principles of fundamental physics such as causality and spacetime symmetries can be directly incorporated into the structure of neural networks. Symbolic regression can often translate solutions learned by AI into compact, human-interpretable equations. In experimental physics, it is becoming possible to estimate and mitigate systematic uncertainties using AI, even when there are a large number of nuisance parameters. In theoretical physics, we are finding ways to merge AI with traditional numerical tools to satisfy stringent requirements that calculations be exact and reproducible. High-energy physicists are well positioned to develop trustworthy AI that can be scrutinised, verified and interpreted, since the five-sigma standard of discovery in our field necessitates it.

It is equally important, however, that we physicists teach ourselves how to think like a machine.

Modern AI tools yield results that are often surprisingly accurate and insightful, but sometimes unstable or biased. This can happen if the problem to be solved is “underspecified”, meaning that we have not provided the machine with a complete list of desired behaviours, such as insensitivity to noise, sensible ways to extrapolate and awareness of uncertainties. An even more challenging situation arises when the machine can identify multiple solutions to a problem, but lacks a guiding principle to decide which is most robust. By thinking like a machine, and recognising that modern AI solves problems through numerical optimisation, we can better understand the intrinsic limitations of training neural networks with finite and imperfect datasets, and develop improved optimisation strategies. By thinking like a machine, we can better translate first principles, best practices and domain knowledge from fundamental physics into the computational language of AI. 

Beyond these innovations, which echo the logical and algorithmic AI that preceded the deep-learning revolution of the past decade, we are also finding surprising connections between thinking like a machine and thinking like a physicist. Recently, computer scientists and physicists have begun to discover that the apparent complexity of deep learning may mask an emergent simplicity. This idea is familiar from statistical physics, where the interactions of many atoms or molecules can often be summarised in terms of simpler emergent properties of materials. In the case of deep learning, as the width and depth of a neural network grows, its behaviour seems to be describable in terms of a small number of emergent parameters, sometimes just a handful. This suggests that tools from statistical physics and quantum field theory can be used to understand AI dynamics, and yield deeper insights into their power and limitations.

If we don’t exploit the full power of AI, we will not maximise the discovery potential of the LHC and other experiments

Ultimately, we need to merge the insights gained from artificial intelligence and physics intelligence. If we don’t exploit the full power of AI, we will not maximise the discovery potential of the LHC and other experiments. But if we don’t build trustable AI, we will lack scientific rigour. Machines may never think like human physicists, and human physicists will certainly never match the computational ability of AI, but together we have enormous potential to learn about the fundamental structure of the universe.

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The need for innovation in machine learning (ML) transcends any single experimental collaboration, and requires more in-depth work than can take place at a workshop. Data challenges, wherein simulated “black box” datasets are made public, and contestants design algorithms to analyse them, have become essential tools to spark interdisciplinary collaboration and innovation. Two have recently concluded. In both cases, contestants were challenged to use ML to figure out “what’s in the box?”

LHC Olympics

The LHC Olympics (LHCO) data challenge was launched in autumn 2019, and the results were presented at the ML4Jets and Anomaly Detection workshops in spring and summer 2020. A final report summarising the challenge was posted to arXiv earlier this year, written by around 50 authors from a variety of backgrounds in theory, the ATLAS and CMS experiments, and beyond. The name of this community effort was inspired by the first LHC Olympics that took place more than a decade ago, before the start of the LHC. In those olympics, researchers were worried about being able to categorise all of the new particles that would be discovered when the machine turned on. Since then, we have learned a great deal about nature at TeV energy scales, with no evidence yet for new particles or forces of nature. The latest LHC Olympics focused on a different challenge – being able to find new physics in the first place. We now know that new physics must be rare and not exactly like what we expected.

In order to prepare for rare and unexpected new physics, organisers Gregor Kasieczka (University of Hamburg), Benjamin Nachman (Lawrence Berkeley National Laboratory) and David Shih (Rutgers University) provided a set of black-box datasets composed mostly of Standard Model (SM) background events. Contestants were charged with identifying any anomalous events that would be a sign of new physics. These datasets focused on resonant anomaly detection, whereby the anomaly is assumed to be localised – a “bump hunt”, in effect. This is a generic feature of new physics produced from massive new particles: the reconstructed parent mass is the resonant feature. By assuming that the signal is localised, one can use regions away from the signal to estimate the background. The LHCO provided one R&D dataset with labels and three black boxes to play with: one with an anomaly decaying into two two-pronged resonances, one without an anomaly, and one with an anomaly featuring two different decay modes (a dijet decay X → qq and a trijet decay X → gY, Y → qq).  There are currently no dedicated searches for these signals in LHC data.

No labels

About 20 algorithms were deployed on the LHCO datasets, including supervised learning, unsupervised learning, weakly supervised learning and semi-supervised learning. Supervised learning is the most widely used method across science and industry, whereby each training example has a label: “background” or “signal”. For this challenge, the data do not have labels as we do not know exactly what we are looking for, and so strategies trained with labels from a different dataset often did not work well. By contrast, unsupervised learning generally tries to identify events that are rarely or never produced by the background; weakly supervised methods use some context from data to provide noisy labels; and semi-supervised methods use some simulation information in order to have a partial set of labels. Each method has its strengths and weaknesses, and multiple approaches are usually needed to achieve a broad coverage of possible signals.

The Dark Machines data challenge focused on developing algorithms broadly sensitive to non-resonant anomalies

The best performance on the first black box in the LHCO challenge, as measured by finding and correctly characterising the anomalous signals, was by a team of cosmologists at Berkeley (George Stein, Uros Seljak and Biwei Dai) who compared the phase-space density between a sliding signal region and sidebands (see “Olympian algorithm” figure). Overall, the algorithms did well on the R&D dataset, and some also did well on the first black box, with methods that made use of likelihood ratios proving particularly effective. But no method was able to detect the anomalies in the third black box, and many teams reported a false signal for the second black box. This “placebo effect’’ illustrates the need for ML approaches to have an accurate estimation of the background and not just a procedure for identifying signals. The challenge for the third black box, however, required algorithms to identify multiple clusters of anomalous events rather than a single cluster. Future innovation is needed in this department.

Dark Machines

A second data challenge was launched in June 2020 within the Dark Machines initiative. Dark Machines is a research collective of physicists and data scientists who apply ML techniques to understand the nature of dark matter – as we don’t know the nature of dark matter, it is critical to search broadly for its anomalous signatures. The challenge was organised by Sascha Caron (Radboud University), Caterina Doglioni (University of Lund) and Maurizio Pierini (CERN), with notable contributions from Bryan Ostidiek (Harvard University) in the development of a common software infrastructure, and Melissa van Beekveld (University of Oxford) for dataset generation. In total, 39 participants arranged in 13 teams explored various unsupervised techniques, with each team submitting multiple algorithms.

By contrast with LHCO, the Dark Machines data challenge focused on developing algorithms broadly sensitive to non-resonant anomalies. Good examples of non-resonant new physics include many supersymmetric models and models of dark matter – anything where “invisible” particles don’t interact with the detector. In such a situation, resonant peaks become excesses in the tails of the missing-transverse-energy distribution. Two datasets were provided: R&D datasets including a concoction of SM processes and many signal samples for contestants to develop their approaches on; and a black-box dataset mixing SM events with events from unspecified signal processes. The challenge has now formally concluded, and its outcome was posted on arXiv in May, but the black-box has not been opened to allow the community to continue to test ideas on it.

A wide variety of unsupervised methods have been deployed so far. The algorithms use diverse representations of the collider events (for example, lists of particle four-momenta, or physics quantities computed from them), and both implicit and explicit approaches for estimating the probability density of the background (for example, autoencoders and “normalising flows”). While no single method universally achieved the highest sensitivity to new-physics events, methods that mapped the background to a fixed point and looked for events that were not described well by this mapping generally did better than techniques that had a so-called dynamic embedding. A key question exposed by this challenge that will inspire future innovation is how best to tune and combine unsupervised machine-learning algorithms in a way that is model independent with respect to the new physics describing the signal.

The enthusiastic response to the LHCO and Dark Machines data challenges highlights the important future role of unsupervised ML at the LHC and elsewhere in fundamental physics. So far, just one analysis has been published – a dijet-resonance search by the ATLAS collaboration using weakly-supervised ML – but many more are underway, and these techniques are even being considered for use in the level-one triggers of LHC experiments (see Hunting anomalies with an AI trigger). And as the detection of outliers also has a large number of real-world applications, from fraud detection to industrial maintenance, fruitful cross-talk between fundamental research and industry is possible. 

The LHCO and Dark Machines data challenges are a stepping stone to an exciting experimental programme that is just beginning. 

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How might artificial intelligence make an impact on theoretical physics?

John Ellis (JE): To phrase it simply: where do we go next? We have the Standard Model, which describes all the visible matter in the universe successfully, but we know dark matter must be out there. There are also puzzles, such as what is the origin of the matter in the universe? During my lifetime we’ve been playing around with a bunch of ideas for tackling those problems, but haven’t come up with solutions. We have been able to solve some but not others. Could artificial intelligence (AI) help us find new paths towards attacking these questions? This would be truly stealing theoretical physicists’ lunch.

 Anima Anandkumar (AA): I think the first steps are whether you can understand more basic physics and be able to come up with predictions as well. For example, could AI rediscover the Standard Model? One day we can hope to look at what the discrepancies are for the current model, and hopefully come up with better suggestions.

 JE: An interesting exercise might be to take some of the puzzles we have at the moment and somehow equip an AI system with a theoretical framework that we physicists are trying to work with, let the AI loose and see whether it comes up with anything. Even over the last few weeks, a couple of experimental puzzles have been reinforced by new results on B-meson decays and the anomalous magnetic moment of the muon. There are many theoretical ideas for solving these puzzles but none of them strike me as being particularly satisfactory in the sense of indicating a clear path towards the next synthesis beyond the Standard Model. Is it imaginable that one could devise an AI system that, if you gave it a set of concepts that we have, and the experimental anomalies that we have, then the AI could point the way?

 AA: The devil is in the details. How do we give the right kind of data and knowledge about physics? How do we express those anomalies while at the same time making sure that we don’t bias the model? There are anomalies suggesting that the current model is not complete – if you are giving that prior knowledge then you could be biasing the models away from discovering new aspects. So, I think that delicate balance is the main challenge.

 JE: I think that theoretical physicists could propose a framework with boundaries that AI could explore. We could tell you what sort of particles are allowed, what sort of interactions those could have and what would still be a well-behaved theory from the point of view of relativity and quantum mechanics. Then, let’s just release the AI to see whether it can come up with a combination of particles and interactions that could solve our problems. I think that in this sort of problem space, the creativity would come in the testing of the theory. The AI might find a particle and a set of interactions that would deal with the anomalies that I was talking about, but how do we know what’s the right theory? We have to propose some other experiments that might test it – and that’s one place where the creativity of theoretical physicists will come into play.

 AA: Absolutely. And many theories are not directly testable. That’s where the deeper knowledge and intuition that theoretical physicists have is so critical.

Is human creativity driven by our consciousness, or can contemporary AI be creative? 

AA: Humans are creative in so many ways. We can dream, we can hallucinate, we can create – so how do we build those capabilities into AI? Richard Feynman famously said “What I cannot create, I do not understand.” It appears that our creativity gives us the ability to understand the complex inner workings of the universe. With the current AI paradigm this is very difficult. Current AI is geared towards scenarios where the training and testing distributions are similar, however, creativity requires extrapolation – being able to imagine entirely new scenarios. So extrapolation is an essential aspect. Can you go from what you have learned and extrapolate new scenarios? For that we need some form of invariance or understanding of the underlying laws. That’s where physics is front and centre. Humans have intuitive notions of physics from early childhood. We slowly pick them up from physical interactions with the world. That understanding is at the heart of getting AI to be creative.

 JE: It is often said that a child learns more laws of physics than an adult ever will! As a human being, I think that I think. I think that I understand. How can we introduce those things into AI?

Could AI rediscover the Standard Model?

 AA: We need to get AI to create images, and other kinds of data it experiences, and then reason about the likelihood of the samples. Is this data point unlikely versus another one? Similarly to what we see in the brain, we recently built feedback mechanisms into AI systems. When you are watching me, it’s not just a free-flowing system going from the retina into the brain; there’s also a feedback system going from the inferior temporal cortex back into the visual cortex. This kind of feedback is fundamental to us being conscious. Building these kinds of mechanisms into AI is the first step to creating conscious AI.

 JE: A lot of the things that you just mentioned sound like they’re going to be incredibly useful going forward in our systems for analysing data. But how is AI going to devise an experiment that we should do? Or how is AI going to devise a theory that we should test?

 AA: Those are the challenging aspects for an AI. A data-driven method using a standard neural network would perform really poorly. It will only think of the data that it can see and not about data that it hasn’t seen – what we call “zero-short generalisation”. To me, the past decade’s impressive progress is due to a trinity of data, neural networks and computing infrastructure, mainly powered by GPUs [graphics processing units], coming together: the next step for AI is a wider generalisation to the ability to extrapolate and predict hitherto unseen scenarios.

Across the many tens of orders of magnitude described by modern physics, new laws and behaviours “emerge” non-trivially in complexity (see Emergence). Could intelligence also be an emergent phenomenon?

JE: As a theoretical physicist, my main field of interest is the fundamental building blocks of matter, and the roles that they play very early in the history of the universe. Emergence is the word that we use when we try to capture what happens when you put many of these fundamental constituents together, and they behave in a way that you could often not anticipate if you just looked at the fundamental laws of physics. One of the interesting developments in physics over the past generation is to recognise that there are some universal patterns that emerge. I’m thinking, for example, of phase transitions that look universal, even though the underlying systems are extremely different. So, I wonder, is there something similar in the field of intelligence? For example, the brain structure of the octopus is very different from that of a human, so to what extent does the octopus think in the same way that we do?

 AA: There’s a lot of interest now in studying the octopus. From what I learned, its intelligence is spread out so that it’s not just in its brain but also in its tentacles. Consequently, you have this distributed notion of intelligence that still works very well. It can be extremely camouflaged – imagine being in a wild ocean without a shell to protect yourself. That pressure created the need for intelligence such that it can be extremely aware of its surroundings and able to quickly camouflage itself or manipulate different tools.

 JE: If intelligence is the way that a living thing deals with threats and feeds itself, should we apply the same evolutionary pressure to AI systems? We threaten them and only the fittest will survive. We tell them they have to go and find their own electricity or silicon or something like that – I understand that there are some first steps in this direction, computer programs competing with each other at chess, for example, or robots that have to find wall sockets and plug themselves in. Is this something that one could generalise? And then intelligence could emerge in a way that we hadn’t imagined?

Similarly to what we see in the brain, we recently built feedback mechanisms into AI systems

 AA: That’s an excellent point. Because what you mentioned broadly is competition – different kinds of pressures that drive towards good, robust objectives. An example is generative adversarial models, which can generate very realistic looking images. Here you have a discriminator that challenges the generator to generate images that look real. These kinds of competitions or games are getting a lot of traction and we have now passed the Turing test when it comes to generating human faces – you can no longer tell very easily whether it is generated by AI or if it is a real person. So, I think those kinds of mechanisms that have competition built into the objective they optimise are fundamental to creating more robust and more intelligent systems.

 JE: All this is very impressive – but there are still some elements that I am missing, which seem very important to theoretical physics. Take chess: a very big system but finite nevertheless. In some sense, what I try to do as a theoretical physicist has no boundaries. In some sense, it is infinite. So, is there any hope that AI would eventually be able to deal with problems that have no boundaries?

 AA: That’s the difficulty. These are infinite-dimensional spaces… so how do we decide how to move around there? What distinguishes an expert like you from an average human is that you build your knowledge and develop intuition – you can quickly make judgments and find which narrow part of the space you want to work on compared to all the possibilities. That’s the aspect that is so difficult for AI to figure out. The space is enormous. On the other hand, AI does have a lot more memory, a lot more computational capacity. So can we create a hybrid system, with physicists and machine learning in tandem, to help us harness the capabilities of both AI and humans together? We’re currently exploring theorem provers: can we use the theorems that humans have proven, and then add reinforcement learning on top to create very fast theorem solvers? If we can create such fast theorem provers in pure mathematics, I can see them being very useful for understanding the Standard Model and the gaps and discrepancies in it. It is much harder than chess, for example, but there are exciting programming frameworks and data sets available, with efforts to bring together different branches of mathematics. But I don’t think humans will be out of the loop, at least for now.

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LLP9 played host to six new results, three each from ATLAS and CMS. These included a remarkable new ATLAS paper searching for stopped particles – beyond-the-Standard Model (BSM) LLPs that can be produced in a proton–proton collision and then get stuck in the detector before decaying minutes, days or weeks later. Good hypothetical examples are the so-called gluino R-hadrons that occur in supersymmetric models. Also featured was a new CMS search for displaced di-muon resonances using “data scouting” – a unique method of increasing the number of potential signal events kept at the trigger level by reducing the event information that is retained. Both experiments presented new results searching for the Higgs boson decaying to LLPs (see “LLP candidate” figure).

Long-lived particles can also be produced in a collision inside ATLAS, CMS or LHCb and live long enough to drift entirely outside of the detector volume. To ensure that this discovery avenue is also covered for the future of the LHC’s operation, there is a rich set of dedicated LLP detectors either approved or proposed, and LLP9 featured updates from MoEDAL, FASER, MATHUSLA, CODEX-b, MilliQan, FACET and SND@LHC, as well as a presentation about the proposed forward physics facility for the High-Luminosity LHC (HL-LHC).

Reinterpreting machine learning

The liveliest parts of any LLP community workshop are the brainstorming and hands-on working-group sessions. LLP9 included multiple vibrant discussions and working sessions, including on heavy neutral leptons and the ability of physicists who are not members of experimental collaborations to be able to re-interpret LLP searches – a key issue for the LLP community. At LLP9, participants examined the challenges inherent in re-interpreting LLP results that use machine learning techniques, by now a common feature of particle-physics analyses. For example, boosted decision trees (BDTs) and neural networks (NNs) can be quite powerful for either object identification or event-level discrimination in LLP searches, but it’s not entirely clear how best to give theorists access to the full original BDT or NN used internally by the experiments.

LLP searches at the LHC often must also grapple with background sources that are negligible for the majority of searches for prompt objects. These backgrounds – such as cosmic muons, beam-induced backgrounds, beam-halo effects and cavern backgrounds – are reasonably well-understood for Run 2 and Run 3, but little study has been performed for the upcoming HL-LHC, and LLP9 featured a brainstorming session about what such non-standard backgrounds might look like in the future.

Also looking to the future, two very forward-thinking working-group sessions were held on LLPs at a potential future muon collider and at the proposed Future Circular Collider (FCC). Hadron collisions at ~100 TeV in FCC-hh would open up completely unprecedented discovery potential, including for LLPs, but it’s unclear how to optimise detector designs for both LLPs and the full slate of prompt searches.

Simulating dark showers is a longstanding challenge

Finally, LLP9 hosted an in-depth working-group session dedicated to the simulation of “dark showers”, in collaboration with the organisers of the dark-showers study group connected to the Snowmass process, which is currently shaping the future of US particle physics. Dark showers are a generic and poorly understood feature of a potential BSM dark sector with similarities to QCD, which could have its own “dark hadronisation” rules. Simulating dark showers is a longstanding challenge. More than 50 participants joined for a hands-on demonstration of simulation tools and a discussion of the dark-showers Pythia module, highlighting the growing interest in this subject in the LLP community.

LLP9 was raucous and stimulating, and identified multiple new avenues of research. LLPX, the tenth workshop in the series, will be held in November this year.

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The LHCP format traditionally has plenary sessions in the mornings and late afternoons, with parallel sessions in the middle of the day. This “shape” was kept for the online meeting, with a shorter day to improve the practicality of joining from distant time zones. This resulted in a dense format with seven-fold parallel sessions, allowing all parts of the LHC programme, both experimental and theoretical, to be explored in detail. The overall vitality of the programme is illustrated by the raw statistics: a grand total of 238 talks and 122 posters were presented.

Last year saw a strong focus on the couplings to the second generation

Nine years on from the discovery of the 125 GeV Higgs boson, measurements have progressed to a new level of precision with the full Run-2 data. Both ATLAS and CMS presented new results on Higgs production, helping constrain the dynamics of the production mechanisms via differential and “simplified template” cross-section measurements. While the couplings of the Higgs to third-generation fermions are now established, last year saw a strong focus on the couplings to the second generation. After first evidence for Higgs decays to muons was reported from CMS and ATLAS results earlier in the year, ATLAS presented a new search with the full Run-2 data for Higgs decays to charm quarks using powerful new charm-tagging techniques. Both CMS and ATLAS showed updated searches for Higgs-pair production, with ATLAS being able to exclude a production rate more than 4.1 times the Standard Model (SM) prediction at 95% confidence. This is a process that should be observable with High-Luminosity LHC statistics, if it is as predicted in the SM. A host of searches were also reported, some using the Higgs as a tool to probe for new physics.

Puzzling hints

The most puzzling hints from the LHC Run 1 seem to strengthen in Run 2. LHCb presented analyses relating to the “flavour anomalies” found most notably in b→sµ⁺µ⁻ decays, updated to the full data statistics, in multiple channels. While no result yet passes a 5σ difference from SM expectations, the significances continue to creep upwards. Searches by ATLAS and CMS for potential new particles or effects at high masses that could indicate an associated new-physics mechanism continue to draw a blank, however. This remains a dilemma to be studied with more precision and data in Run 3. Other results in the flavour sector from LHCb included a new measurement of the lifetime of the Ω_c, four times longer than previous measurements (CERN Courier July/August 2021 p17) and the first observation of a mass difference between the mixed D⁰–D⁰ meson mass eigenstates (CERN Courier July/August 2021 p8).

A wealth of results was presented from heavy-ion collisions. Measurements with heavy quarks were prominent here as well. ALICE reported various studies of the differences in heavy-flavour hadron production in proton–proton and heavy-ion collisions, for example using D mesons. CMS reported the first observation of B_c meson production in heavy-ion collisions, and also first evidence for top-quark pair production in lead–lead collisions. ATLAS used heavy-flavour decays to muons to compare suppression of b- and c-hadron production in lead–lead and proton–proton collisions. Beyond the ions, ALICE also showed intriguing new results demonstrating that the relative rates of different types of c-hadron production differ in proton–proton collisions compared to earlier experiments using e⁺e⁻ and ep collisions at LEP and HERA.

Looking forward, the experiments reported on their preparations for the coming LHC Run 3, including substantial upgrades. While some work has been slowed by the pandemic, recommissioning of the detectors has begun in preparation for physics data taking in spring 2022, with the brighter beams expected from the upgraded CERN accelerator chain. One constant to rely on, however, is that LHCP will continue to showcase the fantastic panoply of physics at the LHC.

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More than a century after its discovery, the proton remains a source of intrigue, its charge-radius and spin posing puzzles that are the focus of intense study. But what of its mortal sibling, the neutron? In recent years, discrepancies between measurements of the neutron lifetime using different methods constitute a puzzle with potential implications for cosmology and particle physics. The neutron lifetime determines the ratio of protons to neutrons at the beginning of big-bang nucleosynthesis and thus affects the yields of light elements, and it is also used to determine the CKM matrix-element V_ud in the Standard Model.

The neutron-lifetime puzzle stems from measurements using two techniques. The “bottle” method counts the number of surviving ultra-cold neutrons contained in a trap after a certain period, while the “beam” method uses the decay probability of the neutron obtained from the ratio of the decay rate to an incident neutron flux. Back in the 1990s, the methods were too imprecise to worry about differences between the results. Today, however, the average neutron lifetime measured using the bottle and beam methods, 879.4 ± 0.4 s and 888.0 ± 2.0 s, respectively, stand 8.6 s (or 4σ) apart. 

We think it will take two years to obtain a competitive result from our experiment

Kenji Mishima

In an attempt to shed light on the issue, a team at Japan’s KEK laboratory in collaboration with Japanese universities has developed a new experimental setup. Similar to the beam method, it compares the decay rate to the reaction rate of neutrons in a pulsed beam from the Japan Proton Accelerator Research Complex (J-PARC). The decay rate and the reaction rate are determined by simultaneously detecting electrons from the neutron decay and protons from the reaction ³He → ³H in a 1 m-long time-projection chamber containing diluted ³He, removing some of the systematic uncertainties that affect previous beam methods. The experiment is still in its early stages, and while the first results have been released – τ_n = 898 ± 10(stat)⁺¹⁵_–18 (sys) s – the uncertainty is currently too large to draw conclusions.

“In the current situation, it is important to verify the puzzle by experiments in which different systematic errors dominate,” says Kenji Mishima of KEK, adding that further improvements in the statistical and systematic uncertainties are underway. “We think it will take two years to obtain a competitive result from our experiment.”

Several new-physics scenarios have been proposed as solutions of the neutron lifetime puzzle. These include exotic decay modes involving undetectable particles with a branching ratio of about 1%, such as “mirror neutrons” or dark-sector particles. 

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Recent measurements bolstering the longstanding tension between the experimental and theoretical values of the muon’s anomalous magnetic moment generated a buzz in the community. Though with a much lower significance, a similar puzzle may also be emerging for the anomalous magnetic moment of the electron, a_e.

Depending on which of two recent independent measurements of the fine-structure constant is used in the theoretical calculation of a_e – one obtained at Berkeley in 2018 or the other at Kastler–Brossel Laboratory in Paris in 2020 – the Standard Model prediction stands 2.4σ higher or 1.6σ lower than the best experimental value, respectively. Motivated by this inconsistency, the NA64 collaboration at CERN set out to investigate whether new physics – in the form of a lightweight “X boson” – might be influencing the electron’s behaviour.

The generic X boson could be a sub- GeV scalar, pseudoscalar, vector or axial- vector particle. Given experimental constraints on its decay modes involving Standard Model particles, it is presumed to decay predominantly invisibly, for example into dark-sector particles. NA64 searches for X bosons by directing 100 GeV electrons generated by the SPS onto a target, and looking for missing energy in the detector via electron–nuclei scattering e^–Z → e^–ZX.

The result sets new bounds on the e^–X interaction strength

Analysing data collected in 2016, 2017 and 2018, corresponding to about 3 × 10¹¹ electrons-on-target, the NA64 team found no evidence for such events. The result sets new bounds on the e^–X interaction strength and, as a result, on the contributions of X bosons to a_e: X bosons with a mass below 1 GeV could contribute at most between one part in 10¹⁵ and one part in 10¹³, depending on the X-boson type and mass. These contributions are too small to explain the current anomaly in the electron’s anomalous magnetic moment, says NA64 spokesperson Sergei Gninenko. “But the fact that NA64 reached an experimental sensitivity that is better than the current accuracy of the direct measurements of a_e, and of recent high-precision measurements of the fi ne-structure constant, is amazing.”

In a separate analysis, the NA64 team carried out a model-independent search for a particular pseudoscalar X boson with a mass of around 17 MeV. Coupling to electrons and decaying into e⁺e^– pairs, the so-called “X17” has been proposed to explain an excess of e⁺e^– pairs created during nuclear transitions of excited ⁸Be and ⁴He nuclei reported by the “ATOMKI” experiment in Hungary since 2015.

The e-X17 coupling strength is constrained by data: too large and the X17 would contribute too much to a_e; too small and the X17 would decay too rarely and too far away from the ATOMKI target. In 2019, the NA64 team excluded a large range of couplings, although at large values, for a vector-like X17. More recently, they searched for a pseudoscalar X17, which has a lifetime about half that of the vector version for the same coupling strength. Re-analysing a sample of approximately 8.4 × 10¹⁰ electrons-on-target collected in 2017 and 2018 with 100 and 150 GeV electrons, respectively, the collaboration has now excluded couplings in the range 2.1–3.2 × 10^–4 for a 17 MeV X-boson.

“We plan to further improve the sensitivity to vector and pseudoscalar X17’s after long shutdown 2, and also try to reconstruct the mass of X17, to be sure that if we see the signal it is the ATOMKI boson,” says Gninenko.

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The Higgs boson was hypothesised to explain electroweak symmetry breaking nearly 50 years before its discovery. Its eventual discovery at the LHC took half a century of innovative accelerator and detector development, and extensive data analysis. Today, several outstanding questions in particle physics could be answered by higgsinos – theorised supersymmetric partners of an extended Higgs field. The higgsinos are a triplet of electroweak states, two neutral and one charged. If the lightest neutral state is stable, it can provide an explanation of astronomically observed dark matter. Furthermore, an intimate connection between higgsinos and the Higgs boson could explain why the mass of the Higgs boson is so much lighter than suggested by theoretical arguments. While higgsinos may not be much heavier than the Higgs boson, they would be produced more rarely and are significantly more challenging to find, especially if they are the only supersymmetric particles near the electroweak scale.

Higgsinos mix with other supersymmetric electroweak states, the wino and the bino, to form the physical particles that would be observed

The ATLAS collaboration recently released a set of results based on the full LHC Run 2 dataset that explore some of the most challenging experimental scenarios involving higgsinos. Each result tests different assumptions. Owing to quantum degeneracy, the higgsinos mix with other supersymmetric electroweak states, the wino and the bino, to form the physical particles that would be observed by the experiment. The mass difference between the lightest neutral and charged states, ∆m, depends on this mixing. Depending on the model assumptions, the phenomenology varies dramatically, requiring different analysis techniques and stimulating the development of new tools.

If ∆m is only a few hundred MeV, the small phase space suppresses the decay from the heavier states to the lightest one. The long-lived charged state flies partway through the inner tracker before decaying, and its short track can be measured. A search targeting this anomalous “disappearing track” signature was performed by exploiting novel requirements on the quality of the signal candidate and the ability of the ATLAS inner detectors to reconstruct short tracks. Finding that the number of short tracks is as expected from background processes alone, this search rules out higgsinos with lifetimes of a fraction of a nanosecond for masses up to 210 GeV.

If higgsinos mix somewhat with other supersymmetric electroweak states, they will decay promptly to the lightest stable higgsino and low-energy Standard Model particles. These soft decay products are extremely challenging to detect at the LHC, and ATLAS has performed several searches for events with two or three leptons to maximise the sensitivity to different values of ∆m. Each search features innovative optimisation and powerful discriminants to reject background. For the first time, ATLAS has performed a statistical combination of these searches, constraining higgsino masses to be larger than 150 GeV for ∆m above 2 GeV.

A final result targets higgsinos in models in which the lightest supersymmetric particle is not stable. In these scenarios, higgsinos may decay to triplets of quarks. A search designed around an adversarial neural network and employing a completely data-driven background estimation technique was developed to distinguish these rare decays from the overwhelming multi-jet background. This search is the first at the LHC to obtain sensitivity to this higgsino model, and rules out scenarios of the pair production of higgsinos with masses between 200 and 320 GeV (figure 1). 

Together, these searches set significant constraints on higgsino masses, and for certain parameters provide the first extension of sensitivity since LEP. With the development of new techniques and more data to come, ATLAS will continue to seek higgsinos at higher masses, and to test other theoretical and experimental assumptions.

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The ATLAS, CMS and LHCb collaborations perform precise measurements of Standard Model (SM) processes and direct searches for physics beyond the Standard Model (BSM) in a vast variety of channels. Despite the multitude of BSM scenarios tested this way by the experiments, it still constitutes only a small subset of the possible theories and parameter combinations to which the experiments are sensitive. The (re)interpretation of the LHC results in order to fully understand their implications for new physics has become a very active field, with close theory–experiment interaction and with new computational tools and related infrastructure being developed. 

From 15 to 19 February, almost 300 theorists and experimental physicists gathered for a week-long online workshop to discuss the latest developments. The topics covered ranged from advances in public software packages for reinterpretation to the provision of detailed analysis information by the experiments, from phenomenological studies to global fits, and from long-term preservation to public data.

Open likelihoods

One of the leading questions throughout the workshop was that of public likelihoods. The statistical model of an experimental analysis provides its complete mathematical description; it is essential information for determining the compatibility of the observations with theoretical predictions. In his keynote talk “Open science needs open likelihoods’’, Harrison Prosper (Florida State University) explained why it is in our scientific interest to make the publication of full likelihoods routine and straightforward. The ATLAS collaboration has recently made an important step in this direction by releasing full likelihoods in a JSON format, which provides background estimates, changes under systematic variations, and observed data counts at the same fidelity as used in the experiment, as presented by Eric Schanet (LMU Munich). Matthew Feickert (University of Illinois) and colleagues gave a detailed tutorial on how to use these likelihoods with the pyhf python package. Two public reinterpretation tools, MadAnalysis5 presented by Jack Araz (IPPP Durham) and SModelS presented by Andre Lessa (UFABC Santo Andre) can already make use of pyhf and JSON likelihoods, and others are to follow. An alternative approach to the plain-text JSON serialisation is to encode the experimental likelihood functions in deep neural networks, as discussed by Andrea Coccaro (INFN Genova) who presented the DNNLikelihood framework. Several more contributions from CMS, LHCb and from theorists addressed the question of how to present and use likelihood information, and this will certainly stay an active topic at future workshops.  

The question of making research data findable, accessible, interoperable and reusable is a burning one throughout modern science

A novelty for the Reinterpretation workshop was that the discussion was extended to experiences and best practices beyond the LHC, to see how experiments in other fields address the need for publicly released data and reusable results. This included presentations on dark-matter direct detection, the high-intensity frontier, and neutrino oscillation experiments. Supporting Prosper’s call for data reusability 40 years into the future – “for science 2061” – Eligio Lisi (INFN Bari) pointed out the challenges met in reinterpreting the 1998 Super-Kamiokande data, initially published in terms of the then-sufficient two-flavour neutrino-oscillation paradigm, in terms of contemporary three-neutrino descriptions, and beyond. On the astrophysics side, the LIGO and Virgo collaborations actively pursue an open-science programme. Here, Agata Trovato (APC Paris) presented the Gravitational Wave Open Science Center, giving details on the available data, on their format and on the tools to access them. An open-data policy also exists at the LHC, spearheaded by the CMS collaboration, and Edgar Carrera Jarrin (USF Quito) shared experiences from the first CMS open-data workshop. 

The question of making research data findable, accessible, interoperable and reusable (“FAIR” in short) is a burning one throughout modern science. In a keynote talk, the head of the GO FAIR Foundation, Barend Mons, explained the FAIR Guiding Principles together with the technical and social aspects of FAIR data management and data reuse, using the example of COVID-19 disease modelling. There is much to be learned here for our field. 

The wrap-up session revolved around the question of how to implement the recommendations of the Reinterpretation workshop in a more systematic way. An important aspect here is the proper recognition, within the collaborations as well as the community at large, of the additional work required to this end. More rigorous citation of HEPData entries by theorists may help in this regard. Moreover, a “Reinterpretation: Auxiliary Mat­erial Presentation” (RAMP) seminar series will be launched to give more visibility and explicit recognition to the efforts of preparing and providing extensive mat­erial for reinterpretation. The first RAMP meetings took place on 9 and 23 April.

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It has been almost a century since Dirac formulated his famous equation, and 75 years since the first QED calculations by Schwinger, Tomonaga and Feynman were used to explain the small deviations in hydrogen’s hyperfine structure. These calculations also predicted that deviations from Dirac’s prediction a = (g–2)/2, where g is the gyromagnetic ratio e/2m_e, should be non-zero and thus “anomalous”. The result is famously engraved on Schwinger’s tombstone, standing as a monument to the importance of this result and a marker of things to come.

In January 1957 Garwin and collaborators at Columbia published the first measurements of g for the recently discovered muon, accurate to 5%, followed two months later by Cassels and collaborators at Liverpool with uncertainties of less than 1%. Leon Lederman is credited with initiating the CERN campaign of g–2 experiments from 1959 to 1979, starting with a borrowed 83 × 52 × 10 cm magnet from Liverpool and ending with a dedicated storage ring and a precision of better than 10 ppm.

Why was CERN so interested in the muon? In a 1981 review, Combley, Farley and Picasso commented that the CERN results for a_μ had a higher sensitivity to new physics by “a modification to the photon propagator or new couplings” by a factor (m_μ/m_e)². Revealing a deeper interest, they also admitted “… this activity has brought us no nearer to the understanding of the muon mass [200 times that of the electron].”

With the end of the CERN muon programme, focus turned to Brookhaven and the E821 experiment, which took up the challenge of measuring a_μ 20 times more precisely, providing sensitivity to virtual particles with masses beyond the reach of the colliders at the time. In 2004 the E821 collaboration delivered on its promise, reporting results accurate to about 0.6 ppm. At the time this showed a 2–3σ discrepancy with respect to the Standard Model (SM) – tantalising, but far from conclusive.

Spectacular progress
The theoretical calculation of g–2 made spectacular progress in step with experiment. Almost eclipsed by the epic 2012 achievement of calculating the QED contributions to five loops from 12,672 Feynman diagrams, huge advances in calculating the hadronic vacuum polarisation contributions to a_μ have been made. A reappraisal of the E821 data using this information suggested at least a 3.5σ discrepancy with the SM. It was this that provided the impetus to Lee Roberts and colleagues to build the improved muon g–2 experiments at Fermilab, the first results from which are described in this issue, and at J-PARC. Full results from the Fermilab experiment alone should reduce the a_μ uncertainties by at least another factor of three – down to a level that really challenges what we know about the SM.

Muon g–2 is a clear demonstration that theory and experiment must progress hand in hand

Of course, the interpretation of the new results relies on the choice of theory baseline. For example, one could choose, as the Fermilab experiment has, to use the consensus “International Theory Initiative” expectation for a_μ. One could also take into account the new results provided by LHCb’s recent R_K measurement, which hint that muons might behave differently than electrons. There will inevitably be speculation over the coming months about the right approach. Whatever one’s choice, muon g–2 is a clear demonstration that theory and experiment must progress hand in hand.

Perhaps the most important lesson is the continued cross-fertilisation and impetus to the physics delivered both at CERN and at Fermilab by recent results. The g–2 experiment, an international collaboration between dozens of labs and universities in seven countries, has benefited from students who cut their teeth on LHC experiments. Likewise, students who have worked at the precision frontier at Fermilab are now armed with the expertise of making blinded ppm measurements and are keen to see how they can make new measurements at CERN, for example at the proposed MUonE experiment, or at other muon experiments due to come online this decade.

“It remains to be seen whether or not future refinement of the [SM] will call for the discerning scrutiny of further measurements of even greater precision,” concluded Combley, Farley and Picasso in their 1981 review – a wise comment that is now being addressed.

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A fermion’s spin tends to twist to align with a magnetic field – an effect that becomes dramatically macroscopic when electron spins twist together in a ferromagnet. Microscopically, the tiny magnetic moment of a fermion interacts with the external magnetic field through absorption of photons that comprise the field. Quantifying this picture, the Dirac equation predicts fermion magnetic moments to be precisely two in units of Bohr magnetons, e/2m. But virtual lines and loops add an additional 0.1% or so to this value, giving rise to an “anomalous” contribution known as “g–2” to the particle’s magnetic moment, caused by quantum fluctuations. Calculated to tenth order in quantum electrodynamics (QED), and verified experimentally to about two parts in 10¹⁰, the electron’s magnetic moment is one of the most precisely known numbers in the physical sciences. While also measured precisely, the magnetic moment of the muon, however, is in tension with the Standard Model.

Tricky comparison

The anomalous magnetic moment of the muon was first measured at CERN in 1959, and prior to 2021, was most recently measured by the E821 experiment at Brookhaven National Laboratory (BNL) 16 years ago. The comparison between theory and data is much trickier than for electrons. Being short-lived, muons are less suited to experiments with Penning traps, whereby stable charged particles are confined using static electric and magnetic fields, and the trapped particles are then cooled to allow precise measurements of their properties. Instead, experiments infer how quickly muon spins precess in a storage ring – a situation similar to the wobbling of a spinning top, where information on the muon’s advancing spin is encoded in the direction of the electron that is emitted when it decays. Theoretical calculations are also more challenging, as hadronic contributions are no longer so heavily suppressed when they emerge as virtual particles from the more massive muon.

All told, our knowledge of the anomalous magnetic moment of the muon is currently three orders of magnitude less precise than for electrons. And while everything tallies up, more or less, for the electron, BNL’s longstanding measurement of the magnetic moment of the muon is 3.7σ greater than the Standard Model prediction (see panel “Rising to the moment”). The possibility that the discrepancy could be due to virtual contributions from as-yet-undiscovered particles demands ever more precise theoretical calculations. This need is now more pressing than ever, given the increased precision of the experimental value expected in the next few years from the Muon g–2 collaboration at Fermilab in the US and other experiments such as the Muon g–2/EDM collaboration at J-PARC in Japan. Hotly anticipated results from the first data run at Fermilab’s E989 experiment were released on 7 April. The new result is completely consistent with the BNL value but with a slightly smaller error, leading to a slightly larger discrepancy of 4.2σ with the Standard Model when the measurements are combined (see Fermilab strengthens muon g-2 anomaly).

Hadronic vacuum polarisation

The value of the muon anomaly, a_μ, is an important test of the Standard Model because currently it is known very precisely – to roughly 0.5 parts per million (ppm) – in both experiment and theory. QED dominates the value of a_μ, but due to the non-perturbative nature of QCD it is strong interactions that contribute most to the error. The theoretical uncertainty on the anomalous magnetic moment of the muon is currently dominated by so-called hadronic vacuum polarisation (HVP) diagrams. In HVP, a virtual photon briefly explodes into a “hadronic blob”, before being reabsorbed, while the magnetic-field photon is simultaneously absorbed by the muon. While of order α² in QED, it is all orders in QCD, making for very difficult calculations.

Rising to the moment

In the Standard Model, the magnetic moment of the muon is computed order-by-order in powers of a for QED (each virtual photon represents a factor of α), and to all orders in as for QCD.

At the lowest order in QED, the Dirac term (pictured left) accounts for precisely two Bohr magnetons and arises purely from the muon (μ) and the real external photon (γ) representing the magnetic field.

 

At higher orders in QED, virtual Standard Model particles, depicted by lines forming loops, contribute to a fractional increase of aμ with respect to that value: the so-called anomalous magnetic moment of the muon. It is defined to be a_μ = (g–2)/2, where g is the gyromagnetic ratio of the muon – the number of Bohr magnetons, e/2m, which make up the muon’s magnetic moment. According to the Dirac equation, g = 2, but radiative corrections increase its value.

The biggest contribution is from the Schwinger term (pictured left, O(α)) and higher-order QED diagrams.

 

a_μ^QED = (116 584 718.931 ± 0.104) × 10^–11

Electroweak lines (pictured left) also make a well-defined contribution. These diagrams are suppressed by the heavy masses of the Higgs, W and Z bosons.

a_μ^EW = (153.6 ± 1.0) × 10–11

The biggest QCD contribution is due to hadronic vacuum polarisation (HVP) diagrams. These are computed from leading order (pictured left, O(α²)), with one “hadronic blob” at all orders in as (shaded) up to next-to-next-to-leading order (NNLO, O(α⁴), with three hadronic blobs) in the HVP.

 

 

Hadronic light-by-light scattering (HLbL, pictured left at O(α³) and all orders in α_s (shaded)), makes a smaller contribution but with a larger fractional uncertainty.

 

 

 

Neglecting lattice–QCD calculations for the HVP in favour of those based on e⁺e^– data and phenomenology, the total anomalous magnetic moment is given by

a_μ^SM = a_μ^QED + a_μ^EW + a_μ^HVP + a_μ^HLbL = (116 591 810 ± 43) × 10^–11.

This is somewhat below the combined value from the E821 experiment at BNL in 2004 and the E989 experiment at Fermilab in 2021.

a_μ^exp = (116 592 061 ± 41) × 10^–11

The discrepancy has roughly 4.2σ significance:

a_μ^exp– a_μ^SM = (251 ± 59) × 10^–11.

Historically, and into the present, HVP is calculated using a dispersion relation and experimental data for the cross section for e⁺e^– → hadrons. This idea was born of necessity almost 60 years ago, before QCD was even on the scene, let alone calculable. The key realisation is that the imaginary part of the vacuum polarisation is directly related to the hadronic cross section via the optical theorem of wave-scattering theory; a dispersion relation then relates the imaginary part to the real part. The cross section is determined over a relatively wide range of energies, in both exclusive and inclusive channels. The dominant contribution – about three quarters – comes from the e⁺e^– → π⁺π^– channel, which peaks at the rho meson mass, 775 MeV. Though the integral converges rapidly with increasing energy, data are needed over a relatively broad region to obtain the necessary precision. Above the τ mass, QCD perturbation theory hones the calculation.

Several groups have computed the HVP contribution in this way, and recently a consensus value has been produced as part of the worldwide Muon g–2 Theory Initiative. The error stands at about 0.58% and is the dominant part of the theory error. It is worth noting that a significant part of the error arises from a tension between the most precise measurements, by the BaBar and KLOE experiments, around the rho–meson peak. New measurements, including those from experiments at Novosibirsk, Russia and Japan’s Belle II experiment, may help resolve the inconsistency in the current data and reduce the error by a factor of two or so. 

The alternative approach, of calculating the HVP contribution from first principles using lattice QCD, is not yet at the same level of precision, but is getting there. Consistency between the two approaches will be crucial for any claim of new physics.

Lattice QCD

Kenneth Wilson formulated lattice gauge theory in 1974 as a means to rid quantum field theories of their notorious infinities – a process known as regulating the theory – while maintaining exact gauge invariance, but without using perturbation theory. Lattice QCD calculations involve the very large dimensional integration of path integrals in QCD. Because of confinement, a perturbative treatment including physical hadronic states is not possible, so the complete integral, regulated properly in a discrete, finite volume, is done numerically by Monte Carlo integration.

Lattice QCD has made significant improvements over the last several years, both in methodology and invested computing time. Recently developed methods (which rely on low-lying eigenmodes of the Dirac operator to speed up calculations) have been especially important for muon–anomaly calculations. By allowing state-of-the-art calculations using physical masses, they remove a significant systematic: the so-called chiral extrapolation for the light quarks. The remaining systematic errors arise from the finite volume and non-zero lattice spacing employed in the simulations. These are handled by doing multiple simulations and extrapolating to the infinite-volume and zero-lattice-spacing limits. 

The HVP contribution can readily be computed using lattice QCD in Euclidean space with space-like four-momenta in the photon loop, thus yielding the real part of the HVP directly. The dispersive result is currently more precise (see “Off the mark” figure”), but further improvements will depend on consistent new e⁺e^– scattering datasets.

Rapid progress in the last few years has resulted in first lattice results with sub-percent uncertainty, closing in on the precision of the dispersive approach. Since these lattice calculations are very involved and still maturing, it will be crucial to monitor the emerging picture once several precise results with different systematic approaches are available. It will be particularly important to aim for statistics-dominated errors to make it more straightforward to quantitatively interpret the resulting agreement with the no-new-physics scenario or the dispersive results. In the shorter term, it will also be crucial to cross-check between different lattice and dispersive results using additional observables, for example based on the vector–vector correlators.

With improved lattice calculations in the pipeline from a number of groups, the tension between lattice QCD and phenomenological calculations may well be resolved before the Fermilab and J-PARC experiments announce their final results. Interestingly, there is a new lattice result with sub-percent precision (BMW 2020) that is in agreement both with the no-new-physics point within 1.3σ, and with the dispersive-data-driven result within 2.1σ. Barring a significant re-evaluation of the phenomenological calculation, however, HVP does not appear to be the source of the discrepancy with experiments. 

The next most likely Standard Model process to explain the muon anomaly is hadronic light-by-light scattering. Though it occurs less frequently since it includes an extra virtual photon compared to the HVP contribution, it is much less well known, with comparable uncertainties to HVP.

Hadronic light-by-light scattering

In hadronic light-by-light scattering (HLbL), the magnetic field interacts not with the muon, but with a hadronic “blob”, which is connected to the muon by three virtual photons. (The interaction of the four photons via the hadronic blob gives HLbL its name.) A miscalculation of the HLbL contribution has often been proposed as the source of the apparently anomalous measurement of the muon anomaly by BNL’s E821 collaboration.

Since the so-called Glasgow consensus (the fruit of a 2009 workshop) first established a value more than 10 years ago, significant progress has been made on the analytic computation of the HLbL scattering contribution. In particular, a dispersive analysis of the most important hadronic channels has been carried out, including the leading pion–pole, sub-leading pion loop and rescattering diagrams including heavier pseudoscalars. These calculations are analogous in spirit to the dispersive HVP calculations, but are more complicated, and the experimental measurements are more difficult because form factors with one or two virtual photons are required. 

The project to calculate the HLbL contribution using lattice QCD began more than 10 years ago, and many improvements to the method have been made to reduce both statistical and systematic errors since then. Last year we published, with colleagues Norman Christ, Taku Izubuchi and Masashi Hayakawa, the first ever lattice–QCD calculation of the HLbL contribution with all errors controlled, finding a_μ^{HLbL, lattice} = (78.7 ± 30.6 (stat) ± 17.7 (sys)) × 10^–11. The calculation was not easy: it took four years and a billion core-hours on the Mira supercomputer at Argonne National Laboratory’s Large Computing Facility. 

Our lattice HLbL calculations are quite consistent with the analytic and data-driven result, which is approximately a factor of two more precise. Combining the results leads to a_μ^HLbL = (90 ± 17) × 10^–11, which means the very difficult HLbL contribution cannot explain the Standard Model discrepancy with experiment. To make such a strong conclusion, however, it is necessary to have consistent results from at least two completely different methods of calculating this challenging non-perturbative quantity. 

New physics?

If current theory calculations of the muon anomaly hold up, and the new experiments reduce its uncertainty by the hoped-for factor of four, then a new-physics explanation will become impossible to ignore. The idea would be to add particles and interactions that have not yet been observed but may soon be discovered at the LHC or in future experiments. New particles would be expected to contribute to the anomaly through Feynman diagrams similar to the Standard Model topographies (see “Rising to the moment” panel).

Calculations of the anomalous magnetic moment of the muon are not finished

The most commonly considered new-physics explanation is supersymmetry, but the increasingly stringent lower limits placed on the masses of super-partners by the LHC experiments make it increasingly difficult to explain the muon anomaly. Other theories could do the job too. One popular idea that could also explain persistent anomalies in the b-quark sector is heavy scalar leptoquarks, which mediate a new interaction allowing leptons and quarks to change into each other. Another option involves scenarios whereby the Standard Model Higgs boson is accompanied by a heavier Higgs-like boson.

The calculations of the anomalous magnetic moment of the muon are not finished. As a systematically improvable method, we expect more precise lattice determinations of the hadronic contributions in the near future. Increasingly powerful algorithms and hardware resources will further improve precision on the lattice side, and new experimental measurements and analysis methods will do the same for dispersive studies of the HVP and HLbL contributions.

To confidently discover new physics requires that these two independent approaches to the Standard Model value agree. With the first new results on the experimental value of the muon anomaly in almost two decades showing perfect agreement with the old value, we anxiously await more precise measurements in the near future. Our hope is that the clash of theory and experiment will be the beginning of an exciting new chapter of particle physics, heralding new discoveries at current and future particle colliders. 

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“Today is an extraordinary day, long awaited not only by us but by the whole international physics community,” says Graziano Venanzoni of the INFN, who is co-spokesperson of the Fermilab muon g-2 collaboration. “A large amount of credit goes to our young researchers who, with their talent, ideas and enthusiasm, have allowed us to achieve this incredible result.”

Today is an extraordinary day, long awaited not only by us but by the whole international physics community

Graziano Venanzoni

The Fermilab result was unblinded during a Zoom meeting on 25 February in the presence of around 200 collaborators from around the world. “We were all very excited to finally know our result and the meeting was very emotional,” says Venanzoni. The analysis took almost three years from data taking to the release of the result and the collaboration decided to unblind only when all the steps of the analysis were completed and there were no outstanding questions. Venanzoni adds that no further analysis was completed after the unblinding and the results are unchanged.

The previous Brookhaven measurement left physicists pondering whether the presence of unknown particles in loops could be affecting the muon’s behaviour. It was clear that further measurements were needed, but it turned out to be much cheaper to move the apparatus to Fermilab than to build a new, more precise experiment at Brookhaven. So in the summer of 2013, the experiment’s 14-m diameter, 1.45 T superconducting magnet was transported from Long Island to the suburbs of Chicago. The Fermilab team reassembled the magnet and spent a year “shimming” its field, making it three times more uniform than the one it created at Brookhaven. Along with a new beamline to deliver a purer muon beam, Fermilab’s muon g-2 reincarnation required entirely new instrumentation, along with new detectors and a control room.

When a muon travels through the strong external magnetic field of a storage ring, the direction of its magnetic moment precesses at a rate that depends on its strength g. The Dirac equation predicts that all fermions have a g-factor equal to two. But higher order loops add an “anomalous” moment, a_μ = (g-2)/2, which can be calculated extremely precisely. At Fermilab, muons with an energy of about 3.1 GeV are vertically focused in the storage ring via quadrupoles, and their precession frequency is determined from decays to electrons using 24 electromagnetic calorimeters located along the ring’s inner circumference. The intense polarised muon beam suppresses the pion contamination that challenged the Brookhaven measurement, while new calibration systems and simulations allow better control of systematic uncertainties.

It is so gratifying to finally be resolving this mystery

Chris Polly

The Fermilab muon g-2 collaboration took its first dataset in 2018, with over eight billion muon decays resulting in an overall uncertainty approximately 15% better than Brookhaven’s. Data analysis on the second and third runs is already under way, while a fourth run is ongoing and a fifth is planned. The collaboration is targeting a final precision of around 0.14 ppm – four times greater than the previous measurement.

“After the 20 years that have passed since the Brookhaven experiment ended, it is so gratifying to finally be resolving this mystery,” said Fermilab’s Chris Polly, a co-spokesperson for the current experiment and a graduate student on the Brookhaven experiment. “So far we have analysed less than 6% of the data that the experiment will eventually collect. Although these first results are telling us that there is an intriguing difference with the Standard Model, we will learn much more in the next couple of years.”

Theory baseline
Developments in the theory community are equally vital. The Fermilab muon g-2 collaboration takes as its theory baseline the value for a_μ obtained last year by the Muon g-2 Theory Initiative. Uncertainties in the calculation are dominated by hadronic contributions, in particular a term called the hadronic vacuum polarization (HVP). The Theory Initiative incorporates the HVP value obtained by well-established “dispersive methods”, which combine fundamental properties of quantum field theory with experimental measurements of low-energy hadronic processes. An alternative approach gaining traction is to calculate the HVP contribution using lattice QCD. In a paper published in Nature today, one group reports lattice calculations of HVP which, if included in the theory result, would significantly reduce the discrepancy between the experimental and theoretical values for a_μ. The result is in 2σ tension with the value obtained from the dispersive approach, and is currently dominated by systematic uncertainties stemming from approximations used in the lattice calculations, say Muon g-2 Theory Initiative members.

“This being the first lattice result at sub-percent precision, it is premature to draw firm conclusions from this comparison,” reads a statement from the Muon g-2 Theory Initiative steering committee. “Indeed, given the complexity of the computations, independent results from different lattice groups with commensurate uncertainties are needed to test and check the lattice calculations against each other. Being entirely based on Standard Model theory, once the lattice results are well tested and precise enough, they will play an important role in understanding how new physics enters into the discrepancy.”

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The past century has seen ever stronger links forged between the physics of elementary particles and the universe at large. But the picture is mostly incomplete. For example, numerous observations indicate that 87% of the matter of the universe is dark, suggesting the existence of a new matter constituent. Given a plethora of dark-matter candidates, numerical tools are essential to advance our understanding. Fostering cooperation in the development of such software, the TOOLS 2020 conference attracted around 200 phenomenologists and experimental physicists for a week-long online workshop in November.

The viable mass range for dark matter spans 90 orders of magnitude, while the uncertainty about its interaction cross section with ordinary matter is even larger (see “Theoretical landscape” figure). Dark matter may be new particles belonging to theories beyond-the-Standard Model (BSM), an aggregate of new or SM particles, or very heavy objects such as primordial black holes (PBHs). On the latter subject, Jérémy Auffinger (IP2I Lyon) updated TOOLS 2020 delegates on codes for very light PBHs, noting that “BlackHawk” is the first open-source code for Hawking-radiation calculations.

Flourishing models

Weakly interacting massive particles (WIMPs) have enduring popularity as dark-matter candidates, and are amenable to search strategies ranging from colliders to astrophysical observations. In the absence of any clear detection of WIMPs at the electroweak scale, the number of models has flourished. Above the TeV scale, these include general hidden-sector models, FIMPs (feebly interacting massive particles), SIMPs (strongly interacting massive particles), super-heavy and/or composite candidates and PBHs. Below the GeV scale, besides FIMPs, candidates include the QCD axion, more generic ALPs (axion-like particles) and ultra-light bosonic candidates. ALPs are a class of models that received particular attention at TOOLS 2020, and is now being sought in fixed-target experiments across the globe.

For each dark-matter model, astro­particle physicists must compute the theoretical predictions and characteristic signatures of the model and confront those predictions with the experimental bounds to select the model parameter space that is consistent with observations. To this end, the past decade has seen the development of a huge variety of software – a trend mapped and encouraged by the TOOLS conference series, initiated by Fawzi Boudjema (LAPTh Annecy) in 1999, which has brought the community together every couple of years since.

Models connecting dark matter with collider experiments are becoming ever more optimised to the needs of users

Three continuously tested codes currently dominate generic BSM dark-matter model computations. Each allows for the computation of relic density from freeze-out and predictions for direct and indirect detection, often up to next-to-leading corrections. Agreement between them is kept below the percentage level. “micrOMEGAs” is by far the most used code, and is capable of predicting observables for any generic model of WIMPs, including those with multiple dark-matter candidates. “DarkSUSY” is more oriented towards supersymmetric theories, but it can be used for generic models as the code has a very convenient modular structure. Finally, “MadDM” can compute WIMP observables for any BSM model from MeV to hundreds of TeV. As MadDM is a plugin of MadGraph, it inherits unique features such as its automatic computation of new dark-matter observables, including indirect-detection processes with an arbitrary number of final-state particles and loop-induced processes. This is essential for analysing sharp spectral features in indirect-detection gamma-ray measurements that cannot be mimicked by any known astrophysical background.

Both micrOMEGAs and MadDM permit the user to confront theories with recast experimental likelihoods for several direct and indirect detection experiments. Jan Heisig (UCLouvain) reported that this is a work in progress, with many more experimental data sets to be included shortly. Torsten Bringmann (University of Oslo) noted that a strength of DarkSUSY is the modelling of qualitatively different production mechanisms in the early universe. Alongside the standard freeze-out mechanism, several new scenarios can arise, such as freeze-in (FIMP models, as chemical and kinetic equilibrium cannot be achieved), dark freeze-out, reannihilation and “cannibalism”, to name just a few. Freeze-in is now supported by micrOMEGAs.

Models connecting dark matter with collider experiments are becoming ever more optimised to the needs of users. For example, micrOMEGAs interfaces with SModelS, which is capable of quickly applying all possible LHC-relevant supersymmetric searches. The software also includes long-lived particles, as commonly found in FIMP models. As MadDM is embedded in MadGraph, noted Benjamin Fuks (LPTHE Paris), tools such as MadAnalysis may be used to recast CMS and ATLAS searches. Celine Degrande (UCLouvain) described another nice tool, FeynRules, which produces model files in both the MadDM and micrOMEGAs formats given the Lagrangian for the BSM model, providing a very useful automatised chain from the model directly to the dark-matter observables, high-energy predictions and comparisons with experimental results. Meanwhile, MadDump expands MadGraph’s predictions and detector simulations from the high-energy collider limits to fixed-target experiments such as NA62. To complete a vibrant landscape of development efforts, Tomas Gonzalo (Monash) presented the GAMBIT collaboration’s work to provide tools for global fits to generic dark-matter models.

A phenomenologist’s dream

Huge efforts are underway to develop a computational platform to study new directions in experimental searches for dark matter, and TOOLS 2020 showed that we are already very close to the phenomenologist’s dream for WIMPs. TOOLS 2020 wasn’t just about dark matter either – it also covered developments in Higgs and flavour physics, precision tests and general fitting, and other tools. Interested parties are welcome to join in the next TOOLS conference due to take place in Annecy in 2022.

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The Standard Model (SM) cannot be the complete theory of particle physics. Neutrino masses evade it. No viable dark-matter candidate is contained within it. And under its auspices the electric dipole moment of the neutron, experimentally compatible with zero, requires the cancellation of two non-vanishing SM parameters that are seemingly unrelated – the strong-CP problem. The physics explaining these mysteries may well originate from new phenomena at energy scales inaccessible to any collider in the foreseeable future. Fortunately, models involving such scales can be probed today and in the next decade by a series of experiments dedicated to searching for very weakly interacting slim particles (WISPs).

WISPs are pseudo Nambu–Goldstone bosons (pNGBs) that arise automatically in extensions of the SM from global symmetries which are broken both spontaneously and explicitly. NGBs are best known for being “eaten” by the longitudinal degrees of freedom of the W and Z bosons in electroweak gauge-symmetry breaking, which underpins the Higgs mechanism, but theorists have also postulated a bevy of pNGBs that get their tiny masses by explicit symmetry breaking and are potentially discoverable as physical particles. Typical examples arising in theoretically well-motivated grand-unified theories are axions, flavons and majorons. Axions arise from a broken “Peccei–Quinn” symmetry and could potentially explain the strong-CP problem, while flavons and majorons arise from broken flavour and lepton symmetries.

Being light and very weakly interacting, WISPs would be non-thermally produced in the early universe and thus remain non-relativistic during structure formation. Such particles would inevitably contribute to the dark matter of the universe. WISPs are now the target of a growing number and type of experimental searches that are complementary to new-physics searches at colliders.

Among theorists and experimentalists alike, the axion is probably the most popular WISP. Recently, massive efforts have been undertaken to improve the calculations of model-dependent relic-axion production in the early universe. This has led to a considerable broadening of the mass range compatible with the explanation of dark matter by axions. The axion could make up all of the dark matter in the universe for a symmetry-breaking scale f_a between roughly 10⁸ and 10¹⁹ GeV (the lower limit being imposed by astrophysical arguments, the upper one by the Planck scale), corresponding to axion masses from 10^–13 eV to 10 meV. For other light pNGBs, generically dubbed axion-like particles (ALPs), the parameter range is even broader. With many plausible relic-ALP-production mechanisms proposed by theorists, experimentalists need to cover as much of the unexplored parameter range as possible.

Although the strengths of the interactions between axions or ALPs and SM particles are very weak, being inversely proportional to f_a, several strategies for observing them are available. Limits and projected sensitivities span several orders of magnitude in the mass-coupling plane (see “The field of play” figure).

IAXO’s design profited greatly from experience with the ATLAS toroid

Since axions or ALPs can usually decay to two photons, an external static magnetic field can substitute one of the two photons and induce axion-to-photon conversion. Originally proposed by Pierre Sikivie, this inverse Primakoff effect can classically be described by adding source terms proportional to B and E to Maxwell’s equations. Practically, this means that inside a static homogeneous magnetic field the presence of an axion or ALP field induces electric-field oscillations – an effect readily exploited by many experiments searching for WISPs. Other processes exploited in some experimental searches and suspected to lead to axion production are their interactions with electrons, leading to axion bremsstrahlung, and their interactions with nucleons or nuclei, leading to nucleon-axion bremsstrahlung or oscillations of the electric dipole moment of the nuclei or nucleons.

The potential to make fundamental discoveries from small-scale experiments is a significant appeal of experimental WISP physics, however the most solidly theoretically motivated WISP parameter regions and physics questions require setups that go well beyond “table-top” dimensions. They target WISPs that flow through the galactic halo, shine from the Sun, or spring into existence when lasers pass through strong magnetic fields in the laboratory.

Dark-matter halo

Haloscopes target the detection of dark-matter WISPs in the halo of our galaxy, where non-relativistic cold-dark-matter axions or ALPs induce electric field oscillations as they pass through a magnetic field. The frequency of the oscillations corresponds to the axion mass, and the amplitude to B/f_a. When limits or projections are given for these kinds of experiments, it is assumed that the particle under scrutiny homogeneously makes up all of the dark matter in the universe, introducing significant cosmological model dependence.

The furthest developed currently operating haloscopes are based on resonant enhancement of the axion-induced electric-field oscillations in tunable resonant cavities. Using this method, the presently running ADMX project at the University of Washington has the sensitivity to discover dark-matter axions with masses of a few µeV. Nuclear resonance methods could be sensitive to halo dark-matter axions with mass below 1 neV and “fuzzy” dark-matter ALPs down to 10^–22 eV within the next decade, for example at the CASPEr experiments being developed at the University of Mainz and Boston University. Meanwhile, experiments based on classical LC circuits, such as ABRACADABRA at MIT, are being designed to measure ALP- or axion-induced magnetic field oscillations in the centre of a toroidal magnet. These could be sensitive in a mass range between 10 neV and 1 µeV.

ALPS II is the first laser-based setup to fully exploit resonance techniques

For dark-matter axions with masses up to approximately 50 µeV, promising developments in cavity technologies such as multiple matched cavities and superconducting or diel­ectric cavities are ongoing at several locations, including at CAPP in South Korea, the University of Western Australia, INFN Legnaro and the RADES detector, which has taken data as part of the CAST experiment at CERN. Above ~40 µeV, however, the cavity concept becomes more and more challenging, as sensitivity scales with the volume of the resonant cavity, which decreases dramatically with increasing mass (as roughly 1/m_a³). To reach sensitivity at higher masses, in the region of a few hundred µeV, a novel “dielectric haloscope” is being developed by the MADMAX (Magnetized Disk and Mirror Axion experiment) collaboration for potential installation at DESY. It exploits the fact that static magnetic-field boundaries between media with different dielectric constants lead to tiny power emissions that compensate the discontinuity in the axion-induced electric fields in neighbouring media. If multiple surfaces are stacked in front of each other, this should lead to constructive interference, boosting the emitted power from the expected axion dark matter in the desired mass range to detectable levels. Other novel haloscope concepts, based on meta-materials (“plasma haloscopes”, for example) and topological insulators, are also currently being developed. These could have sensitivity to even higher axion masses, up to a few meV.

Staying in tune

In principle, axion-dark-matter detection should be relatively simple, given the very high number density of particles – approximately 3 × 10¹³ axions/cm³ for an axion mass of 10 µeV – and the well-established technique of resonant axion-to-photon conversion. But, as the axion mass is unknown, the experiments must be painstakingly tuned to each possible mass value in turn. After about 15 years of steady progress, the ADMX experiment has reached QCD-axion dark-matter sensitivity in the mass regime of a few µeV.

ADMX uses tunable microwave resonators inside a strong solenoidal magnetic field, and modern quantum sensors for readout. Unfortunately, however, this technology is not scalable to the higher axion-mass regions as preferred, for example, by cosmological models where Peccei–Quinn symmetry breaking happened after an inflationary phase of the universe. That’s where MADMAX comes in. The collaboration is working on the dielectric-haloscope concept – initiated and led by scientists at the Max Planck Institute for Physics in Munich – to investigate the mass region around 100 µeV.

Astrophysical hints

Weakly interacting slim particles (WISPs) could be produced in hot astrophysical plasmas and transport energy out of stars, including the Sun, stellar remnants and other dense sources. Observed lifetimes and energy-loss rates can therefore probe their existence. For the axion, or an axion-like particle (ALP) with sub-MeV mass that couples to nucleons, the most stringent limit, f_a > ~10⁸ GeV, stems from the duration of the neutrino signal from the progenitor neutron star of Supernova 1987A.

Tantalisingly, there are stellar hints from observations of red giants, helium-burning stars, white dwarfs and pulsars that seem to indicate energy losses with slight excesses with respect to those expected from standard energy emission by neutrinos. These hints may be explained by axions with masses below 100 meV or sub-keV-mass ALPs with a coupling to both electrons and photons.

Other observations suggest that TeV photons from distant blazars are less absorbed than expected by standard interactions with extragalactic background light – the so-called transparency hint. This could be explained by the conversion of photons into ALPs in the magnetic field of the source, and back to photons in astrophysical magnetic fields. Interestingly, these would have about the same ALP–photon coupling strength as indicated by the observed stellar anomalies, though with a mass that is incompatible with both ALPs which can explain dark matter and with QCD axions (see “The field of play” figure).

MADMAX will use a huge ~9 T superconducting dipole magnet with a bore of about 1.35 m and a stored energy of roughly 480 MJ. Such a magnet has never been built before. The MADMAX collaboration teamed up with CEA-IRFU and Bilfinger-Noell and successfully worked out a conceptual design. First steps towards qualifying the conductor are under way. The plan is for the magnet to be installed at DESY inside the old iron yoke of the former HERA experiment H1. DESY is already preparing the required infrastructure, including the liquid-helium supply necessary to cool the magnet. R&D for the dielectric booster, with up to 80 adjustable 1.25 m² disks, is in full swing.

A first prototype, containing a more modest 20 discs of 30 cm diameter, will be tested in the “Morpurgo” magnet at CERN during future accelerator shutdowns (see “Haloscope home” figure). With a peak field strength of 1.6 T, its dipole field will allow new ALP-dark-matter parameter regions to be probed, though the main purpose of the prototype is to demonstrate the operation of the booster system in cryogenic surroundings inside a magnetic field. The MADMAX collaboration is extremely happy to have found a suitable magnet at CERN for such tests. If sufficient funds can be acquired within the next two to three years for magnet construction, and provided that the prototype efforts at CERN are successful, MADMAX could start data taking at DESY in 2028.

While direct dark-matter search experiments like ADMX and MADMAX offer by far the highest sensitivity for axion searches, this is based on the assumption that the dark matter problem is solved by axions, and if no signal is discovered any claim of an exclusion limit must rely on specific cosmological assumptions. Therefore, other less model-dependent experiments, such as helioscopes or light shining through a wall (LSW) experiments, are extremely beneficial in addition to direct dark-matter searches.

Solar axions

In contrast to dark-matter axions or ALPs, those produced in the Sun or in the laboratory should have considerable momentum. Indeed, solar axions or ALPs should have energies of a few keV, corresponding to the temperature at which they are produced. These could be detected by helioscopes, which seek to use the inverse Primakoff effect to convert solar axions or ALPs into X-rays in a magnet pointed towards the Sun, as at the CERN Axion Solar Telescope (CAST) experiment. Helioscopes could cover the mass range compatible with the simplest axion models, in the vicinity of 10 meV, and could be sensitive to ALPs with masses below 1 eV without any tuning at all.

The CAST helioscope, which reused an LHC prototype dipole magnet, has driven this field in the past decade, and provides the most sensitive exclusion limits to date. Going beyond CAST calls for a much larger magnet. For the next-generation International Axion Observatory (IAXO) helioscope, CERN members of the international collaboration worked out a conceptual design for a 20 m-long toroidal magnet with eight 60 cm-diameter bores. IAXO’s design profited greatly from experience with the ATLAS toroid.

In the past three years, the collaboration, led by the University of Zaragoza, has been concentrating its activities on the BabyIAXO prototype in order to finesse the magnet concept, the X-ray telescopes necessary to focus photons from solar axion conversion and the low-background detectors. BabyIAXO will increase the signal-to-noise ratio of CAST by two orders of magnitude; IAXO by a further two orders of magnitude.

In December 2020 the directorates of CERN and DESY signed a collaboration agreement regarding BabyIAXO: CERN will provide the detailed design of the prototype magnet including its cryostat, while DESY will design and prepare the movable platform and infrastructure (see “Prototype” figure). BabyIAXO will be located at DESY in Hamburg. The collaboration hopes to attract the remaining funds for BabyIAXO so construction can begin in 2021 and first science runs could take place in 2025. The timeline for IAXO will depend strongly on experiences during the construction and operation of BabyIAXO, with first light potentially possible in 2028.

Light shining through a wall

In contrast to haloscopes, helioscopes do not rely on the assumption that all dark matter is made up by axions. But light-shining-through-wall (LSW) experiments are even less model dependent with respect to ALP production. Here, intense laser light could be converted to axions or ALPs inside a strong magnetic field by the Primakoff effect. Behind a light-impenetrable wall they would be re-converted to photons and detected at the same wavelength as the laser light. The disadvantage of LSW experiments is that they only reach sensitivity to ALPs with a mass up to a few hundred µeV with comparably high coupling to photons. However, this is sensitive enough to test the parameter range consistent with the transparency hint and parts of the mass range consistent with the stellar hints (see “Astrophysical hints” panel).

The Any Light Particle Search (ALPS II) at DESY follows this approach. By seeking to observe light shining through a wall, any ALPs would be generated in the experiment itself, removing the need to make assumptions about their production. ALPS II is based on 24 modified superconducting dipole magnets that have been straightened by brute-force deformation, following their former existence in the proton accelerator of the HERA complex. With the help of two 124 m-long high-finesse optical resonators, encompassed by the magnets on both sides of the wall, ALPS II is also the first laser-based setup to fully exploit resonance techniques. Two readout systems capable of measuring a 1064 nm photon flux down to a rate of 2 × 10^–5 s^–1 have been developed by the collaboration. Compared to the present best LSW limits provided by OSQAR at CERN, the signal-to-noise ratio will rise by no less than 12 orders of magnitude at ALPS II. Nevertheless, MADMAX would surpass ALPS II in the sensitivity for the axion-photon coupling strength by more than three orders of magnitude. This is the price to pay for a model-independent experiment – however, ALPS II principally targets not dark-matter candidates but ALPs indicated by astrophysical phenomena.

Tunelling ahead

The installation of the 24 dipole magnets in a straight section of the HERA tunnel was completed in 2020. Three clean rooms at both ends and in the centre of the experiment were also installed, and optics commissioning is under way. A first science run is expected for autumn 2021.

In the overlapping mass region up to 0.1 meV, the sensitivities of ALPS II and BabyIAXO are roughly equal. In the event of a discovery, this would provide a unique opportunity to study the new WISP. Excitingly, a similar case might be realised for IAXO: combining the optics and detectors of ALPS II with simplified versions of the dipole magnets being studied for FCC-hh would provide an LSW experiment with “IAXO sensitivity” regarding the axion-photon coupling, albeit in a reduced mass range. This has been outlined as the putative JURA (Joint Undertaking on Research for Axions) experiment in the context of the CERN-led Physics Beyond Colliders study.

The past decade has delivered significant developments in axion and ALP theory and phenomenology. This has been complemented by progress in experimental methods to cover a large fraction of the interesting axion and ALP parameter range. In close collaboration with universities and institutes across the globe, CERN, DESY and the Max Planck society will together pave the road to the exciting results that are expected this decade.

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Supersymmetry is a popular extension of the Standard Model (SM) that has the potential to resolve several open questions in particle physics. As a result of a postulated new symmetry between fermions and bosons, the theory predicts a “superpartner” for each SM particle. The lightest of these new particles could be what makes up dark matter, while additional new superpartners could resolve the question of why the Higgs boson has a relatively low mass. Many searches for supersymmetry have already been performed by the ATLAS and CMS collaborations, but most have focused on strongly interacting superpartners that could be very heavy. It is possible, however, that electroweak production of supersymmetric particles is the dominant or only source of superpartners accessible at the LHC.

Supersymmetric events are expected to have an imbalance in transverse momentum

The unprecedented data volume of LHC Run 2 provides a unique opportunity to search for rare processes such as electroweak production of supersymmetric particles. A recent result from the CMS collaboration uses the Run-2 dataset to search for the superpartners of the electroweak bosons, called charginos and neutralinos. Events with three or more charged leptons, or two leptons of the same charge, were analysed. Such events are relatively rare in the SM, and, if they exist, charginos and neutralinos are predicted to create an excess of events with these topologies. Supersymmetric events are also expected to have an apparent imbalance in transverse momentum, because the lightest supersymmetric particle should evade detection. Correlations between the multiple leptons in the events, and between the leptons and the momentum imbalance, can be used to define a set of discriminating variables sensitive to chargino and neutralino production. These variables are used to assign the selected events into several search regions that address different possible signals of the production and decay of supersymmetric particles. Making such a multivariate binning optimal in every corner of phase-space, and for any possible manifestation of supersymmetry, is a challenging task.

Parametric machine learning

Events with three electrons and/or muons provide the bulk of the sensitivity by striking the best balance between signal purity and yields. A novel search approach is used that aims at better capturing the complexity of the events than is possible using predetermined search regions: parametric machine learning. The aim is to achieve the maximum sensitivity for any parameter choice nature might have made, as supersymmetry is not one model, but a class of models. Variations in the masses of the superpartners can substantially modify the observable signatures. Parametric neural networks were trained to find charginos and neutralinos with the unknown mass parameters added as input variables to the training. The network can evaluate the data at fixed values of the mass parameters, effectively performing a dedicated search for a signal with given masses in the data (figure 1).

The parametric neural network, together with a new optimised event binning of the other event categories, makes this analysis the most powerful search for charginos and neutralinos carried out by the CMS collaboration so far. The neural network alone results in a sensitivity boost that ranges from 30% to more than 100%. Substantial improvements occur for models where the decay of the charginos and neutralinos are mediated by the superpartners of leptons. The improvements become even larger when the mass splitting between sleptons and the chargino is relatively small. The data show no evidence for electroweak superpartner production, and chargino masses up to 1450 GeV, compared to 1150 GeV in earlier CMS searches for this scenario, are excluded at 95% confidence.

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The European strategy for particle physics (ESPP), updated by the CERN Council in June 2020, lays the foundations for a bright future for accelerator-based particle physics. Its 20 recommendations – covering the components of a compelling scientific programme for the short, medium and long terms, as well as the societal and environmental impact of the field, public engagement and support for early-career scientists – set out an ambitious but prudent approach to realise the post-LHC future in Europe within the worldwide context.

Full exploitation of the LHC and its high-luminosity upgrade is a major priority, both in terms of its physics potential and its role as a springboard to a future energy-frontier machine. The ESPP identified an electron–positron Higgs factory as the highest priority next collider. It also recommended that Europe, together with its international partners, investigate the technical and financial feasibility of a future hadron collider at CERN with a centre-of-mass energy of at least 100 TeV, with an electron–positron Higgs and electroweak factory as a possible first stage. Reinforced R&D on a range of accelerator technologies is another ESPP priority, as is continued support for a diverse scientific programme.

Implementation starts now

It is CERN’s role, in strong collaboration with other laboratories and institutions in Europe and beyond, to help translate the visionary scientific objectives of the ESPP update into reality. CERN’s recently approved medium-term plan (MTP), which covers the period 2021–2025, provides a first implementation of the ESPP vision.

Starting this year, CERN will deploy efforts on the feasibility study for a Future Circular Collider (FCC) as recommended by the ESPP update. One of the first goals is to verify that there are no showstoppers to building a 100 km tunnel in the Geneva region, and to gather pledges for the necessary funds to build it. The estimated FCC cost cannot be met only from CERN’s budget, and special contributions from non-Member States as well as new funding mechanisms will be required. Concerning the enabling technologies, the first priority is to demonstrate that the superconducting high-field magnets needed for 100 TeV (or more) proton–proton collisions in a 100 km tunnel can be made available on the mid-century time scale. To this end CERN is implementing a reinforced magnet R&D programme in partnership with industry and other institutions in Europe and beyond. Fresh resources will be used to explore low- and high-temperature superconducting materials, to develop magnet models towards industrialisation and cost reduction, and to build the needed test infrastructure. These studies will also have vast applications outside the field. Minimising the environmental impact of the tunnel, the colliders and detectors will be another major focus, as well as maximising the benefits to society from the transfer of FCC-related technologies.

The 2020 MTP includes resources to continue R&D on key technologies for the Compact Linear Collider and for the establishment of an international design study for a muon collider. Further advanced accelerator technologies will be pursued, as well as detector R&D and a new initiative on quantum technologies.

Continued progress requires a courageous, global experimental venture involving all the tools at our disposal

Scientific diversity is an important pillar of CERN’s programme and will continue to be supported. Resources for the CERN-hosted Physics Beyond Colliders study have been increased in the 2020 MTP and developments for long-baseline neutrino experiments in the US and Japan will continue at an intense pace via the CERN Neutrino Platform.

Immense impact

The discovery of the Higgs boson, a particle with unprecedented characteristics, has contributed to turning the focus of particle physics towards deep structural questions. Furthermore, many of the open questions in the microscopic world are increasingly intertwined with the universe at large. Continued progress on this rich and ambitious path of fundamental exploration requires a courageous, global experimental venture involving all the tools at our disposal: high-energy colliders, low-energy precision tests, observational cosmology, cosmic rays, dark-matter searches, gravitational waves, neutrinos, and many more. High-energy colliders, in particular, will continue to be an indispensable and irreplaceable tool to scrutinise nature at the smallest scales. If the FCC can be realised, its impact will be immense, not only on CERN’s future, but also on humanity’s knowledge.

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Detecting LLPs at the LHC experiments requires a paradigm shift with respect to the usual data-analysis and trigger strategies. To that end, more than 200 experimentalists and theorists met online from 16 to 19 November for the eighth workshop of the LHC LLP community.

Dark quarks would undergo fragmentation and hadronisation, resulting in “dark showers”

Strong theoretical motivations underpin searches for LLPs. For example, dark matter could be part of a larger dark sector, parallel to the Standard Model (SM), with new particles and interactions. If dark quarks could be produced at the LHC, they would undergo fragmentation and hadronisation in the dark sector resulting in characteristic “dark showers” — one of the focuses of the workshop. Collider signatures for dark showers depend on the fraction of unstable particles they contain and their lifetime, with a range of categories presenting their own analysis challenges: QCD-like jets, semi-visible jets, emerging jets, and displaced vertices with missing transverse energy. Delegates agreed on the importance of connecting collider-level searches for dark showers with astrophysical and cosmological scales. In a similar spirit of collaboration across communities, a joint session with the HEP Software Foundation focused on triggering and reconstruction software for dedicated LLP detectors.

Heavy neutral leptons

The discovery of heavy neutral leptons (HNLs) could address different open questions of the SM. For example, neutrinos are expected to be left-handed and massless in the SM, but oscillate between flavours as their wavefunction evolves, providing evidence for as-yet immeasurably small masses. One way to fix this problem is to complete the field pattern of the SM with right-handed HNLs. The number and other characteristics of HNLs depend on the model considered, but in many cases HNLs are long-lived and connect to other important questions of the SM, such as dark matter and the baryon asymmetry of the universe. There are many ongoing searches for HNLs at the LHC and many more proposed elsewhere. During the November workshop the discussion touched on different models and simulations, reviewing what is available and what is needed for the different signal benchmarks.

Another focus was the reinterpretation of previous LLP searches. Recasting public results is common practice at the LHC and a good way to increase physics impact, but reinterpreting LLP searches is more difficult than prompt searches due to the use of non-standard selections and analysis-specific objects.

The latest results from CERN experiments were presented. ATLAS reported the first LHC search for sleptons using displaced-lepton final states, greatly improving sensitivity compared to LEP. CMS presented a search for strongly interacting massive particles with trackless jets, and a search for long-lived particles decaying to jets with displaced vertices. LHCb reported searches for low -mass di-muon resonances and a search for heavy neutrinos in the decay of a W boson into two muons and a jet, and the NA62 experiment at CERN’s SPS presented a search for π⁰ decays to invisible particles. These results bring important new constraints on the properties and parameters of LLP models.

Dedicated detectors

A series of dedicated LLP detectors at CERN — including the Forward Physics Facility for the HL-LHC, the CMS forward detector, FASER, Codex-b and Codex-ß, MilliQan, MoEDAL-MAPP, MATHUSLA, ANUBIS, SND@LHC, and FORMOSA – are in different stages between proposal and operation. These additional detectors, located at various distances from the LHC experiments, have diverse strengths: some, like MilliQan, look for specific particles (milli-charged particles, in that case), whereas others, like Mathusla, offer a very low background environment in which to search for neutral LLPs. These complementary efforts will, in the near future, provide all the different pieces needed to build the most complete picture possible of a variety of LLP searches, from axion-like particles to exotic Higgs decays, potentially opening the door to a dark sector.

ATLAS reported the first LHC search for sleptons using displaced-lepton final states

The workshop featured a dedicated session on future colliders for the first time. Designing these experiments with LLPs in mind would radically boost discovery chances. Key considerations will be tracking and the tracking volume, timing information, trigger and DAQ, as well as potential additional instrumentation in tunnels or using the experimental caverns.

Together with the range of new results presented and many more in the pipeline, the 2020 LLP workshop was representative of a vibrant research community, constantly pushing the “lifetime frontier”.

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Since the discovery of the Higgs boson in 2012, great progress has been made in our understanding of the Standard Model (SM) and the prospects for the discovery of new physics beyond it. Despite excellent advances in Higgs-sector measurements, searches for WIMP dark matter and exploration of very rare processes in the flavour realm, however, no unambiguous signals of new fundamental physics have been seen. This is the reason behind the explosion of interest in feebly interacting particles (FIPs) over the past decade or so.

The inaugural FIPs 2020 workshop, hosted online by CERN from 31 August to 4 September, convened almost 200 physicists from around the world. Structured around the four “portals” that may link SM particles and fields to a rich dark sector – axions, dark photons, dark scalars and heavy neutral leptons – the workshop highlighted the synergies and complementarities among a great variety of experimental facilities, and called for close collaboration across different physics communities.

Today, conventional experimental efforts are driven by arguments based on the naturalness of the electroweak scale. They result in searches for new particles with sizeable couplings to the SM, and masses near the electroweak scale. FIPs represent an alternative paradigm to the traditional beyond-the-SM physics explored at the LHC. With masses below the electroweak scale, FIPs could belong to a rich dark sector and answer many open questions in particle physics (see “Four portals” figure). Diverse searches using proton beams (CERN and Fermilab), kaon beams (CERN and JPARC), neutrino beams (JPARC and Fermilab) and muon beams (PSI) today join more idiosyncratic experiments across the globe in a worldwide search for FIPs.

FIPs can arise from the presence of feeble couplings in the interactions of new physics with SM particles and fields. These may be due to a dimensionless coupling constant or to a “dimensionful” scale, larger than that of the process being studied, which is defined by a higher dimension operator that mediates the interaction. The smallness of these couplings can be due to the presence of an approximate symmetry that is only slightly broken, or to the presence of a large mass hierarchy between particles, as the absence of new-physics signals from direct and indirect searches seems to suggest.

Take the axion, for example. This is the particle that may be responsible for the conservation of charge–parity symmetry in strong interactions. It may also constitute a fraction or the entirety of dark matter, or explain the hierarchical masses and mixings of the SM fermions – the flavour puzzle.

Or take dark photons or dark Z′ bosons, both examples of new vector gauge bosons. Such particles are associated with extensions of the SM gauge group, and, in addition to indicating new forces beyond the four we know, could lead to evidence of dark-matter candidates with thermal origins and masses in the MeV to GeV range.

Exotic Higgs bosons could also have been responsible for cosmological inflation

Then there are exotic Higgs bosons. Light dark scalar or pseudoscalar particles related to the SM Higgs may provide novel ways of addressing the hierarchy problem, in which the Higgs mass can be stabilised dynamically via the time evolution of a so-called “relaxion” field. They could also have been responsible for cosmological inflation.

Finally, consider right-handed neutrinos, often referred to as sterile neutrinos or heavy neutral leptons, which could account for the origin of the tiny, nearly-degenerate masses of the neutrinos of the SM and their oscillations, as well as providing a mechanism for our universe’s matter–antimatter asymmetry.

Scientific diversity

No single experimental approach can cover the large parameter space of masses and couplings that FIPs models allow. The interconnections between open questions require that we construct a diverse research programme incorporating accelerator physics, dark-matter direct detection, cosmology, astrophysics, and precision atomic experiments, with a strong theoretical involvement. The breadth of searches for axions or axion-like particles (ALPs) is a good indication of the growing interest in FIPs (see “Scaling the ALPs” figure). Experimental efforts here span particle and astroparticle physics. In the coming years, helioscopes, which aim to detect solar axions by their conversion into photons (X-rays) in a strong magnetic field, will improve the sensitivity by more than 10 orders of magnitude in mass in the sub-eV range. Haloscopes, which work by converting axions into visible photons inside a resonant microwave cavity placed inside a strong magnetic field, will complement this quest by increasing the sensitivity for small couplings by six orders of magnitude (down to the theoretically motivated gold band in a mass region where the axions can be a dark-matter candidate). Accelerator-based experiments, meanwhile, can probe the strongly motivated QCD scale (MeV–GeV) and beyond for larger couplings. All these results
will be complemented by a lively theo­retical activity aimed at interpreting astrophysical signals within axion and ALP models.

FIPs 2020 triggered lively discussions that will continue in the coming months via topical meetings on different subjects. Topics that motivated particular interest between communities included possible ways of comparing results from direct-detection dark-matter experiments in the MeV–GeV range against those obtained at extracted beam line and collider experiments; the connection between right-handed neutrino properties and active neutrino parameters; and the interpretation of astrophysical and cosmological bounds, which often overwhelm the interpretation of each of the four portals.

The next FIPs workshop will take place at CERN next year.

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On 17 January 1957, a few months after Chien-Shiung Wu’s discovery of parity violation, Wolfgang Pauli wrote to Victor Weisskopf: “Ich glaube aber nicht, daß der Herrgott ein schwacher Linkshänder ist” (I cannot believe that God is a weak left-hander). But maximal parity violation is now well established within the Standard Model (SM). The weak interaction only couples to left-handed particles, as dramatically seen in the continuing absence of experimental evidence for right-handed neutrinos. In the same way, the polarisation of photons originating from transitions that involve the weak interaction is expected to be completely left-handed.

The LHCb collaboration recently tested the handedness of photons emitted in rare flavour-changing transitions from a b-quark to an s-quark. These are mediated by the bosons of the weak interaction according to the SM – but what if new virtual particles contribute too? Their presence could be clearly signalled by a right-handed contribution to the photon polarisation.

New virtual particles could be clearly signalled by a right-handed contribution to the photon polarisation

The b → sγ transition is rare. Fewer than one in a thousand b-quarks transform into an s-quark and a photon. This process has been studied for almost 30 years at particle colliders around the world. By precise measurements of its properties, physicists hope to detect hints of new heavy particles that current colliders are not powerful enough to produce.

The probability of this b-quark decay has been measured in previous experiments with a precision of about 5%, and found to agree with the SM prediction, which bears a similar theoretical uncertainty. A promising way to go further is to study the polarisation of the emitted photon. Measuring the b → sγ polarisation is not easy though. The emitted photons are too energetic to be analysed by a polarimeter and physicists must find innovative ways to probe them indirectly. For example, a right-handed polarisation contribution could induce a charge-parity asymmetry in the B⁰ → K_Sπ⁰γ or B_s⁰ → φγ decays. It could also contribute to the total rate of radiative b → sγ decays, containing any strange meson, B → X_sγ.

The LHCb collaboration has pioneered a new method to perform this measurement using virtual photons and the largest sample of the very rare B⁰ → K^*0e⁺e^– decay ever collected. First, the sub-sample of decays that come from B⁰ → K^*0γ with a virtual photon that mat­erialises in an electron–positron pair is isolated. The angular distributions of the B⁰ → K^*0e⁺e^– decay products are then used as a polarimeter to measure the handedness of the photon. The number of decays with a virtual photon is small compared to the decays with a real photon, but these latter decays cannot be used as the information on the polarisation is lost.

The size of the right-handed contribution to b → sγ is encoded in the magnitude of the complex parameter C′₇/C₇. This is a ratio of the right- and left-handed Wilson coefficients that are used in the effective description of b → s transitions. The new B⁰ → K^*0e⁺e^– analysis by the LHCb collaboration constrains the value of C′₇/C₇, and thus the photon polarisation, with unprecedented precision (figure 1). The measurement is compatible with the SM prediction.

This result showcases the exceptional capability of the LHCb experiment to study b → sγ transitions. The uncertainty is currently dominated by the data sample size, and thus more accurate studies are foreseen with the large data sample expected in Run 3 of the LHC. More precise measurements may yet unravel a small right-handed polarisation.

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The Standard Model (SM) groups quarks and leptons separately to account for their rather different observed properties, but might they be unified through a new particle that couples to both and turns one into the other? Such “leptoquarks” emerge quite naturally in several theo­ries that extend the SM. Searches for leptoquarks have been an important part of the LHC’s research programme since the beginning, and have received additional attention recently in the light of hints of deviations from the principle of lepton universality – the so-called flavour anomalies.

In a recent CMS analysis, where the events collected in pp collisions during Run 2 (137 fb^–1) are analysed, researchers have challenged the SM by investigating a previously unexplored leptoquark signature involving the third generation of fermions. The motivation for considering the third generation is to confront the principle of lepton universality, which asserts that the couplings of leptons with gauge bosons are flavour independent. This principle is built into the SM, but has recently been put under stress by a series of anomalies observed in precision measurements of certain B-meson decays by the LHCb, Belle and BaBar collaborations. A possible explanation for these anomalies, which are still under investigation and not yet confirmed, lies in the existence of leptoquarks that preferentially couple to the heaviest fermions.

These results are the most stringent limits to date on the presence of leptoquarks that couple preferentially to the third generation

The new CMS search looks for both single and pair production of leptoquarks. It considers leptoquarks that decay to a quark (top or bottom) and a lepton (tau or neutrino), targeting the signature with a top quark, a tau lepton, missing transverse momentum due to a neutrino, and, in the case of double production, an additional bottom-quark jet. This is the first search to simultaneously consider both production mechanisms by categorising events with one or two jets originating from a bottom quark. The analysis also includes a dedicated selection for the case of a large mass splitting between the leptoquark and the top quark, which would boost the top quark and could cause its decay products to be inseparable given the spatial resolution of jets.

The observations are found to be in agreement with the SM prediction, and exclusion limits are derived in the plane of the leptoquark–lepton–quark vertex coupling λ and the leptoquark mass. The results are derived separately for hypothetical spin-0 and spin-1 (figure 1) leptoquarks, reflecting the two types allowed by theoretical models. The analy­sis assumes that the leptoquark decays half the time to each of the possible quark–lepton flavour pairs, for example, in the case of a spin-1 leptoquark, to a top quark and a neutrino, or to a bottom quark and a tau lepton. CMS finds a range of lower limits on the leptoquark mass between 0.98 and 1.73 TeV, at 95% confidence, depending on λ and the spin.

These results are the most stringent limits to date on the presence of leptoquarks that couple preferentially to the third generation of fermions. They also probe the parameter space preferred by the B-physics anomalies in several models, excluding relevant portions. As theories predict leptoquark masses as high as many tens of TeV, the pursuit of this promising solution for the unification of quarks and leptons must continue. The CMS collaboration has a broad programme for further investigations that will exploit the larger data samples from Run 3 and the high-luminosity LHC under different hypotheses. If leptoquarks exist, they may well be revealed in the coming data.

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But what if the glimpses of BSM physics that atomic spectroscopists have so painstakingly searched for over the past decades are not effects that persist over the many weeks or months of a typical measurement campaign, but rather transient events that occur only sporadically? For example, might not cataclysmic astrophysical events such as black-hole mergers or supernova explosions produce hypothetical ultralight bosonic fields impossible to generate in the laboratory? Or might not Earth occasionally pass through some invisible “cloud” of a substance (such as dark matter) produced in the early universe? Such transient phenomena could easily be missed by experimenters when data are averaged over long times to increase the signal-to-noise ratio.

Detecting such unconventional events represents several challenges. If a transient signal heralding new physics was observed with a single detector, it would be exceedingly difficult to confidently distinguish the exotic-physics signal from the many sources of noise that plague precision atomic physics measurements. However, if transient interactions occur over a global scale, a network of such detectors geographically distributed over Earth could search for specific patterns in the timing and amplitude of such signals that would be unlikely to occur randomly. By correlating the readouts of many detectors, local effects can be filtered away and exotic physics could be distinguished from mundane physics.

This idea forms the basis for the Global Network of Optical Magnetometers to search for Exotic physics (GNOME), an international collaboration involving 14 institutions from all over the world (see “Correlated” figure). Such an idea, like so many others in physics, is not entirely new. The same concept is at the heart of the worldwide network of interferometers used to observe gravitational waves (LIGO, Virgo, GEO, KAGRA, TAMA, CLIO), and the global network of proton-precession magnetometers used to monitor geomagnetic and solar activity. What distinguishes GNOME from other global sensor networks is that it is specifically dedicated to searching for signals from BSM physics that have evaded detection in earlier experiments.

GNOME is a growing network of more than a dozen optical atomic magnetometers, with stations in Europe, North America, Asia and Australia. The project was proposed in 2012 by a team of physicists from the University of California at Berkeley, Jagiellonian University, California State University – East Bay, and the Perimeter Institute. The network started taking preliminary data in 2013, with the first dedicated science-run beginning in 2017. With more data on the way, the GNOME collaboration, consisting of more than 50 scientists from around the world, is presently combing the data for signs of the unexpected, with its first results expected later this year.

Exotic-physics detectors

Optical atomic magnetometers (OAMs) are among the most sensitive devices for measuring magnetic fields. However, the atomic vapours that are the heart of GNOME’s OAMs are placed inside multi-layer shielding systems, reducing the effects of external magnetic fields by a factor of more than a million. Thus, in spite of using extremely sensitive magnetometers, GNOME sensors are largely insensitive to magnetic signals. The reasoning is that many BSM theories predict the existence of exotic fields that couple to atomic spins and would penetrate through magnetic shields largely unaffected. Since the OAM signal is proportional to the spin-dependent energy shift regardless of whether or not a magnetic field causes the energy shift, OAMs – even enclosed within magnetic shields – are sensitive to a broad class of exotic fields.

The basic principle behind OAM operation (see “Optical rotation” figure) involves optically measuring spin-dependent energy shifts by controlling and monitoring an ensemble of atomic spins via angular momentum exchange between the atoms and light. The high efficiency of optical pumping and probing of atomic spin ensembles, along with a wide array of clever techniques to minimise atomic spin relaxation (even at high atomic vapour densities), have enabled OAMs to achieve sensitivities to spin-dependent energy shifts at levels well below 10^–20 eV after only one second of integration. One of the 14 OAM installations, at California State University – East Bay, is shown in the “Benchtop physics” image.

However, one might wonder: do any of the theoretical scenarios suggesting the existence of exotic fields predict signals detectable by a magnetometer network while also evading all existing astrophysical and laboratory constraints? This is not a trivial requirement, since previous high-precision atomic spectroscopy experiments have established stringent limits on BSM physics. In fact, OAM techniques have been used by a number of research groups (including our own) over the past several decades to search for spin-dependent energy shifts caused by exotic fields sourced by nearby masses or polarised spins. Closely related work has ruled out vast areas of BSM parameter space by comparing measurements of hyperfine structure in simple hydrogen-like atoms to QED calculations. Furthermore, if exotic fields do exist and couple strongly enough to atomic spins, they could cause noticeable cooling of stars and affect the dynamics of supernovae. So far, all laboratory experiments have produced null results and all astrophysical observations are consistent with the SM. Thus if such exotic fields exist, their coupling to atomic spins must be extremely feeble.

Despite these constraints and requirements, theoretical scenarios both consistent with existing constraints and that predict effects measurable with GNOME do exist. Prime examples, and the present targets of the GNOME collaboration’s search efforts, are ultralight bosonic fields. A canonical example of an ultralight boson is the axion. The axion emerged from an elegant solution, proposed by Roberto Peccei and Helen Quinn in the late 1970s, to the strong–CP problem. The Peccei–Quinn mechanism explains the mystery of why the strong interaction, to the highest precision we can measure, respects the combined CP symmetry whereas quantum chromodynamics naturally accommodates CP violation at a level ten orders of magnitude larger than present constraints. If CP violation in the strong interaction can be described not by a constant term but rather by a dynamical (axion) field, it could be significantly suppressed by spontaneous symmetry breaking at a high energy scale. If the symmetry breaking scale is at the grand-unification-theory (GUT) scale (~10¹⁶ GeV), the axion mass is around 10^-10 eV, and at the Planck scale (10¹⁹ GeV) around 10^-13 eV – both many orders of magnitude less massive than even neutrinos. Searching for ultralight axions therefore offers the exciting possibility of probing physics at the GUT and Planck scales, far beyond the direct reach of any existing collider.

Beyond the Standard Model

In addition to the axion, there are a wide range of other hypothetical ultralight bosons that couple to atomic spins and could generate signals potentially detectable with GNOME. Many theories predict the existence of spin-0 bosons with properties similar to the axion (so-called axion-like particles, ALPs). A prominent example is the relaxion, proposed by Peter Graham, David Kaplan and Surjeet Rajendran to explain the hierarchy problem: the mystery of why the electroweak force is about 24 orders-of-magnitude stronger than the gravitational force. In 2010, Asimina Arvanitaki and colleagues found that string theory suggests the existence of many ALPs of widely varying masses, from 10^-33 eV to 10^-10 eV. From the perspective of BSM theories, ultralight bosons are ubiquitous. Some predict ALPs such as “familons”, “majorons” and “arions”. Others predict new ultralight spin-1 bosons such as dark and hidden photons. There is even a possibility of exotic spin-0 or spin-1 gravitons: while the graviton for a quantum theory of gravity matching that described by general relativity must be spin-2, alternative gravity theories (for example torsion gravity and scalar-vector-tensor gravity) predict additional spin-0 and/or spin-1 gravitons.

It also turns out that such ultralight bosons could explain dark matter. Most searches for ultralight bosonic dark matter assume the bosons to be approximately uniformly distributed throughout the dark matter halo that envelopes the Milky Way. However, in some theoretical scenarios, the ultralight bosons can clump together into bosonic “stars” due to self-interactions. In other scenarios, due to a non-trivial vacuum energy landscape, the ultralight bosons could take the form of “topological” defects, such as domain walls that separate regions of space with different vacuum states of the bosonic field (see “New domains” figure). In either of these cases, the mass-energy associated with ultralight bosonic dark matter would be concentrated in large composite structures that Earth might only occasionally encounter, leading to the sort of transient signals that GNOME is designed to search for.

Yet another possibility is that intense bursts of ultralight bosonic fields might be generated by cataclysmic astrophysical events such as black-hole mergers. Much of the underlying physics of coalescing singularities is unknown, possibly involving quantum-gravity effects far beyond the reach of high-energy experiments on Earth, and it turns out that quantum gravity theories generically predict the existence of ultralight bosons. Furthermore, if ultralight bosons exist, they may tend to condense in gravitationally bound halos around black holes. In these scenarios, a sizable fraction of the energy released when black holes merge could plausibly be emitted in the form of ultralight bosonic fields. If the energy density of the ultralight bosonic field is large enough, networks of atomic sensors like GNOME might be able to detect a signal.

In order to use OAMs to search for exotic fields, the effects of environmental magnetic noise must be reduced, controlled, or cancelled. Even though the GNOME magnetometers are enclosed in multi-layer magnetic shields so that signals from external electromagnetic fields are significantly suppressed, there is a wide variety of phenomena that can mimic the sorts of signals one would expect from ultralight bosonic fields. These include vibrations, laser instabilities, and noise in the circuitry used for data acquisition. To combat these spurious signals, each GNOME station uses auxiliary sensors to monitor electromagnetic fields outside the shields (which could leak inside the shields at a far-reduced level), accelerations and rotations of the apparatus, and overall magnetometer performance. If the auxiliary sensors indicate data may be suspect, the data are flagged and ignored in the analysis (see “Spurious signals” figure).

GNOME data that have passed this initial quality check can then be scanned to see if there are signals matching the patterns expected based on various exotic physics hypotheses. For example, to test the hypothesis that dark matter takes the form of ALP domain walls, one searches for a signal pattern resulting from the passage of Earth through an astronomical-sized plane having a finite thickness given by the ALP’s Compton wavelength. The relative velocity between the domain wall and Earth is unknown, but can be assumed to be randomly drawn from the velocity distribution of virialised dark matter, having an average speed of about one thousandth the speed of light. The relative timing of signals appearing in different GNOME magnetometers should be consistent with a single velocity v: i.e. nearby stations (in the direction of the wall propagation) should detect signals with smaller delays and stations that are far apart should detect signals with larger delays, and furthermore the time delays should occur in a sensible sequence. The energy shift that could lead to a detectable signal in GNOME magnetometers is caused by an interaction of the domain-wall field φ with the atomic spin S whose strength is proportional to the scalar product of the spin with the gradient of the field, S∙∇φ. The gradient of the domain-wall field ∇φ is proportional to its momentum relative to S, and hence the signals appearing in different GNOME magnetometers are proportional to S∙v. Both the signal-timing pattern and the signal-amplitude pattern should be consistent with a single value of v; signals inconsistent with such a pattern can be rejected as noise.

If such exotic fields exist, their coupling to atomic spins must be extremely feeble

To claim discovery of a signal heralding BSM physics, detections must be compared to the background rate of spurious false-positive events consistent with the expected signal pattern but not generated by exotic physics. The false-positive rate can be estimated by analysing time-shifted data: the data stream from each GNOME magnetometer is shifted in time relative to the others by an amount much larger than any delays resulting from propagation of ultralight bosonic fields through Earth. Such time-shifted data can be assumed to be free of exotic-physics signals, so any detections are necessarily false positives: merely random coincidences due to noise. When the GNOME data are analysed without timeshifts, to be regarded as an indication of BSM physics, the signal amplitude must surpass the 5σ threshold as compared to the background determined with the time-shifted data. This means that, for a year-long data set, an event due to noise coincidentally matching the assumed signal pattern throughout the network would occur only once every 3.5 million years.

Inspiring efforts

Having already collected over a year of data, and with more on the way, the GNOME collaboration is presently combing the data for signs of BSM physics. New results based on recent GNOME science runs are expected in 2020. This would represent the first ever search for such transient exotic spin-dependent effects. Improvements in magnetometer sensitivity, signal characterisation, and data-analysis techniques are expected to improve on these initial results over the next several years. Significantly, GNOME has inspired similar efforts using other networks of precision quantum sensors: atomic clocks, interferometers, cavities, superconducting gravimeters, etc. In fact, the results of searches for exotic transient signals using clock networks have already been reported in the literature, constraining significant parameter space for various BSM scenarios. We would suggest that all experimentalists should seriously consider accurately time-stamping, storing, and sharing their data so that searches for correlated signals due to exotic physics can be conducted a posteriori. One never knows what nature might be hiding just beyond the frontier of the precision of past measurements.

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Who needs the WIMP if we can have the axion?

Elena Aprile

“Thanks to our unprecedented low event rate in electronic recoils background, and thanks to our large exposure, both in detector mass and time, we could afford to look for signatures of rare and new phenomena expected at the lowest energies where one usually finds lots of background,” says XENON spokesperson Elena Aprile, of Columbia University in New York. “I am especially intrigued by the possibility to detect axions produced in the Sun,” she says. “Who needs the WIMP if we can have the axion?”

The XENON collaboration has been in pursuit of WIMPs, a leading bosonic cold-dark-matter candidate, since 2005 with a programme of 10 kg, 100 kg and now 1 tonne liquid-xenon TPCs. Particles scattering in the liquid xenon create both scintillation light and ionisation electrons; the latter drift upwards in an electric field towards a gaseous phase where electroluminescence amplifies the charge signal into a light signal. Photomultiplier tubes record both the initial scintillation light and the later electroluminescence, to reveal 3D particle tracks, and the relative magnitudes of the two signals allows nuclear and electronic recoils to be differentiated. XENON1T derives its world-leading limit on WIMPs – the strictest 90% confidence limit being a cross-section of 4.1×10⁻⁴⁷ cm² for WIMPs with a mass of 30 GeV – from the very low rate of nuclear recoils observed by XENON1T from February 2017 to February 2018.

A surprise was in store, however, in the same data set, which also revealed 285 electronic recoils at the lower end of XENON1T’s energy acceptance, from 1 to 7 keV, over the expected background of 232±15. The sole background-modelling explanation for the excess that the collaboration has not been able to rule out is a minute concentration of tritium in the liquid xenon. With a half-life of 12.3 years and a relatively low amount of energy liberated in the decay of 18.6 keV, an unexpected contribution of tritium decays is favoured over XENON1T’s baseline background model at approximately 3σ. “We can measure extremely tiny amounts of various potential background sources, but unfortunately, we are not sensitive to a handful of tritium atoms per kilogram,” explains deputy XENON1T spokesperson Manfred Lindner, of the Max Planck Institute for Nuclear Physics in Heidelberg. Cryogenic distillation plus running the liquid xenon through a getter is expected to remove any tritium below the level that would be relevant, he says, but this needs to be cross-checked. The question is whether a minute amount of tritium could somehow remain in liquid xenon or if some makes it from the detector materials into the liquified xenon in the detector. “I personally think that the observed excess could equally well be a new background or new physics. About 3σ implies of course a certain statistical chance for a fluctuation, but I find it intriguing to have this excess not at some random place, but towards the lower end of the spectrum. This is interesting since many new-physics scenarios generically lead to a 1/E or 1/E² enhancement which would be cut off by our detection threshold.”

Solar axions

One solution proposed by the collaboration is solar axions. Axions are a consequence of a new U(1) symmetry proposed in 1977 to explain the immeasurably small degree of CP violation in quantum chromodynamics – the so-called strong CP problem — and are also a dark-matter candidate. Though XENON1T is not expected to be sensitive to dark-matter axions, should they exist they would be produced by the sun at energies consistent with the XENON1T excess. According to this hypothesis, the axions would be detected via the “axioelectric” effect, an axion analogue of the photoelectric effect. Though a good fit phenomenologically, and like tritium favoured over the background-only hypothesis at approximately 3σ, the solar-axion explanation is disfavoured by astrophysical constraints. For example, it would lead to a significant extra energy loss in stars.

Axion helioscopes such as the CERN Axion Solar Telescope (CAST) experiment, which directs a prototype LHC dipole magnet at the Sun and could convert solar axions into X-ray photons, will help in testing the hypothesis. “It is not impossible to have an axion model that shows up in XENON but not in CAST,” says deputy spokesperson Igor Garcia Irastorza of University of Zaragoza, “but CAST already constraints part of the axion interpretation of the XENON signal.” Its successor, the International Axion Observatory (IAXO), which is set to begin data taking in 2024, will have improved sensitivity. “If the XENON1T signal is indeed an axion, IAXO will find it within the first hours of running,” says Garcia Irastorza.

A second new-physics explanation cited for XENON1T’s low-energy excess is an enhanced rate of solar neutrinos interacting in the detector. In the Standard Model, neutrinos have a negligibly small magnetic moment, however, should they be Majorana rather than Dirac fermions, and identical to their antiparticles, their magnetic moment should be larger, and proportional to their mass, though still not detectable. New physics beyond the Standard Model could, however, enhance the magnetic moment further. This leads to a larger interaction cross section at low energies and an excess of low-energy electron recoils. XENON1T fits indicate that solar Majorana neutrinos with an enhanced magnetic moment are also favoured over the background-only hypothesis at the level of 3σ.

The absorption of dark photons could explain the observed excess.

Joachim Kopp

The community has quickly chimed in with additional ideas, with around 40 papers appearing on the arXiv preprint server since the result was released. One possibility is a heavy dark-matter particle that annihilates or decays to a second, much lighter, “boosted dark-matter” particle which could scatter on electrons via some new interaction, notes CERN theorist Joachim Kopp. Another class of dark-matter model that has been proposed, he says, is “inelastic dark matter”, where dark-matter particles down-scatter in the detector into another dark-matter state just a few keV below the original one, with the liberated energy then seen in the detector. “An explanation I like a lot is in terms of dark photons,” he says. “The Standard Model would be augmented by a new U(1) gauge symmetry whose corresponding gauge boson, the dark photon, would mix with the Standard-Model photon. Dark photons could be abundant in the Universe, possibly even making up all the dark matter. Their absorption in the XENON1T detector could explain the observed excess.”

“The strongest asset we have is our new detector, XENONnT,” says Aprile. Despite COVID-19, the collaboration is on track to take first data before the end of 2020, she says. XENONnT will boast three times the fiducial volume of XENON1T and a factor six reduction in backgrounds, and should be able to verify or refute the signal within a few months of data taking. “An important question is if the signal has an annual modulation of about 7% correlated to the distance of the sun,” notes Lindner. “This would be a strong hint that it could be connected to new physics with solar neutrinos or solar axions.”

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A new experiment at Karlsruhe Institute of Technology (KIT) called FUNK – Finding U(1)s of a Novel Kind – has reported its first results in the search for ultralight dark matter. Using a large spherical mirror as an electromagnetic dark-matter antenna, the FUNK team has set an improved limit on the existence of hidden photons as candidates for dark matter with masses in the eV range.

Despite overwhelming astronomical evidence for the existence of dark matter, direct searches for dark-matter particles at colliders and dedicated nuclear-recoil experiments have so far come up empty handed. With these searches being mostly sensitive to heavy dark-matter particles, namely weakly interacting massive particles (WIMPs), the search for alternative light dark-matter candidates is growing in momentum. Hidden photons, a cold, ultralight dark-matter candidate, arise in extensions of the Standard Model which contain a new U(1) gauge symmetry and are expected to couple very weakly to charged particles via kinetic mixing with regular photons. Laboratory experiments that are sensitive to such hidden or dark photons include helioscopes such as the CAST experiment at CERN, and “light-shining-through-a-wall” methods such as ALPS experiment at DESY.

FUNK exploits a novel “dish-antenna” method first proposed in 2012, whereby a hidden photon crossing a metallic spherical mirror surface would cause faint electromagnetic waves to be emitted almost perpendicularly to the mirror surface, and be focused on the radius point. The experiment was conceived in 2013 at a workshop at DESY when it was realised that there was a perfectly suited mirror — a prototype for the Pierre Auger Observatory with a surface area of 14 m² – in the basement of KIT. Various photodetectors placed at the radius point allow FUNK to search for a signal in different wavelength ranges, corresponding to different hidden-photon masses. The dark-matter nature of a possible signal can then be verified by observing small daily and seasonal movements of the spot around the radius point as Earth moves through the dark-matter field. The broadband dish-antenna technique is able to scan hidden photons over a large parameter space.

The mass range of viable hidden-photon dark matter is huge

Joerg Jaeckel

Completed in 2018, the experiment took data during last year in several month-long runs using low-noise PMTs. In the mass range 2.5 – 7 eV, the data exclude a hidden-photon coupling stronger than 10⁻¹² in kinetic mixing. “This is competitive with limits derived from astrophysical results and partially exceeds those from other existing direct-detection experiments,” says FUNK principal investigator Ralph Engel of KIT. So far two other experiments of this type have reported search results for hidden photons in this energy range — the dish-antenna at the University of Tokyo and the SHUKET experiment at Paris-Saclay – though FUNK’s factor-of-ten larger mirror surface brings a greater experimental sensitivity, says the team. Other experiments, such as NA64 at CERN which employs missing-energy techniques, are setting stringent bounds on the strength of dark-photon couplings for masses in the MeV range and above.

“The mass range of viable hidden-photon dark matter is huge,” says FUNK collaborator Joerg Jaeckel of Heidelberg University. “For this reason, techniques which can scan over a large parameter space are especially useful even if they cannot explore couplings as small as is possible with some other dedicated methods. A future exploitation of the setup in other wavelength ranges is possible, and FUNK therefore carries an enormous physics potential.”

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Supersymmetry is an attractive extension of the Standard Model, and aims to answer some of the most fundamental open questions in modern particle physics. For example: why is the Higgs boson so light? What is dark matter and how does it fit in with our understanding of the universe? Do electroweak and strong forces unify at smaller distances?

Supersymmetry predicts a new partner for each elementary particle, including the heaviest particle ever observed – the top quark. If the partner of the top quark (the top squark, or “stop”) were not too heavy, the quantum corrections to the Higgs boson mass would largely cancel, thereby stabilising its small value of 125 GeV. Moreover, the lightest supersymmetric particle (LSP) may be stable and weakly interacting, providing a dark-matter candidate. Signs of the top squark, and thus supersymmetry, may yet be lurking in the enormous number of proton–proton collisions provided by the LHC.

Two new searches

The ATLAS collaboration recently released two new searches, each looking to detect pairs of top squarks by exploring the full LHC dataset corresponding to an integrated luminosity of 139 fb^–1 recorded during Run 2. Each top squark decays to a top quark and an LSP that escapes the detector without interacting. Thus, our experimental signature is an event that is energetically unbalanced, with two sets of top-quark remnants and a large amount of missing energy.

A challenge for such searches is that the masses of the supersymmetric particles are unknown, leaving a large range of possibilities to explore. Depending on the mass difference between the top squark and the LSP, the final decay products can be (very) soft or (very) energetic, calling for different reconstruction techniques and sparking the development of new approaches. For example, novel “soft b-tagging” techniques, based on either pure secondary-vertex information or jets built from tracks, were implemented for the first time in these analyses to extend the sensitivity to lower kinematic regimes. This allowed the searches to probe small top squark–LSP mass differences down to 5 GeV for the first time.

Leptoquark decays would exhibit a similar experimental signature to top-squark decays

Other sophisticated analysis strategies, including the use of machine-learning techniques, improved the discrimination between the signal and Standard-Model background and maximised the sensitivity of the analysis. Furthermore, these two searches are designed in such a way as to fully complement one another. Together they greatly extend the reach in the top squark mass versus LSP mass plane, including the challenging region where the top squark masses are very close to the top mass (figure 1). No evidence of new physics was found in any of these searches.

Beyond supersymmetry, these search results are intriguing for other new-physics scenarios. For example, the decay of a hypothetical top quark–neutrino hybrid, called a leptoquark, would exhibit a similar experimental signature to a top-squark decay. The results also constrain models predicting dark matter produced with a pair of top quarks that do not originate from supersymmetry.

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Physics beyond the Standard Model must exist, to account for dark matter, the smallness of neutrino masses and the dominance of matter over antimatter in the universe; but we have no real clue of its energy scale. It is also widely recognised that new and more precise tools will be needed to be certain that the 125 GeV boson discovered in 2012 is indeed the particle postulated by Brout, Englert, Higgs and others to have modified the base potential of the whole universe, thanks to its coupling to itself, liberating energy for the masses of the W and Z bosons.

To tackle these big questions, and others, the Future Circular Collider (FCC) study, launched in 2014, proposed the construction of a new 100 km circular tunnel to first host an intensity-frontier 90 to 365 GeV e⁺e^– collider (FCC-ee), and then an energy-frontier (> 100 TeV) hadron collider, which could potentially also allow electron–hadron collisions. Potentially following the High-Luminosity LHC in the late 2030s, FCC-ee would provide 5 × 10¹² Z decays – over five orders of magnitude more than the full LEP era, followed by 10⁸ W pairs, 10⁶ Higgs bosons (ZH events) and 10⁶ top-quark pairs. In addition to providing the highest parton centre-of-mass energies foreseeable today (up to 40 TeV), FCC-hh would also produce more than 1013 top quarks and W bosons, and 50 billion Higgs bosons per experiment.

Rising to the challenge

Following the publication of the four-volume conceptual design report and submissions to the European strategy discussions, the third FCC Physics and Experiments Workshop was held at CERN from 13 to 17 January, gathering more than 250 participants for 115 presentations, and establishing a considerable programme of work for the coming years. Special emphasis was placed on the feasibility of theory calculations matching the experimental precision of FCC-ee. The theory community is rising to the challenge. To reach the required precision at the Z-pole, three-loop calculations of quantum electroweak corrections must include all the heavy Standard Model particles (W^±, Z, H, t).

In parallel, a significant focus of the meeting was on detector designs for FCC-ee, with the aim of forming experimental proto-collaborations by 2025. The design of the interaction region allows for a beam vacuum tube of 1 cm radius in the experiments – a very promising condition for vertexing, lifetime measurements and the separation of bottom and charm quarks from light-quark and gluon jets. Elegant solutions have been found to bring the final-focus magnets close to the interaction point, using either standard quadrupoles or a novel magnet design using a superposition of off-axis (“canted”) solenoids. Delegates discussed solutions for vertexing, tracking and calorimetry during a Z-pole run at FCC-ee, where data acquisition and trigger electronics would be confronted with visible Z decays at 70 kHz, all of which would have to be recorded in full detail. A new subject was π/K/p identification at energies from 100 MeV to 40 GeV – a consequence of the strategy process, during which considerable interest was expressed in the flavour-physics programme at FCC-ee.

Physicists cannot refrain from investigating improvements

The January meeting showed that physicists cannot refrain from investigating improvements, in spite of the impressive statistics offered by the baseline design of FCC-ee. Increasing the number of interaction points from two to four is a promising way to nearly double the total delivery of luminosity for little extra power consumption, but construction costs and compatibility with a possible subsequent hadron collider must be determined. A bolder idea discussed at the workshop aims to improve both luminosity (by a factor of 10) and energy reach (perhaps up to 600 GeV), by turning FCC-ee into a 100 km energy-recovery linac. The cost, and how well this would actually work, are yet to be established. Finally, a tantalising possibility is to produce the Higgs boson directly in the s-channel: e⁺e^– → H, sitting exactly at a centre-of-mass energy equal to that of the Higgs boson. This would allow unique access to the tiny coupling of the Higgs boson to the electron. As the Higgs width (4.2 MeV in the Standard Model) is more than 20 times smaller than the natural energy spread of the beam, this would require a beam manipulation called monochromatisation and a careful running procedure, which a task force was nominated to study.

The ability to precisely probe the self-coupling of the Higgs boson is the keystone of the FCC physics programme. As said above, this self-interaction is the key to the electroweak phase transition, and could have important cosmological implications. Building on the solid foundation of precise and model-independent measurements of Higgs couplings at FCC-ee, FCC-hh would be able to access Hμμ, Hγγ, HZγ and Htt couplings at sub-percent precision. Further study of double Higgs production at FCC-hh shows that a measurement of the Higgs self-coupling could be done with a statistical precision of a couple of percent with the full statistics – which is to say that after the first few years of running the precision will already have been reduced to below 10%. This is much faster than previously realised, and definitely constituted the highlight of the workshop

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While CPV is well established in the weak interactions of quarks (most recently in the charm system by the LHCb collaboration), and is explained in the SM by the existence of a phase in the CKM matrix, the amount of CPV observed is many orders of magnitude too small to account for the observed cosmological matter-antimatter imbalance. Searching for additional sources of CPV is a major programme in particle physics, with a moderate-significance suggestion of CPV in lepton interactions recently announced by the T2K collaboration. It is likely that sources of CPV from phenomena beyond the scope of the SM are needed, and the detailed properties of the Higgs sector are one of several possible hiding places.

Based on the full LHC Run 2 dataset, ATLAS and CMS studied events where the Higgs boson is produced in association with one or two top quarks before decaying into two photons. The latter (ttH) process, which accounts for around 1% of the Higgs bosons produced at the LHC, was observed by both collaborations in 2018. But the tH production channel is predicted to be about six times rarer. This is due to destructive interference between higher order diagrams involving W bosons, and makes the tH process particularly sensitive to new-physics processes.

Exploring the CP properties of these interactions is non-trivial

According to the SM, the Higgs boson is “CP-even” – that is, it is possible to rotate-away any CP-odd phase from the scalar mass term. Previous probes of the interaction between the Higgs and vector bosons by CMS and ATLAS support the CP-even nature of the Higgs boson, determining its quantum numbers to be most consistent with J^PC = 0⁺⁺, though small CP-odd contributions from a more complex coupling structure are not excluded. The presence of a CP-odd component, together with the dominant CP-even one, would imply CPV, altering the kinematic properties of the ttH process and modifying tH production. Exploring the CP properties of these interactions is non-trivial, and requires the full capacities of the detectors and analysis techniques.

The collaborations employed machine-learning (Boosted Decision Tree) algorithms to disentangle the relative fractions of the CP-even and CP-odd components of top-Higgs interactions. The CMS collaboration observed ttH production at significance of 6.6σ, and excluded a pure CP-odd structure of the top-Higgs Yukawa coupling at 3.2σ. The ratio of the measured ttH production rate to the predicted production rate was found by CMS to be 1.38 with an uncertainty of about 25%. ATLAS data also show agreement with the SM. Assuming a CP-even coupling, ATLAS observed ttH with a significance of 5.2σ. Comparing the strength of the CP-even and CP-odd components, the collaboration favours a CP-mixing angle very close to 0 (indicating no CPV) and excludes a pure CP-odd coupling at 3.9σ. ATLAS did not observe tH production, setting an upper limit on its rate of 12 times the SM expectation.

In addition to further probing the CP properties of the top–Higgs interaction with larger data samples, ATLAS and CMS are searching in other Higgs-boson interactions for signs of CPV.

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The Belle II collaboration at the SuperKEKB collider in Japan has published its first physics analysis: a search for Z′ bosons, which are hypothesised to couple the Standard Model (SM) with the dark sector. The team scoured four months of data from a pilot run in 2018 for evidence of invisibly decaying Z′ bosons in the process e⁺e⁻→μ⁺μ⁻Z′, and for  lepton-flavour violating Z′ bosons in e⁺e⁻→e^±μ^∓Z′, by looking for missing energy recoiling against two clean lepton tracks. “This is the first ever search for the process e⁺e⁻→μ⁺μ⁻Z′ where the Z′ decays invisibly,” says Belle II spokesperson Toru Iijima of Nagoya University.

The team did not find any excess of events, yielding preliminary sensitivity to the coupling g′ in the so-called L_μ−L_τ extension of the SM, wherein the Z′ couples only to muon and tau-lepton flavoured SM particles and the dark sector. This model also has the potential to explain anomalies in b → sμ⁺μ⁻ decays reported by LHCb and the longstanding muon g-2 anomaly, claims the team.

The results come a little over a year since the first collisions were recorded in the fully instrumented Belle II detector on 25 March 2019. Following in the footsteps of Belle at the KEKB facility, the new SuperKEKB b-factory plans to achieve a 40-fold increase on the luminosity of its predecessor, which ran from 1999 to 2010. First turns were achieved in February 2016, and first collisions between its asymmetric-energy electron and positron beams were achieved in April 2018. The machine has now reached a luminosity of 1.4 × 10³⁴ cm^-2 s^-1 and is currently integrating around 0.7 fb^-1 each day, exceeding the peak luminosity of the former PEP-II/BaBar facility at SLAC, notes Iijima.

By summer the team aims to exceed the Belle/KEKB record of 2.1 × 10³⁴ cm^-2 s^-1 by implementing a nonlinear “crab waist” focusing scheme. First used at the electron-positron collider DAΦNE at INFN Frascati, and not to be confused with the crab-crossing technology used to boost the luminosity at KEKB and planned for the high-luminosity LHC, the scheme stabilises e⁺e^– beam-beam blowup using carefully tuned sextupole magnets located symmetrically on either side of the interaction point. “The 100 fb^-1 sample which we plan to integrate by summer will allow us to provide our first interesting results in B physics,” says Tom Browder of the University of Hawaii, who was Belle II spokesperson until last year.

Flavour debut

Belle II will make its debut in flavour physics at a vibrant moment, complementing  efforts to resolve hints of anomalies seen at the LHC, such as the recent test of lepton-flavour universality in beauty-baryon decays by the LHCb collaboration.

We will then look for the star attraction of the dark sector, the dark photon

Tom Browder

As well as updating searches for  invisible decays of the Z′ with one to two orders of magnitude more data, Belle II will now conduct further dark-sector studies including a search for axion-like particles decaying to two photons, the Z′ decaying to visible final states and dark-Higgstrahlung with a μ⁺μ^– pair and missing energy, explains Browder. “We will then look for the star attraction of the dark sector, the dark photon, with the difficult signature of e⁺e^– to a photon and nothing else.”

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The LHCb collaboration has confirmed previous hints of odd behaviour in the way B mesons decay into a K^*and a pair of muons, bringing fresh intrigue to the pattern of flavour anomalies that has emerged during the past few years. At a seminar at CERN on 10 March, Eluned Smith of RWTH Aachen University presented an updated analysis of the angular distributions of B⁰→K^*0μ⁺μ^– decays based on around twice as many events than were used for the collaboration’s previous measurement reported in 2015. The result reveals a mild increase in the overall tension with the Standard Model (SM) prediction, though, at 3.3σ, more data are needed to determine the source of the effect.

The B⁰→K^*0μ⁺μ^– decay is a promising system with which to explore physics beyond the SM. A flavour-changing neutral-current process, it involves a quark transition (b→s) which is forbidden at the lowest perturbative order in the SM, and therefore occurs only around once for every million B decays. The decay proceeds instead via higher-order penguin and box processes, which are sensitive to the presence of new, heavy particles. Such particles would enter in competing processes and could significantly change the B⁰→K^*0μ⁺μ^– decay rate and the angular distribution of its final-state particles. Measuring angular distributions as a function of the invariant mass squared (q²) of the muon pair is of particular interest because it is possible to construct variables that depend less on hadronic modelling uncertainties.

Potentially anomalous behaviour in an angular variable called P₅′ came to light in 2013, when LHCb reported a 3.7σ local deviation with respect to the SM in one q² bin, based on 1fb^-1 of data. In 2015, a global fit of different angular distributions of the B⁰→K^*0μ⁺μ^– decays using the total Run 1 data sample of 3 fb^-1 reaffirmed the puzzle, showing discrepancies of 3.4σ (later reduced to 3.0σ when using new theory calculations with an updated description of potentially large hadronic effects). In 2016, the Belle experiment at KEK in Japan performed its own angular analysis of B⁰→K^*0μ⁺μ^– using data from electron—positron collisions and found a 2.1σ deviation in the same direction and in the same q² region as the LHCb anomaly.

We as a community have been eagerly waiting for this measurement and LHCb has not disappointed

Jure Zupan

The latest LHCb result includes additional Run 2 data collected during 2016, corresponding to a total integrated luminosity of 4.7fb^-1. It shows that the local tension of P₅′ in two q² bins between 4 and 8 GeV²/c⁴ reduces from 2.8 and 3.0σ, as observed in the previous analysis, to 2.5 and 2.9σ. However, a global fit to several angular observables shows that the overall tension with the SM increases from 3.0 to 3.3σ. The results of the fit also find a better overall agreement with predictions of new-physics models that contain additional vector or axial-vector contributions. However, the collaboration also makes it clear that the discrepancy could be explained by an unexpectedly large hadronic effect that is not accounted for in the SM predictions.

“We as a community have been eagerly waiting for this measurement and LHCb has not disappointed,” says theorist Jure Zupan of the University of Cincinnati. “The new measurements have moved closer to the SM predictions in the angular observables so that the combined significance of the excess remained essentially the same. It is thus becoming even more important to understand well and scrutinise the SM predictions and the claimed theory errors.”

Flavour puzzle
The latest result makes LHCb’s continued measurements of lepton-flavour universality even more important, he says. In recent years, LHCb has also found that the ratio of the rates of muonic and electronic B decays departs from the SM prediction, suggesting a violation of the key SM principle of lepton-flavour universality. Though not individually statistically significant, the measurements are theoretically very clean, and the most striking departure – in the variable known as R_K — concerns B decays that proceed via the same b→s transition as B⁰→K^*0μ⁺μ^–. This has led physicists to speculate that the two effects could be caused by the same new physics, with models involving leptoquarks or new gauge bosons in principle able to accommodate both sets of anomalies.

An update on R_K based on additional Run 2 data is hotly anticipated, and the collaboration is also planning to add data from 2017-18 to the B⁰→K^*0μ⁺μ^– angular analysis, as well as working on further analyses with b-quark transitions in mesons. LHCb also recently brought the decays of beauty baryons, which also depend on b→s transitions, to bear on the subject. Departures from the norm have also been spotted in B decays to D mesons, which involve tree-level b→c quark transitions. Such decays probe lepton-flavour universality via comparisons between tau leptons and muons and electrons but, as with R_K, the individual measurements are not highly significant.

“We have not seen evidence of new physics, but neither were the B physics anomalies ruled out,” says Zupan of the LHCb result. “The wait for the clear evidence of new physics continues.”

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Three major conclusions can be drawn frofm these first 10 years. First and foremost, Run 1 has shown that the Higgs boson – the previously missing, last ingredient of the Standard Model (SM) – exists. Secondly, the exploration of energy scales as high as several TeV has further consolidated the robustness of the SM, providing no compelling evidence for phenomena beyond the SM (BSM). Nevertheless, several discoveries of new phenomena within the SM have emerged, underscoring the power of the LHC to extend and deepen our understanding of the SM dynamics, and showing the unparalleled diversity of phenomena that the LHC can probe with unprecedented precision.

Exceeding expectations

Last but not least, we note that 10 years of LHC operations, data taking and data interpretation, have overwhelmingly surpassed all of our most optimistic expectations. The accelerator has delivered a larger than expected luminosity, and the experiments have been able to operate at the top of their ideal performance and efficiency. Computing, in particular via the Worldwide LHC Computing Grid, has been another crucial driver of the LHC’s success. Key ingredients of precision measurements, such as the determination of the LHC luminosity, or of detection efficiencies and of backgrounds using data-driven techniques beyond anyone’s expectations, have been obtained thanks to novel and powerful techniques. The LHC has also successfully provided a variety of beam and optics configurations, matching the needs of different experiments and supporting a broad research programme. In addition to the core high-energy goals of the ATLAS and CMS experiments, this has enabled new studies of flavour physics and of hadron spectroscopy, of forward-particle production and total hadronic cross sections. The operations with beams of heavy nuclei have reached a degree of virtuosity that made it possible to collide not only the anticipated lead beams, but also beams of xenon, as well as combined proton–lead, photon–lead and photon-photon collisions, opening the way to a new generation of studies of matter at high density.

Theoretical calculations have evolved in parallel to the experimental progress. Calculations that were deemed of impossible complexity before the start of the LHC have matured and become reality. Next-to-leading-order (NLO) theoretical predictions are routinely used by the experiments, thanks to a new generation of automatic tools. The next frontier, next-to-next-to-leading order (NNLO), has been attained for many important processes, reaching, in a few cases, the next-to-next-to-next-to-leading order (N³LO), and more is coming.

Aside from having made these first 10 years an unconditional success, all these ingredients are the premise for confident extrapolations of the physics reach of the LHC programme to come.

To date, more than 2700 peer-reviewed physics papers have been published by the seven running LHC experiments (ALICE, ATLAS, CMS, LHCb, LHCf, MoEDAL and TOTEM). Approximately 10% of these are related to the Higgs boson, and 30% to searches for BSM phenomena. The remaining 1600 or so report measurements of SM particles and interactions, enriching our knowledge of the proton structure and of the dynamics of strong interactions, of electroweak (EW) interactions, of flavour properties, and more. In most cases, the variety, depth and precision of these measurements surpass those obtained by previous experiments using dedicated facilities. The multi-purpose nature of the LHC complex is unique, and encompasses scores of independent research directions. Here it is only possible to highlight a fraction of the milestone results from the LHC’s expedition so far.

Entering the Higgs world

The discovery by ATLAS and CMS of a new scalar boson in July 2012, just two years into LHC physics operations, was a crowning early success. Not only did it mark the end of a decades-long search, but it opened a new vista of exploration. At the time of the discovery, very little was known about the properties and interactions of the new boson. Eight years on, the picture has come into much sharper focus.

The structure of the Higgs-boson interactions revealed by the LHC experiments is still incomplete. Its couplings to the gauge bosons (W, Z, photon and gluons) and to the heavy third-generation fermions (bottom and top quarks, and tau leptons) have been detected, and the precision of these measurements is at best in the range of 5–10%. But the LHC findings so far have been key to establish that this new particle correctly embodies the main observational properties of the Higgs boson, as specified by the Brout–Englert–Guralnik–Hagen–Higgs–Kibble EW-symmetry breaking mechanism, referred hereafter as “BEH”, a cornerstone of the SM. To start with, the measured couplings to the W and Z bosons reflect the Higgs’ EW charges and are proportional to the W and Z masses, consistently with the properties of a scalar field breaking the SM EW symmetry. The mass dependence of the Higgs interactions with the SM fermions is confirmed by the recent ATLAS and CMS observations of the H → bb and H → ττ decays, and of the associated production of a Higgs boson together with a tt quark pair (see figure 1).

These measurements, which during Run 2 of the LHC have surpassed the five-sigma confidence level, provide the second critical confirmation that the Higgs fulfills the role envisaged by the BEH mechanism. The Higgs couplings to the photon and the gluon (g), which the LHC experiments have probed via the H → γγ decay and the gg → H production, provide a third, subtler test. These couplings arise from a combination of loop-level interactions with several SM particles, whose interplay could be modified by the presence of BSM particles, or interactions. The current agreement with data provides a strong validation of the SM scenario, while leaving open the possibility that small deviations could emerge from future higher statistics.

The process of firmly establishing the identification of the particle discovered in 2012 with the Higgs boson goes hand-in-hand with two research directions pioneered by the LHC: seeking the deep origin of the Higgs field and using the Higgs boson as a probe of BSM phenomena.

The breaking of the EW symmetry is a fact of nature, requiring the existence of a mechanism like BEH. But, if we aim beyond a merely anthropic justification for this mechanism (i.e. that, without it, physicists wouldn’t be here to ask why), there is no reason to assume that nature chose its minimal implementation, namely the SM Higgs field. In other words: where does the Higgs boson detected at the LHC come from? This summarises many questions raised by the possibility that the Higgs boson is not just “put in by hand” in the SM, but emerges from a larger sector of new particles, whose dynamics induces the breaking of the EW symmetry. Is the Higgs elementary, or a composite state resulting from new confining forces? What generates its mass and self-interaction? More generally, is the existence of the Higgs boson related to other mysteries, such as the origin of dark matter (DM), of neutrino masses or of flavour phenomena?

The Higgs boson is becoming an increasingly powerful exploratory tool to probe the origin of the Higgs itself

Ever since the Higgs-boson discovery, the LHC experiments have been searching for clues to address these questions, exploring a large number of observables. All of the dominant production channels (gg fusion, associated production with vector bosons and with top quarks, and vector-boson fusion) have been discovered, and decay rates to WW, ZZ, γγ, bb and ττ were measured. A theoretical framework (effective field theory, EFT) has been developed to interpret in a global fashion all these measurements, setting strong constraints on possible deviations from the SM. With the larger data set accumulated during Run 2, the production properties of the Higgs have been studied with greater detail, simultaneously testing the accuracy of theoretical calculations, and the resilience of SM predictions.

To explore the nature of the Higgs boson, what has not been seen as yet can be as important as what was seen. For example, lack of evidence for Higgs decays to the fermions of the first and second generation is consistent with the SM prediction that these should be very rare. The H → μμ decay rate is expected to be about 3 × 10^–3 times smaller than that of H → ττ; the current sensitivity is two times below, and ATLAS and CMS hope to first observe this decay during the forthcoming Run 3, testing for the first time the couplings of the Higgs boson to second-generation fermions. The SM Higgs boson is expected to conserve flavour, making decays such as H → μτ, H → eτ or t → Hc too small to be seen. Their observation would be a major revolution in physics, but no evidence has shown up in the data so far. Decays of the Higgs to invisible particles could be a signal of DM candidates, and constraints set by the LHC experiments are complementary to those from standard DM searches. Several BSM theories predict the existence of heavy particles decaying to a Higgs boson. For example, heavy top partners, T, could decay as T → Ht, and heavy bosons X decay as X → HV (V = W, Z). Heavy scalar partners of the Higgs, such as charged Higgs states, are expected in theories such as supersymmetry. Extensive and thorough searches of all these phenomena have been carried out, setting strong constraints on SM extensions.

As the programme of characterising the Higgs properties continues, with new challenging goals such as the measurement of the Higgs self-coupling through the observation of Higgs pair production, the Higgs boson is becoming an increasingly powerful exploratory tool to probe the origin of the Higgs itself, as well as a variety of solutions to other mysteries of particle physics.

Interactions weak and strong

The vast majority of LHC processes are controlled by strong interactions, described by the quantum-chromodynamics (QCD) sector of the SM. The predictions of production rates for particles like the Higgs or gauge bosons, top quarks or BSM states, rely on our understanding of the proton structure, in particular of the energy distribution of its quark and gluon components (the parton distribution functions, PDFs). The evolution of the final states, the internal structure of the jets emerging from quark and gluons, the kinematical correlations between different objects, are all governed by QCD. LHC measurements have been critical, not only to consolidate our understanding of QCD in all its dynamical domains, but also to improve the precision of the theoretical interpretation of data, and to increase the sensitivity to new phenomena and to the production of BSM particles.

Collisions galore

Approximately 10⁹ proton–proton (pp) collisions take place each second inside the LHC detectors. Most of them bear no obvious direct interest for the search of BSM phenomena, but even simple elastic collisions, pp → pp, which account for about 30% of this rate, have so far failed to be fully understood with first-principle QCD calculations. The ATLAS ALFA spectrometer and the TOTEM detector have studied these high-rate processes, measuring the total and elastic pp cross sections, at the various beam energies provided by the LHC. The energy dependence of the relation between the real and imaginary part of the pp forward scattering amplitude has revealed new features, possibly described by the exchange of the so-called odderon, a coherent state of three gluons predicted in the 1970s.

The structure of the final states in generic pp collisions, aside from defining the large background of particles that are superimposed on the rarer LHC processes, is of potential interest to understand cosmic-ray (CR) interactions in the atmosphere. The LHCf detector measured the forward production of the most energetic particles from the collision, those driving the development of the CR air showers. These data are a unique benchmark to tune the CR event generators, reducing the systematics in the determination of the nature of the highest-energy CR constituents (protons or heavy nuclei?), a step towards solving the puzzle of their origin.

On the opposite end of the spectrum, rare events with dijet pairs of mass up to 9 TeV have been observed by ATLAS and CMS. The study of their angular distribution, a Rutherford-like scattering experiment, has confirmed the point-like nature of quarks, down to 10^–18 cm. The overall set of production studies, including gauge bosons, jets and top quarks, underpins countless analyses. Huge samples of top quark pairs, produced at 15 Hz, enable the surgical scrutiny of this mysteriously heavy quark, through its production and decays. New reactions, unobservable before the LHC, were first detected. Gauge-boson scattering (e.g. W⁺ W⁺ → W⁺ W⁺), a key probe of electroweak symmetry breaking proposed in the 1970s, is just one example. By and large, all data show an extraordinary agreement with theoretical predictions resulting from decades of innovative work (figure 2). Global fits to these data refine the proton PDFs, improving the predictions for the production of Higgs bosons or BSM particles.

The cross sections σ of W and Z bosons provide the most precise QCD measurements, reaching a 2% systematic uncertainty, dominated by the luminosity uncertainty. Ratios such as σ(W⁺)/σ(W^–) or σ(W)/σ(Z), and the shapes of differential distributions, are known to a few parts in 1000. These data challenge the theoretical calculations’ accuracy, and require caution to assess whether small discrepancies are due to PDF effects, new physics or yet imprecise QCD calculations.

Precision is the keystone to consolidate our description of nature

As already mentioned, the success of the LHC owes a lot to its variety of beam and experimental conditions. In this context, the data at the different centre-of-mass energies provided in the two runs are a huge bonus, since the theoretical prediction for the energy-dependence of rates can be used to improve the PDF extraction, or to assess possible BSM interpretations. The LHCb data, furthermore, cover a forward kinematical region complementary to that of ATLAS and CMS, adding precious information.

The precise determination of the W and Z production and decay kinematics has also allowed new measurements of fundamental parameters of the weak interaction: the W mass (m_W) and the weak mixing angle (sinθ_W). The measurement of sinθ_W is now approaching the precision inherited from the LEP experiments and SLD, and will soon improve to shed light on the outstanding discrepancy between those two measurements. The m_W precision obtained by the ATLAS experiment, Δm_W = 19 MeV, is the best worldwide, and further improvements are certain. The combination with the ATLAS and CMS measurements of the Higgs boson mass (Δm_H ≅ 200 MeV) and of the top quark mass (Δm_top ≲ 500 MeV), provides a strong validation of the SM predictions (see figure 3). For both m_W and sinθ_W the limiting source of systematic uncertainty is the knowledge of the PDFs, which future data will improve, underscoring the profound interplay among the different components of the LHC programme.

QCD matters

The understanding of the forms and phases that QCD matter can acquire is a fascinating, broad and theoretically challenging research topic, which has witnessed great progress in recent years. Exotic multi-quark bound states, beyond the usual mesons (qq) and baryons (qqq), were initially discovered at e⁺e^– colliders. The LHCb experiment, with its large rates of identified charm and bottom final states, is at the forefront of these studies, notably with the first discovery of heavy pentaquarks (qqqcc) and with discoveries of tetraquark candidates in the charm sector (qccq), accompanied by determinations of their quantum numbers and properties. These findings have opened a new playground for theoretical research, stimulating work in lattice QCD, and forcing a rethinking of established lore.

The study of QCD matter at high density is the core task of the heavy-ion programme. While initially tailored to the ALICE experiment, all active LHC experiments have since joined the effort. The creation of a quark–gluon plasma (QGP) led to astonishing visual evidence for jet quenching, with 1 TeV jets shattered into fragments as they struggle their way out of the dense QGP volume. The thermodynamics and fluctuations of the QGP have been probed in multiple ways, indicating that the QGP behaves as an almost perfect fluid, the least viscous fluid known in nature. The ability to explore the plasma interactions of charm and bottom quarks is a unique asset of the LHC, thanks to the large production rates, which unveiled new phenomena such as  the recombination of charm quarks, and the sequential melting of bb bound states.

While several of the qualitative features of high-density QCD were anticipated, the quantitative accuracy, multitude and range of the LHC measurements have no match. Examples include ALICE’s precise determination of dynamical parameters such as the QGP shear-viscosity-to-entropy-density ratio, or the higher harmonics of particles’ azimuthal correlations. A revolution ensued in the sophistication of the required theoretical modelling. Unexpected surprises were also discovered, particularly in the comparison of high-density states in PbPb collisions with those occasionally generated by smaller systems such as pp and pPb. The presence in the latter of long-range correlations, various collective phenomena and an increased strange baryon abundance (figure 4), resemble behaviour typical of the QGP. Their deep origin is a mysterious property of QCD, still lacking an explanation. The number of new challenging questions raised by the LHC data is almost as large as the number of new answers obtained!

Flavour physics

Understanding the structure and the origin of flavour phenomena in the quark sector is one of the big open challenges of particle physics. The search for new sources of CP violation, beyond those present in the CKM mixing matrix, underlies the efforts to explain the baryon asymmetry of the universe. In addition to flavour studies with Higgs bosons and top quarks, more than 10¹⁴ charm and bottom quarks have been produced so far by the LHC, and the recorded subset has led to landmark discoveries and measurements. The rare B_s → μμ decay, with a minuscule rate of approximately 3 × 10^–9, has been discovered by the LHCb, CMS and ATLAS experiments. The rarer B_d → μμ decay is still unobserved, but its expected ~10^–10 rate is within reach. These two results alone had a big impact on constraining the parameter space of several BSM theories, notably supersymmetry, and their precision and BSM sensitivity will continue improving. LHCb has discovered DD mixing and the long-elusive CP violation in D-meson decays, a first for up-type quarks (figure 5). Large hadronic non-perturbative uncertainties make the interpretation of these results particularly challenging, leaving under debate whether the measured properties are consistent with the SM, or signal new physics. But the experimental findings are a textbook milestone in the worldwide flavour physics programme.

LHCb produced hundreds more measurements of heavy-hadron properties and flavour-mixing parameters. Examples include the most precise measurement of the CKM angle γ = (74.0^+5.0_–5.8)^o and, with ATLAS and CMS, the first measurement of φ_s, the tiny CP-violation phase of B_s → J/ψϕ, whose precisely predicted SM value is very sensitive to new physics. With a few notable exceptions, all results confirm the CKM picture of flavour phenomena. Those exceptions, however, underscore the power of LHC data to expose new unexpected phenomena: B → D^(*) ℓν (ℓ = μ,τ) and B → K^(*)ℓ⁺ℓ^– (ℓ = e,μ) decays hint at possible deviations from the expected lepton flavour universality. The community is eagerly waiting for further developments.

Beyond the Standard Model

Years of model building, stimulated before and after the LHC start-up by the conceptual and experimental shortcomings of the SM (e.g. the hierarchy problem and the existence of DM), have generated scores of BSM scenarios to be tested by the LHC. Evidence has so far escaped hundreds of dedicated searches, setting limits on new particles up to several TeV (figure 6). Nevertheless, much was learned. While none of the proposed BSM scenarios can be conclusively ruled out, for many of them survival is only guaranteed at the cost of greater fine-tuning of the parameters, reducing their appeal. In turn, this led to rethinking the principles that implicitly guided model building. Simplicity, or the ability to explain at once several open problems, have lost some drive. The simplest realisations of BSM models relying on supersymmetry, for example, were candidates to at once solve the hierarchy problem, provide DM candidates and set the stage for the grand unification of all forces. If true, the LHC should have piled up evidence by now. Supersymmetry remains a preferred candidate to achieve that, but at the price of more Byzantine constructions. Solving the hierarchy problem remains the outstanding theoretical challenge. New ideas have come to the forefront, ranging from the Higgs potential being determined by the early-universe evolution of an axion field, to dark sectors connected to the SM via a Higgs portal. These latter scenarios could also provide DM candidates alternative to the weakly-interacting massive particles, which so far have eluded searches at the LHC and elsewhere.

With such rapid evolution of theoretical ideas taking place as the LHC data runs progressed, the experimental analyses underwent a major shift, relying on “simplified models”: a novel model-independent way to represent the results of searches, allowing published results to be later reinterpreted in view of new BSM models. This amplified the impact of experimental searches, with a surge of phenomenological activity and the proliferation of new ideas. The cooperation and synergy between experiments and theorists have never been so intense.

Having explored the more obvious search channels, the LHC experiments refocused on more elusive signatures. Great efforts are now invested in searching corners of parameter space, extracting possible subtle signals from large backgrounds, thanks to data-driven techniques, and to the more reliable theoretical modelling that has emerged from new calculations and many SM measurements. The possible existence of new long-lived particles opened a new frontier of search techniques and of BSM models, triggering proposals for new dedicated detectors (Mathusla, CODEX-b and FASER, the last of which was recently approved for construction and operation in Run 3). Exotic BSM states, like the milli-charged particles present in some theories of dark sectors, could be revealed by MilliQan, a recently proposed detector. Highly ionising particles, like the esoteric magnetic monopoles, have been searched for by the MoEDAL detector, which places plastic tracking films cleverly in the LHCb detector hall.

While new physics is still eluding the LHC, the immense progress of the past 10 years has changed forever our perspective on searches and on BSM model building.

Final considerations

Most of the results only parenthetically cited, like the precision on the mass of the top quark, and others not even quoted, are the outcome of hundreds of years of person-power work, and would have certainly deserved more attention here. Their intrinsic value goes well beyond what was outlined, and they will remain long-lasting textbook material, until future work at the LHC and beyond improves them.

Theoretical progress has played a key role in the LHC’s progress, enhancing the scope and reliability of the data interpretation. Further to the developments already mentioned, a deeper understanding of jet structure has spawned techniques to tag high-p_T gauge and Higgs bosons, or top quarks, now indispensable in many BSM searches. Innovative machine-learning ideas have become powerful and ubiquitous. This article has concentrated only on what has already been achieved, but the LHC and its experiments have a long journey of exploration ahead.

The terms precision and discovery, applied to concrete results rather than projections, well characterise the LHC 10-year legacy. Precision is the keystone to consolidate our description of nature, increase the sensitivity to SM deviations, give credibility to discovery claims, and to constrain models when evaluating different microscopic origins of possible anomalies. The LHC has already fully succeeded in these goals. The LHC has also proven to be a discovery machine, and in a context broader than just Higgs and BSM phenomena. Altogether, it delivered results that could not have been obtained otherwise, immensely enriching our understanding of nature.

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Anomalies, which I take to mean data that disagree with the scientific paradigm of the day, are the bread and butter of phenomenologists working on physics beyond the Standard Model (SM). Are they a mere blip or the first sign of new physics? A keen understanding of statistics is necessary to help decide which “bumps” to work on.

Take the excess in the rate of di-photon production at a mass of around 750 GeV spotted in 2015 by the ATLAS and CMS experiments. ATLAS had a 4σ peak with respect to background, which CMS seemed to confirm, although its signal was less clear. Theorists produced an avalanche of papers speculating on what the signal might mean but, in the end, the signal was not confirmed in new data. In fact, as is so often the case, the putative signal stimulated some very fruitful work. For example, it was realised that ultra-peripheral collisions between lead ions could produce photon-photon resonances, leading to an innovative and unexpected search programme in heavy-ion physics. Other authors proposed using such collisions to measure the anomalous magnetic moment of the tau lepton, which is expected to be especially sensitive to new physics, and in 2018 ATLAS and CMS found the first evidence for (non-anomalous) high-energy light-by-light scattering in lead-lead ultra-peripheral collisions.

Some anomalies have disappeared during the past decade not primarily because they were statistical fluctuations, but because of an improved understanding of theory. One example is the forward-backward asymmetry (A_FB) of top–antitop production at the Tevatron. At large transverse momentum, A_FB was measured to be much too large compared to SM predictions, which were at next-to-leading order in QCD with some partial next-to-next-to leading order (NNLO) corrections. The complete NNLO corrections, calculated in a Herculean effort, proved to contribute much more than was previously thought, faithfully describing top–antitop production both at the Tevatron and at the LHC.

Other anomalies are still alive and kicking. Arguably, chief among them is the long-standing oddity in the measurement of the anomalous magnetic moment of the muon, which is about 4σ discrepant with the SM predictions. Spotted 20 years ago, many papers have been written in an attempt to explain it, with contributions ranging from supersymmetric particles to leptoquarks. A similarly long-standing anomaly is a 3.8σ excess in the number of electron antineutrinos emerging from a muon–antineutrino beam observed by the LSND experiment and backed up more recently by MiniBooNE. Again, numerous papers attempting to explain the excess, e.g. in terms of the existence of a fourth “sterile” neutrino, have been written, but the jury is still out.

Some anomalies are more recent, and unexpected. The so-called “X17” anomaly reported at a nuclear physics experiment in Hungary, for instance, shows a significant excess in the rate of certain nuclear decays of ⁸Be and ⁴He nuclei (see Rekindled Atomki anomaly merits closer scrutiny) which has been interpreted as being due to the creation of a new particle of mass 17 MeV. Though possible theoretically, one needs to work hard to make this new particle not fall afoul of other experimental constraints; confirmation from an independent experiment is also needed. Personally, I am not pursuing this: I think that the best new-physics ideas have already been had by other authors.

When working on an anomaly, beyond-the-SM phenomenologists hypothesise a new particle and/or interaction to explain it, check to see if it works quantitatively, check to see if any other measurements rule the explanation out, then provide new ways in which the idea can be tested. After this, they usually check where the new physics might fit into a larger theoretical structure, which might explain some other mysteries. For example, there are currently many anomalies in measurements of B meson decays, each of which isn’t particularly statistically significant (typically 2–3σ away from the SM) but taken together they form a coherent picture with a higher significance. The exchange of hypothesised Z′ or leptoquark quanta provide working explanations, the larger structure also shedding light on the pattern of masses of SM fermions, and most of my research time is currently devoted to studying them.

The coming decade will presumably sort several current anomalies into discoveries, or those that “went away”. Belle II and future LHCb measurements should settle the B anomalies, while the anomalous muon magnetic moment may even be settled this year by the g-2 experiment at Fermilab. Of course, we hope that new anomalies will appear and stick. One anomaly from the late 1990s – that type 1a supernovae have an anomalous acceleration at large red-shifts – turned out to reveal the existence of dark-energy and produce the dominant paradigm of cosmology today. This reminds us that all surprising discoveries were anomalies at some stage.

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