The conference mixed updates on theoretical developments in Higgs-boson pair production, searches for new physics in the scalar sector, and the most recent results from Run 2 and Run 3 of the LHC. Among the highlights was the first Run 3 analysis released by ATLAS on the search for di-Higgs production in the bbγγ final state – a particularly sensitive channel for probing the Higgs self-coupling. This result builds on earlier Run 2 analyses and demonstrates significantly improved sensitivity, now comparable to the full Run 2 combination of all channels. These gains were driven by the use of new b-tagging algorithms, improved mass resolution through updated analysis techniques, and the availability of nearly twice the dataset.

Complementing this, CMS presented the first search for ttHH production – a rare process that would provide additional sensitivity to the Higgs self-coupling and Higgs–top interactions. Alongside this, ATLAS presented first experimental searches for triple Higgs boson production (HHH), one of the rarest processes predicted by the SM. Work on more traditional final states such as bbττ and bbbb is ongoing at both experiments, and continues to benefit from improved reconstruction techniques and larger datasets. 

Beyond current data, the workshop featured discussions of the latest combined projection study by ATLAS and CMS, prepared as part of the input to the upcoming European Strategy Update. It extrapolates results of the Run 2 analyses to expected conditions of the High-Luminosity LHC (HL-LHC), estimating future sensitivities to the Higgs self-coupling and di-Higgs cross-section in scenarios with vastly higher luminosity and upgraded detectors. Under these assumptions, the combined sensitivity of ATLAS and CMS to di-Higgs production is projected to reach a significance of 7.6σ, firmly establishing the process. 

These projections provide crucial input for analysis strategy planning and detector design for the next phase of operations at the HL-LHC. Beyond the HL-LHC, efforts are already underway to design experiments at future colliders that will enhance sensitivity to the production of Higgs pairs, and offer new insights into electroweak symmetry breaking.

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The discovery of the Higgs boson at the LHC in 2012 provided strong experimental support for the Brout–Englert–Higgs mechanism of spontaneous electroweak symmetry breaking (EWSB) as predicted by the Standard Model. The EWSB explains how the W and Z bosons, the mediators of the weak interaction, acquire mass: their longitudinal polarisation states emerge from the Goldstone modes of the Higgs field, linking the mass generation of vector bosons directly to the dynamics of the process.

Yet, its ultimate origins remain un­known and the Standard Model may only offer an effective low-energy description of a more fundamental theo­ry. Exploring this possibility requires precise tests of how EWSB operates, and vector boson scattering (VBS) provides a particularly sensitive probe. In VBS, two electroweak gauge bosons scatter off one another. The cross section remains finite at high energies only because there is an exact cancellation between the pure gauge-boson interactions and the Higgs-boson mediated contributions, an effect analogous to the role of the Z boson propagator in WW production at electron–positron colliders. Deviations from the expected behaviour could signal new dynamics, such as anomalous couplings, strong interactions in the Higgs sector or new particles at higher energy scales.

This result lays the groundwork for future searches for new physics hidden within the electroweak sector

VBS interactions are among the rarest observed so far at the LHC, with cross sections as low as one femtobarn. To disentangle them from the background, researchers rely on the distinctive experimental signature of two high-energy jets in the forward detector regions produced by the initial quarks that radiate the bosons, with minimal hadronic activity between them. Using the full data set from Run 2 of the LHC at a centre-of-mass energy of 13 TeV, the CMS collaboration carried out a comprehensive set of VBS measurements across several production modes: WW (with both same and opposite charges), WZ and ZZ, studied in five final states where both bosons decay leptonically and in two semi-leptonic configurations where one boson decays into leptons and the other into quarks. To enhance sensitivity further, the data from all the measurements have now been combined in a single joint fit, with a complete treatment of uncertainty correlations and a careful handling of events selected by more than one analysis. 

All modes, one analysis

To account for possible deviations from the expected predictions, each process is characterised by a signal strength parameter (μ), defined as the ratio of the measured production rate to the cross section predicted by the Standard Model. A value of μ near unity indicates consistency with the Standard Model, while significant deviations may suggest new physics. The results, summarised in figure 1, display good agreement with the Standard Model predictions: all measured signal strengths are consistent with unity within their respective uncertainties. A mild excess with respect to the leading-order theoretical predictions is observed across several channels, highlighting the need for more accurate modelling, in particular for the measurements that have reached a level of precision where systematic effects dominate. By presenting the first evidence for all charged VBS production modes from a single combined statistical analysis, this CMS result lays the groundwork for future searches for new physics hidden within the electroweak sector.

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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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Measuring the polarisation of same electric charge (same sign) W-boson pairs in VBS directly tests the predicted EW interactions at high energies through precision measurements. Furthermore, beyond-the-SM scenarios predict modifications to VBS, some affecting specific polarisation states, rendering such measurements valuable avenues for uncovering new physics.

Using the full proton–proton collision dataset from LHC Run 2 (2015–2018, 140 fb^–1 at 13 TeV), the ATLAS collaboration recently published the first evidence for longitudinally polarised W bosons in the electroweak production of same-sign W-boson pairs in final states including two same-sign leptons (electrons or muons) and missing transverse momentum, along with two jets (EW W^±W^±jj). This process is categorised by the polarisation states of the W bosons: fully longitudinal (W_L^±W_L^±jj), mixed (W_L^±W_T^±jj), and fully transverse (W_T^±W_T^±jj). Measuring the polarisation states is particularly challenging due to the rarity of the VBS events, the presence of two undetected neutrinos, and the absence of a single kinematic variable that efficiently distinguishes between polarisation states. To overcome this, deep neural networks (DNNs) were trained to exploit the complex correlations between event kinematic variables that characterise different polarisations. This approach enabled the separation of the fully longitudinal W_L^±W_L^±jj from the combined W_T^±W^±jj (W_L^±W_T^±jj plus W_T^±W_T^±jj) processes as well as the combined W_L^±W^±jj (W_L^±W_L^±jj plus W_L^±W_T^±jj) from the purely transverse W_T^±W_T^±jj contribution.

To measure the production of W_L^±W_L^±jj and W_L^±W^±jj processes, a first DNN (inclusive DNN) was trained to distinguish EW W^±W^±jj events from background processes. Variables such as the invariant mass of the two highest-energy jets provide strong discrimination for this classification. In addition, two independent DNNs (signal DNNs) were trained to extract polarisation information, separating either W_L^±W_L^±jj from W_T^±W^±jj or W_L^±W^±jj from W_T^±W_T^±jj, respectively. Angular variables, such as the azimuthal angle difference between the leading leptons and the pseudorapidity difference between the leading and subleading jets, are particularly sensitive to the scattering angles of the W bosons, enhancing the separation power of the signal DNNs. Each DNN is trained using up to 20 kinematic variables, leveraging correlations among them to improve sensitivity.

The signal DNN distributions, within each inclusive DNN region, were used to extract the W_L^±W_L^±jj and W_L^±W^±jj polarisation fractions through two independent maximum-likelihood fits. The excellent separation between the W_L^±W^±jj and W_T^±W_T^±jj processes can be seen in figure 2 for the W_L^±W^±jj fit, achieving better separation for higher scores of the signal DNN, represented in the x-axis. An observed (expected) significance of 3.3 (4.0) standard deviations was obtained for W_L^±W^±jj, providing the first evidence of same-sign WW production with at least one of the W bosons longitudinally polarised. No significant excess of events consistent with W_L^±W_L^±jj production was observed, leading to the most stringent 95% confidence-level upper limits to date on the W_L^±W_L^±jj cross section: 0.45 (0.70) fb observed (expected).

There is still much to understand about the electroweak sector of the Standard Model, and the measurement presented in this article remains limited by the size of the available data sample. The techniques developed in this analysis open new avenues for studying W- and Z-boson polarisation in VBS processes during the LHC Run 3 and beyond.

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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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It’s tough to be a lone dissenting voice, but the CDF collaboration is sticking to its guns. Ongoing cross-checks at the Tevatron experiment reinforce its 2022 measurement of the mass of the W boson, which stands seven standard deviations above the Standard Model (SM) prediction. All other measurements are statistically compatible with the SM, though slightly higher, including the most recent by the CMS collaboration at the LHC, which almost matched CDF’s stated precision of 9.4 MeV (CERN Courier November/December 2024 p7).

With CMS’s measurement came fresh scrutiny for the CDF collaboration, which had established one of the most interesting anomalies in fundamental science – a higher-than-expected W mass might reveal the presence of undiscovered heavy virtual particles. Particular scrutiny focused on the quoted momentum resolution of the CDF detector, which the collaboration claims exceeds the precision of any other collider detector by more than a factor of two. A new analysis by CDF verifies the stated accuracy of 25 parts per million by constraining possible biases using a large sample of cosmic-ray muons.

“The publication lays out the ‘warts and all’ of the tracking aspect and explains why the CDF measurement should be taken seriously despite being in disagreement with both the SM and silicon-tracker-based LHC measurements,” says spokesperson David Toback of Texas A&M University. “The paper should be seen as required reading for anyone who truly wants to understand, without bias, the path forward for these incredibly difficult analyses.”

The 2022 W-mass measurement exclusively used information from CDF’s drift chamber – a descendant of the multiwire proportional chamber invented at CERN by Georges Charpak in 1968 – and discarded information from its inner silicon vertex detector as it offered only marginal improvements to momentum resolution. The new analysis by CDF collaborator Ashutosh Kotwal of Duke University studies possible geometrical defects in the experiment’s drift chamber that could introduce unsuspected biases in the measured momenta of the electrons and muons emitted in the decays of W bosons.

“Silicon trackers have replaced wire-based technology in many parts of modern particle detectors, but the drift chamber continues to hold its own as the technology of choice when high accuracy is required over large tracking volumes for extended time periods in harsh collider environments,” opines Kotwal. “The new analysis demonstrates the efficiency and stability of the CDF drift chamber and its insensitivity to radiation damage.”

The CDF II detector operated at Fermilab’s Tevatron collider from 1999 to 2011. Its cylindrical drift chamber was coaxial with the colliding proton and antiproton beams, and immersed in an axial 1.4 T magnetic field. A helical fit yielded track parameters.

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Schwinger lined us up in his office, and spent several hours assigning thesis subjects. It was a remarkable performance. I was the last in line. Having run out of well-defined thesis problems, he explained to me that weak and electromagnetic interactions share two remarkable features: both are vectorial and both display aspects of universality. Schwinger suggested that I create a unified theory of the two interactions – an electroweak synthesis. How I was to do this he did not say, aside from slyly hinting at the Yang–Mills gauge theory.

By the summer of 1958, I had convinced myself that weak and electromagnetic interactions might be described by a badly broken gauge theory, and Schwinger that I deserved a PhD. I had hoped to partly spend a postdoctoral fellowship in Moscow at the invitation of the recent Russian Nobel laureate Igor Tamm, and sought to visit Niels Bohr’s institute in Copenhagen while awaiting my Soviet visa. With Bohr’s enthusiastic consent, I boarded the SS Île de France with my friend Jack Schnepps. Following a memorable and luxurious crossing – one of the great ship’s last – Jack drove south to Padova to work with Milla Baldo-Ceolin’s emulsion group in Padova, and I took the slow train north to Copenhagen. Thankfully, my Soviet visa never arrived. I found the SU(2) × U(1) structure of the electroweak model in the spring of 1960 at Bohr’s famous institute at Blegsdamvej 19, and wrote the paper that would earn my share of the 1979 Nobel Prize.

We called the new quark flavour “charm”, completing two weak doublets of quarks to match two weak doublets of leptons, and establishing lepton–quark symmetry, which holds to this day

A year earlier, in 1959, Augusto Gamba, Bob Marshak and Susumo Okubo had proposed lepton–hadron symmetry, which regarded protons, neutrons and lambda hyperons as the building blocks of all hadrons, to match the three known leptons at the time: neutrinos, electrons and muons. The idea was falsified by the discovery of a second neutrino in 1962, and superseded in 1964 by the invention of fractionally charged hadron constituents, first by George Zweig and André Petermann, and then decisively by Murray Gell-Mann with his three flavours of quarks. Later in 1964, while on sabbatical in Copenhagen, James Bjorken and I realised that lepton–hadron symmetry could be revived simply by adding a fourth quark flavour to Gell-Mann’s three. We called the new quark flavour “charm”, completing two weak doublets of quarks to match two weak doublets of leptons, and establishing lepton–quark symmetry, which holds to this day.

Annus mirabilis

1964 was a remarkable year. In addition to the invention of quarks, Nick Samios spotted the triply strange Ω^– baryon, and Oscar Greenberg devised what became the critical notion of colour. Arno Penzias and Robert Wilson stumbled on the cosmic microwave background radiation. James Cronin, Val Fitch and others discovered CP violation. Robert Brout, François Englert, Peter Higgs and others invented spontaneously broken non-Abelian gauge theories. And to top off the year, Abdus Salam rediscovered and published my SU(2) × U(1) model, after I had more-or-less abandoned electroweak thoughts due to four seemingly intractable problems.

Much to my surprise and delight, all of them would be solved within just a few years, with the last theoretical obstacle removed by Makoto Kobayashi and Toshihide Maskawa in 1973 (see “Four intractable problems” panel). A few months later, Paul Musset announced that CERN’s Gargamelle detector had won the race to detect weak neutral-current interactions, giving the electroweak model the status of a predictive theory. Remarkably, the year had begun with Gell-Mann, Harald Fritzsch and Heinrich Leutwyler proposing QCD, and David Gross, Frank Wilczek and David Politzer showing it to be asymptotically free. The Standard Model of particle physics was born.

Charmed findings

But where were the charmed quarks? Early on Monday morning on 11 November, 1974, I was awakened by a phone call from Sam Ting, who asked me to come to his MIT office as soon as possible. He and Ulrich Becker were waiting for me impatiently. They showed me an amazingly sharp resonance. Could it be a vector meson like the ρ or ω and be so narrow, or was it something quite different? I hopped in my car and drove to Harvard, where my colleagues Alvaro de Rújula and Howard Georgi excitedly regaled me about the Californian side of the story. A few days later, experimenters in Frascati confirmed the BNL–SLAC discovery, and de Rújula and I submitted our paper “Is Bound Charm Found?” – one of two papers on the J/ψ discovery printed in Physical Review Letters on 5 July 1965 that would prove to be correct. Among five false papers was one written by my beloved mentor, Julian Schwinger.

The second correct paper was by Tom Appelquist and David Politzer. Well before that November, they had realised (without publishing) that bound states of a charmed quark and its antiquark lying below the charm threshold would be exceptionally narrow due the asymptotic freedom of QCD. De Rújula suggested to them that such a system be called charmonium in an analogy with positronium. His term made it into the dictionary. Shortly afterward, the 1976 Nobel Prize in Physics was jointly awarded to Burton Richter and Sam Ting for “their pioneering work in the discovery of a heavy elementary particle of a new kind” – evidence that charm was not yet a universally accepted explanation. Over the next few years, experimenters worked hard to confirm the predictions of theorists at Harvard and Cornell by detecting and measuring the masses, spins and transitions among the eight sub-threshold charmonium states. Later on, they would do the same for 14 relatively narrow states of bottomonium.

Other experimenters were searching for particles containing just one charmed quark or antiquark. In our 1975 paper “Hadron Masses in a Gauge Theory”, de Rújula, Georgi and I included predictions of the masses of several not-yet-discovered charmed mesons and baryons. The first claim to have detected charmed particles was made in 1975 by Robert Palmer and Nick Samios at Brookhaven, again with a bubble-chamber event. It seemed to show a cascade decay process in which one charmed baryon decays into another charmed baryon, which itself decays. The measured masses of both of the charmed baryons were in excellent agreement with our predictions. Though the claim was not widely accepted, I believe to this day that Samios and Palmer were the first to detect charmed particles.

The SLAC electron–positron collider, operating well above charm threshold, was certainly producing charmed particles copiously. Why were they not being detected? I recall attending a conference in Wisconsin that was largely dedicated to this question. On the flight home, I met my old friend Gerson Goldhaber, who had been struggling unsuccessfully to find them. I think I convinced him to try a bit harder. A couple of weeks later in 1976, Goldhaber and François Pierre succeeded. My role in charm physics had come to a happy ending. 

• This article is adapted from a presentation given at the Institute of High-Energy Physics in Beijing on 20 October 2024 to celebrate the 50th anniversary of the discovery of the J/ψ.

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The portrait of the Higgs boson painted by experimental data is becoming more and more precise. Many new Run 2 and first Run 3 results have developed the picture this year. Highlights included the latest di-Higgs combinations with cross-section upper limits reaching down to 2.5 times the Standard Model (SM) expectations. A few excesses seen in various analyses were also discussed. The CMS collaboration reported a brand new excess of top–antitop events near the top–antitop production threshold, with a local significance of more than 5σ above the background described by perturbative quantum chromodynamics (QCD) only, that could be due to a pseudoscalar top–antitop bound state. A new W-boson mass measurement by the CMS collaboration – a subject deeply connected to electroweak symmetry breaking – was also presented, reporting a value consistent with the SM prediction with a very accurate precision of 9.9 MeV (CERN Courier November/December 2024 p7).

Parton shower event generators were in the spotlight. Historical talks by Torbjörn Sjöstrand (Lund University) and Bryan Webber (University of Cambridge) described the evolution of the PYTHIA and HERWIG generators, the crucial role they played in the discovery of the Higgs boson, and the role they now play in the LHC’s physics programme. Differences in the modelling of the parton–shower systematics by the ATLAS and CMS collaborations led to lively discussions!

The vision talk was given by Lance Dixon (SLAC) about the reconstruction of scattering amplitudes directly from analytic properties, as a complementary approach to Lagrangians and Feynman diagrams. Oliver Bruning (CERN) conveyed the message that the HL-LHC accelerator project is well on track, and Patricia McBride (Fermilab) reached a similar conclusion regarding ATLAS and CMS’s Phase-2 upgrades, enjoining new and young people to join the effort, to ensure they are ready and commissioned for the start of Run 4.

The next Higgs Hunting workshop will be held in Orsay and Paris from 15 to 17 July 2025, following EPS-HEP in Marseille from 7 to 11 July.

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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.”

The post W mass snaps back appeared first on CERN Courier.

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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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.

The post A rich harvest of results in Prague appeared first on CERN Courier.

Following the discovery of the Higgs boson in 2012, the CMS collaboration has been exploring its properties with ever-increasing precision. Data recorded during LHC Run 2 have been used to measure differential production cross-sections of the Higgs boson in different decay channels – a pair of photons, two Z bosons, two W bosons and two tau leptons – and as functions of different observables. These results have now been combined to provide measurements of spectra at the ultimate achievable precision.

Differential cross-section measurements provide the most model-independent way to study Higgs-boson production at the LHC, for which theoretical predictions exist up to next-to-next-to-next-to-leading order in perturbative QCD. One of the most important obser­vables is the transverse momentum (figure 1). This distribution is particularly sensitive both to modelling issues in Standard Model (SM) predictions and possible contributions from physics-beyond-the-SM (BSM).

In the new CMS result, two frameworks are used to test for hints of BSM: the κ-formalism and effective field theories.

The κ-formalism assumes that new physics effects would only affect the couplings between the Higgs boson and other particles. These new physics effects are then parameterised in terms of coefficients, κ. Using this approach, two-dimensional constraints are set on κ_c (the coupling coefficient of the Higgs boson to the charm quark), κ_b (Higgs to bottom) and κ_t (Higgs to top). None show significant deviations from the SM at present.

Effective field theories parametrise deviations from the SM by supplementing the Lagrangian with higher-dimensional operators and their associated Wilson coefficients (WCs). The effect of the operators is suppressed by powers of the putative new-physics energy scale, Λ. Measurements of WCs that differ from zero may hint at BSM physics.

The CMS differential cross-section measurements are parametrised, and constraints are derived on the WCs from a simultaneous fit. In the most challenging case, a set of 31 WCs is used as input to a principal-component analysis procedure in which the most sensitive directions in the data are identified. These directions (expressed as linear combinations of the WCs) are then constrained in a simultaneous fit (figure 2). In the upper panel, the limits on the WCs are converted to lower limits on the new physics scale. The results agree with SM predictions, with a moderate 2σ tension present in one of the directions (EV5). Here the major contribution is provided by the c_Hq3 coefficient, which mostly affects vector-boson fusion, VH production at high Higgs-boson transverse momenta (V = W, Z) and W-boson decays.

The combined results not only provide highly precise measurements of Higgs-boson production, but also place stringent constraints on possible deviations from the SM, deepening our understanding while leaving open the possibility of new physics at higher precision or energy scales.

The post Combining clues from the Higgs boson appeared first on CERN Courier.

The ATLAS collaboration recently released improved results on the Higgs boson’s interaction with second- and third-generation quarks (charm, bottom and top), based on the analysis of data collected during LHC Run 2 (2015–2018). The analyses refine two studies: Higgs-boson decays to charm- and bottom-quark pairs (H → cc and H → bb) in events where the Higgs boson is produced together with a weak boson V (W or Z); and, since the Higgs boson is too light to decay into a top-quark pair, the interaction with top quarks is probed in Higgs production in association with a top-quark pair (ttH) in events with H → bb decays. Sensitivity to H → cc and H → bb in VH production is increased by a factor of three and by 15%, respectively. Sensitivity to ttH, H → bb production is doubled.

Innovative analysis techniques were crucial to these improvements, several involving machine learning techniques, such as state-of-the-art transformers in the extremely challenging ttH(bb) analysis. Both analyses utilised an upgraded algorithm for identifying particle jets from bottom and charm quarks. A bespoke implementation allowed, for the first time, analysis of VH events coherently for both H → cc and H → bb decays. The enhanced classification of the signal from various background processes allowed a tripling of the number of selected ttH, H → bb events, and was the single largest improvement to increase the sensitivity to VH, H → cc. Both analyses improved their methods for estimating background processes including new theoretical predictions and the refined assessment of related uncertainties – a key component to boost the ttH, H → bb sensitivity.

Due to these improvements, ATLAS measured the ttH, H → bb cross-section with a precision of 24%, better than any single measurement before. The signal strength relative to the SM prediction is found to be 0.81 ± 0.21, consistent with the SM expectation of unity. It does not confirm previous results from ATLAS and CMS that left room for a lower-than-expected ttH cross section, dispelling speculations of new physics in this process. The compatibility between new and previous ATLAS results is estimated to be 21%.

In the new analysis VH, H → bb production was measured with a record precision of 18%; WH, H → bb production was observed for the first time with a significance of 5.3σ. Because H → cc decays are suppressed by a factor of 20 relative to H → bb decays, given the difference in quark masses, and are more difficult to identify, no significant sign of this process was found in the data. However, an upper limit on potential enhancements of the VH, H → cc rate of 11.3 times the SM prediction was placed at the 95% confidence level, allowing ATLAS to constrain the Higgs-charm coupling to less than 4.2 times the SM value, the strongest direct constraint to date.

The ttH and VH cross-sections were measured (double-)differentially with increased reach, granularity, and precision (figures 1 and 2). Notably, in the high transverse-momentum regime, where potential new physics effects are not yet excluded, the measurements were extended and the precision nearly doubled. However, neither analysis shows significant deviations from Standard Model predictions.

The significant new dataset from the ongoing Run 3 of the LHC, coupled with further advanced techniques like transformer-based jet identification, promises even more rigorous tests soon, and amplifies the excitement for the High-Luminosity LHC, where further precision will push the boundaries of our understanding of the Higgs boson – and perhaps yield clues to the mystery of the fermion masses.

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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.

The post Look to the Higgs self-coupling appeared first on CERN Courier.

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.

The post Electroweak SUSY after LHC Run 2 appeared first on CERN Courier.

Immediately after the Big Bang, all the particles we know about today were massless and moving at the speed of light. About 10^–12 seconds later, the scalar Higgs field spontaneously broke the symmetry of the electroweak force, separating it into the electromagnetic and weak forces, and giving mass to fundamental particles. Without this process, the universe as we know it would not exist.

Since its discovery in 2012, measurements of the Higgs boson – the particle associated with the new field – have refined our understanding of its properties, but it remains unknown how closely the field’s energy potential resembles the predicted Mexican hat shape. Studying the Higgs potential can provide insights into the dynamics of the early universe, and the stability of the vacuum with respect to potential future changes.

The Higgs boson’s self-coupling strength λ governs the cubic and quartic terms in the equation describing the potential. It can be probed using the pair production of Higgs bosons (HH), though this is experimentally challenging as this process is more than 1000 times less likely than the production of a single Higgs boson. This is partly due to destructive interference between the two leading order diagrams in the dominant gluon–gluon fusion production mode.

The ATLAS collaboration recently compiled a series of results targeting HH decays to bbγγ, bbττ, bbbb, bbll plus missing transverse energy (E_T^miss), and multilepton final states. Each analysis uses the full LHC Run 2 data set. A key parameter is the HH signal strength, μ_HH, which divides the measured HH production rate by the Standard Model (SM) prediction. This combination yields the strongest expected constraints to date on μ_HH, and an observed upper limit of 2.9 times the SM prediction (figure 1). The combination also sets the most stringent constraints to date on the strength of the Higgs boson’s self-coupling of –1.2 < κ_λ < 7.2, where κ_λ = λ/λ_SM, its value relative to the SM prediction.

Each analysis contributes in a complementary way to the global picture of HH interactions and faces its own set of unique challenges.

Despite its tiny branching fraction of just 0.26% of all HH decays, HH → bbγγ provides very good sensitivity to μ_HH thanks to the ATLAS detector’s excellent di-photon mass resolution. It also sets the best constraints on λ due to its sensitivity to HH events with low invariant mass.

The HH → bbττ analysis (7.3% of HH decays) exploits state-of-the-art hadronic–tau identification to control the complex mix of electroweak, multijet and top-quark backgrounds. It yields the strongest limits on μ_HH and the second tightest constraints on λ.

HH → bbbb (34%) has good sensitivity to μ_HH thanks to ATLAS’s excellent b-jet identification, but controlling the multijet background presents a formidable challenge, which is tackled in a fully data-driven fashion.

Studying the Higgs potential can provide insights into the dynamics of the early universe

The decays HH → bbWW and HH → bbττ in fully leptonic final states have very similar characteristics and are thus targeted in a single HH → bbll+E_T^miss analysis. Contributions from the bbZZ decay mode, where one Z decays to charged light leptons and the other to neutrinos, are also considered.

Finally, the HH → multilepton analy­sis is designed to catch decay modes where the HH system cannot be fully reconstructed due to ambiguity in how the decay products should be assigned to the two Higgs bosons. The analysis uses nine signal regions with different multiplicities of light charged leptons, hadronic taus and photons. It is complementary to all the exclusive channels discussed above.

For the ongoing LHC Run 3, ATLAS designed new triggers to enhance sensitivity to the hadronic HH → bbττ and HH → bbbb channels. Improved b-jet identification algorithms will increase the efficiency in selecting HH signals and distinguishing them from background processes. With these and other improvements, our prospects have never looked brighter for homing in on the Higgs self-coupling.

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At the International Conference on High-Energy Physics in Prague in July, the LHCb collaboration presented an updated measurement of the weak mixing angle using the data collected at the experiment between 2016 and 2018. The measurement benefits from the unique forward coverage of the LHCb detector.

The success of electroweak theory in describing a wide range of measurements at different experiments is one of the crowning achievements of the Standard Model (SM) of particle physics. It explains electroweak phenomena using a small number of free parameters, allowing precise measurements of different quantities to be compared to each other. This facilitates powerful indirect searches for beyond-the-SM physics. Discrepancies between measurements might imply that new physics influences one process but not another, and global analyses of high-precision electroweak measurements are sensitive to the presence of new particles at multi-TeV scales. In 2022 the entire field was excited by a measurement of the W-boson mass that is significantly larger than the value predicted within these global analyses by the CDF collaboration, heightening interest in electroweak measurements.

The weak mixing angle is at the centre of electroweak physics. It describes the mixing of the U(1) and SU(2) fields, determines couplings of the Z boson, and can also be directly related to the ratio of the W and Z boson masses. Excitingly, the two most precise measurements to date, from LEP and SLD, are in significant tension. This raises the prospect of non-SM particles potentially influencing one of these measurements, since the weak mixing angle, as a fundamental parameter of nature, should otherwise be the same no matter how it is measured. There is therefore a major programme measuring the weak mixing angle at hadron colliders, with important contributions from CDF, D0, ATLAS, CMS and LHCb.

Since the weak mixing angle controls Z-boson couplings, it can be determined from measurements of the angular distributions of Z-boson decays. The LHCb collaboration measured around 860,000 Z-boson decays to two oppositely charged muons, determining the relative rate at which negatively charged muons are produced closer to the LHC beamline than positively charged muons as a function of the angular separation of the two muons. Corrections are then applied for detector effects. Comparison to theoretical predictions based on different values of the weak mixing angle allows the value best describing the data to be determined (figure 1).

The unique angular coverage of the LHCb detector is well-suited for this measurement for two key reasons. First, the statistical sensitivity to the weak mixing angle is largest in the forward region close to the beamline that the LHCb detector covers. Second, the leading systematic uncertainties in measurements of the weak mixing angle at hadron colliders typically arise from existing knowledge of the proton’s internal structure. These uncertainties are also smallest in the forward region.

The value of the weak mixing angle measured by LHCb is consistent with previous measurements and with SM expectations (see “Weak mixing angle” figure). Notably, the precision of the LHCb measurement remains limited by the size of the data sample collected, such that further improvements are expected with the data currently being collected using the upgraded LHCb detector. In addition, while other experiments profile effects associated with the proton’s internal structure to reduce uncertainties, the unique forward acceptance means that this is not yet necessary at LHCb. This advantage will also be important for future measurements: the small theoretical uncertainty means that the forthcoming Upgrade 2 of the LHCb experiment is expected to achieve a precision more than a factor of two better than the most precise measurements to date.

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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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Packed sessions, more than 100 talks and lively discussions at Rencontres de Moriond electroweak, held from 24 to 31 March in La Thuile, Italy, captured the latest thinking in the field. The Standard Model (SM) emerged intact, while new paths of enquiry were illuminated.

Twelve years after the discovery of the Higgs boson, H, a wide variety of analyses by ATLAS and CMS are bringing the new scalar into sharper focus. This includes its mass, for which CMS has reported the most precise single measurement using the H → ZZ → 4ℓ channel: 125.04 ± 0.11 (stat) ± 0.05 (syst) GeV. A Run 2 legacy mass measurement combining ATLAS and CMS results is under way, while projections for the HL-LHC indicate that an uncertainty at the 10–20 MeV level is attainable. For the H width, which is potentially highly sensitive to new physics but notoriously difficult to measure at a hadron collider, the experiments constrain its value to be less than three times the SM width at 95% confidence level using an indirect method with reasonable assumptions. A precision of about 20% is expected from the full HL-LHC dataset.

New generation

The measured H cross sections in all channels continue to support the simplest incarnation of the SM H sector, with a new result from CMS testing the bbH production mode in the ττ and WW channels. Now that the H couplings to the most massive particles are well established, the focus is moving to the second-generation fermions. Directly probing the shape of the Brout–Englert–Higgs potential, and sensitive to new-physics contributions, the H self-coupling is another key target. HH production has yet to be observed at the LHC due to its very low cross section (the combined ATLAS and CMS limit is currently 2.5–3 times the SM value), but an extensive measurement programme utilising multiple channels is under way and Moriond saw new results presented based on HH → bbbb and HH → γγττ decays (see “Homing in on the Higgs self-interaction“).

Searches for exotic H decays, or for additional low-mass scalar bosons as predicted by two-Higgs-doublet extensions to the SM, were a Moriond highlight. A wide scope of new H-boson (a, A) searches have been released by ATLAS and CMS, including a new search for H → aa → muons by CMS in the mass range 0.2–60 GeV and, on the higher mass side, new limits on H/A → tt by ATLAS and A → ZH → ℓℓ tt by CMS. Although none show significant deviations from the SM, most of the searches are statistically limited and there remains a large amount of phase space available for extended H sectors. Generating much conversation in the corridors was a new-physics interpretation of ATLAS and CMS data in terms of a Higgs-triplet model, based on results  in the HH → γγ channel and top-quark differential distributions.

The LHC experiments are making stunning progress in precision electroweak measurements, as exemplified by a new measurement by CMS of the effective leptonic electroweak mixing angle sin²θ^ℓ_eff= 0.23157 ± 0.00031, the first LHC measurement of the W-boson width by ATLAS, and precise measurements of the W and Z cross sections at 13.6 TeV. ATLAS announced at Moriond the most precise single-experiment test of lepton-flavour universality in comparisons between W-boson decays to muons and electrons. A wide-ranging presentation of electroweak results based on two-photon collisions at the LHC described recent attempts by CMS to extract the anomalous magnetic moment of the tau lepton. And LHCb showcased its capabilities in providing an independent measurement of the W-boson mass and the Z-boson cross section. Participants heard about the increasing relevance of lattice QCD in precision electroweak measurements, for example in determining the running of alpha and the weak mixing angle. A tension between the predictions from lattice QCD and from more traditional dispersive approaches exists, with a similar origin to that for the anomalous magnetic moment of the muon.

Following the recent observation of entanglement in top-quark pairs by ATLAS and CMS, a presentation addressing the intriguing ability of colliders to carry out fundamental tests of quantum mechanics generated much discussion. Offering full access to spin information, collider experiments can study quantum correlations, wavefunction collapse and decoherence at unprecedented energies, possibly enabling a Bell measurement at the HL-LHC and the first observation of toponium.

Seeking signals from beyond

Searches for long-lived particles by ATLAS, CMS and LHCb – including the first at LHC Run 3 by CMS – were high on the Moriond agenda. Heavy gauge and scalar bosons, left–right gauge boson masses and heavy neutral leptons are among other new-physics scenarios being constrained. Casting the net as wide as possible, the LHC experiments are developing AI anomaly-detection algorithms, while the power of effective field theory (EFT) in parameterising the effect of heavy new particles on LHC measurements continues to grow via a diverse range of analyses. Even at O(6) in the SMEFT, no fewer than 59 Wilson coefficients, each related to different underlying physics processes, need to be to measured.

Neutrinoless double-beta decay, which would be an unambiguous sign of new physics, continues to be hunted by a host of experiments

Tensions between theory and experiment remain in some processes involving b → s or b → c quark transitions. Moriond saw much discussion on such processes, including new results from Belle II on the branching ratio of the highly suppressed decay B → Kνν. Participants heard about the need for theory progress, as has been the case recently with impressive calculations of b → sγ. Predictions for b → sμμ – which show a tension with experiment and that are independent of the R(K) parameters clocking the relative rates of B → Kμ⁺μ^– and B → Ke⁺e^– – are excellent ways to probe new physics. Concerning b → c transitions, updates on R(D^*) from Belle II and on R(D^*) and R(D) from LHCb based on the muonic decay of the tau lepton take the world-average tension to 3.17σ. The stability of the SM prediction of R(D^*) was also questioned.

New flavours

The flavour sector is awash with new results. LHCb presented fresh analyses exploring mixing and CP violation in the charm sector – a unique gateway to the flavour structure of up-type quarks – while CMS presented a new measurement of CP violation in B_s → J/ψ K⁺K^– decays. In ultra-rare kaon decays, KOTO presented a new upper limit on the branching ratio of K⁰_L → πνν (< 2 × 10^–9 at 90% confidence level) and projects a sensitivity < 10^–13 with the proposed KOTO II upgrade. NA62 presented a preliminary measurement of the branching ratio of the very rare decay π⁰ → e⁺e^– (5.86 ± 0.37 × 10^–8), in agreement with the SM, and results for K⁺ → πγγ, the latter offering the first evidence that second-order terms must be included in chiral perturbation theory. Belle and Belle II showed new radiative and electroweak penguin results concerning processes such as B⁰ → γγ, and BESIII presented a precise measurement of the CKM matrix element V_cs. A sweeping theory perspective on the mysterious flavour structure of the SM introduced participants to “flavour modular symmetries” – a promising new game in town for a potential theory of flavour based on modular forms, which are well known in mathematics and were used in the proof of Fermat’s last theorem.

The final sessions of Moriond electro­weak turned to neutrinos, dark matter and astroparticle physics. KATRIN is soon to release an update on the neutrino mass limit based on six times more data, with an expected uncertainty of m_ν < 0.5 eV, and is undertaking R&D towards a proposed upgrade (KATRIN++) that would use new technology to push the mass limit down further. The collaboration is also stepping up its search for new physics via high-precision spectroscopy and is working towards an upgrade called TRISTAN that will soon zone in on the sterile neutrino hypothesis.

In Japan, the T2K facility has undergone an extensive renewal period including its first operation with the near-detector ND280 upgrade in August 2023, which increased the acceptance. Designed to explore neutrino mass ordering and leptonic CP violation, T2K data so far show a slight preference for the “normal” mass ordering while admitting a CP-conserving phase at the level of 2σ. However, a joint analysis between T2K and NOvA, a neutrino oscillation experiment in the US with a longer baseline and complementary sensitivity, prefers a more degenerate parameter space where either CP conservation or the inverted ordering are acceptable solutions. The combined data place a strong constraint on Δm₃₂.

Neutrinoless double-beta decay (NDBD), which would reveal the neutrino to be a Majorana particle and be an unambiguous sign of new physics, continues to be hunted by a host of experiments. LEGEND-200’s first physics data was shown, setting up an ultimate goal of placing a lower limit on the NDBD half-life of 10²⁸ years for ⁷⁶Ge. Also located at Gran Sasso, CUORE, which has been collecting data since 2019, will operate for one more year before an upgrade is planned. In parallel, designs for a next-generation tonne-scale upgrade, CUPID, are being finalised. Neutrino aficionados were also treated to scotogenic three-loop models, in which neutrinos gain a Dirac mass term from radiative corrections, and to the latest results from FASER at the LHC, including the first emulsion-detector measurements of the ν_e and ν_μ cross sections at TeV energies, and a search for axion-like particles.

IceCube, which studies resonant disappearance of antineutrinos due to matter effects, showed intriguing results that delve into new-physics territory. Adding sterile neutrinos improves global fits by 7σ, participants heard, but brings inconsistencies too. Generating much interest, the global p-value for the null hypothesis of the sterile neutrino in the muon disappearance channel is 3.1%, in tension with MINOS. The Deep Core IceCube upgrade will increase the number of strings in the observatory, while the more significant Gen-2 upgrade will expand its overall area. A theory overview of the status of sterile neutrinos, taking into account recent results from MiniBooNE, MicroBooNE, PROSPECT, STEREO, GALEX, SAGE, BEST and others, concluded that experimental evidence for such a fourth neutrino state is fading but not excluded. The so-called reactor anomaly is probably explained by smaller uranium contribution than previously accounted for, while the upgraded Neutrino-4 experiment will shed light on tensions with PROSPECT and STEREO.

Cosmological constraints

The status of dark photons was also reviewed. Constraints are being placed from many sources, including colliders, astrophysical and cosmological bounds, haloscopes, and most recently radio telescopes, the James Webb Space Telescope and beam-dump experiments. PandaX-4T, which seeks to constrain WIMP dark matter and NDBD, is about to restart data-taking. LZ, another large liquid-xenon detector, has placed record limits on dark matter based on its first 60 days of data-taking. Results from the first observing run of a novel kind of laser-interferometric detector, LIDA, to observe axion-like particles in the galactic halo are promising.

No particle-physics conference would be complete without the anomalous magnetic moment of the muon

The latest supersymmetry and dark-matter searches at ATLAS and CMS were also presented, including a new result on R-parity violating supersymmetry and fresh limits on the chargino mass. BESIII reported on exotic searches for massive dark photons, muon-philic particles, glueballs and the QCD axion. Searches for axion-like particles are multiplying in many shapes and forms. In terms of flavour probes of axions, the strongest bounds come from NA62. Less conventionally, probing ultralight dark matter by searching for oscillatory behaviour in gravitational waves is gaining traction. Recent NanoGrav data show no signs of such a signal.

All eyes on the muon

No contemporary particle-physics conference would be complete without the anomalous magnetic moment of the muon – a powerful quantity that takes into account all known and unknown particles, for which the measured value is in significant tension with the SM prediction. As the Fermilab Muon g-2 experiment continues to improve the experimental precision (currently 0.2 ppm), all eyes are on how the SM calculation is performed – specifically the systematic uncertainty associated with a process called hadronic vacuum polarisation. A huge amount of work is going into understanding this quantity, both in terms of the calculational machinery and underlying data used. When computed using lattice QCD, the tension between experiment and theory is significantly reduced. However, the calculations are so complex that few groups have been able to execute them. That is set to change this year, Moriond participants heard, as new lattice calculations are unblinded ahead of the Lattice 2024 meeting in August, followed by a decision on whether to include such results in the official SM prediction at the seventh plenary workshop of the Muon g-2 Theory Initiative at KEK in September.

Experimentally and theoretically, all tools are being thrown at the SM in an attempt to find an explanation for dark matter, the cosmological baryon asymmetry, neutrino masses and other outstanding mysteries. The many high-quality talks at this year’s Moriond electroweak session, including an impressive batch of flash talks in dedicated young-researcher sessions, covered all aspects of the adventure and set the standard for future analyses. An incredible interplay between astrophysical, cosmological, collider and other experimental measurements is rapidly eating into the available parameter space for new physics. Ten years ago, the Moriond theory-summary speaker remarked “new physics must be around the corner, but we see no corner”. While the same could be said today, physicists have a much clearer view of the road ahead.

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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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The problem lies with how neutrinos acquire mass. Nonzero neutrino masses are not possible without the existence of new fundamental fields, beyond those that are part of the SM. And we know virtually nothing about the particles associated with them. They could be bosons or fermions, light or heavy, charged or neutral, and experimentally accessible or hopelessly out of reach.

This is the neutrino mass puzzle. At its heart is the particle’s uniquely elusive nature, which is both the source of the problem and the main challenge in resolving it.

Mysterious and elusive

Despite outnumbering other known massive particles in the universe by 10 orders of magnitude, neutrinos are the least understood of the matter particles. Unlike electrons, they do not participate in electromagnetic interactions. Unlike quarks, they do not participate in the strong interactions that bind protons and neutrons together. Neutrinos participate only in aptly named weak interactions. Out of the trillions of neutrinos that the Sun beams through you each second, only a handful will interact with your body during your lifetime.

Neutrino physics has therefore had a rather tortuous and slow history. The existence of neutrinos was postulated in 1930 but only confirmed in the 1950s. The hypothesis that there are different types of neutrinos was first raised in the 1940s but only confirmed in the 1960s. And the third neutrino type, postulated when the tau lepton was discovered in the 1970s, was only directly observed in the year 2000. Nonetheless, over the years neutrino experiments have played a decisive role in the development of the most successful theory in modern physics: the SM. And at the turn of the 21st century, neutrino experiments revealed that there is something missing in its description of particle physics.

Neutrinos are fermions with spin one-half that interact with the charged leptons (the electron, muon and tau lepton) and the particles that mediate the weak interactions (the W and Z bosons). There are three neutrino types, or flavours: electron-type (ν_e), muon-type (ν_μ) and tau-type (ν_τ), and each interacts exclusively with its namesake charged lepton. One of the predictions of the SM is that neutrino masses are exactly zero, but a little over 25 years ago, neutrino experiments revealed that this is not exactly true. Neutrinos have tiny but undeniably nonzero masses.

Mixing it up

The search for neutrino masses is almost as old as Pauli’s 93-year-old postulate that neutrinos exist. They were ultimately discovered around the turn of the millennium through the observation of neutrino flavour oscillations. It turns out that we can produce one of the neutrino flavours (for example ν_μ) and later detect it as a different flavour (for example ν_e) so long as we are willing to wait for the neutrino flavour to change. The probability associated with this phenomenon oscillates in spacetime with a characteristic distance that is inversely proportional to the differences of the squares of the neutrino masses. Given the tininess of neutrino masses and mass splittings, these distances are frequently measured in hundreds of kilometres in particle-physics experiments.

Neutrino oscillations also require the leptons to mix. This means that the neutrino flavour states are not particles with a well defined mass but are quantum superpositions of different neutrino states with well defined masses. The three mass eigenstates are related to the three flavour eigenstates via a three-dimensional mixing matrix, which is usually parameterised in terms of mixing angles and complex phases.

In the last few decades, precision measurements of neutrinos produced in the Sun, in the atmosphere, in nuclear reactors and in particle accelerators in different parts of the world, have measured the mixing parameters at the several percent level. Assuming the mixing matrix is unitary, all but one have been shown to be nonzero. The measurements have revealed that the three neutrino mass eigenvalues are separated by two different mass-squared differences: a small one of order 10^–4 eV² and a large one of order 10^–3 eV². Data therefore reveal that at least two of the neutrino masses are different from zero. At least one of the neutrino masses is above 0.05 eV, and the second lightest is at least 0.008 eV. While neutrino oscillation experiments cannot measure the neutrino masses directly, precise measurements of beta-decay spectra and constraints from the large-scale structure of the universe offer complementary upper limits. The nonzero neutrino masses are constrained to be less than roughly 0.1 eV.

These masses are tiny when compared to the masses of all the other particles (see “Chasm” figure). The mass of the lightest charged fermion, the electron, is of order 10⁶ eV. The mass of the heaviest fermion, the top quark, is of order 10¹¹ eV, as are the masses of the W, Z and Higgs bosons. These particle masses are all at least seven orders of magnitude heavier than those of the neutrinos. No one knows why neutrino masses are dramatically smaller than those of all other massive particles.

The Standard Model and mass

To understand why the SM predicts neutrino masses to be zero, it is necessary to appreciate that particle masses are complicated in this theory. The reason is as follows. The SM is a quantum field theory. Interactions between the fields are strictly governed by their properties: spin, various “local” charges, which are conserved in interactions, and – for fermions like the neutrinos, charged leptons and quarks – another quantum number called chirality.

In quantum field theories, mass is the interaction between a right-chiral and a different left-chiral field. A naive picture is that the mass-interaction constantly converts left-chiral states into right-chiral ones (and vice versa) and the end result is a particle with a nonzero mass. It turns out, however, that for all known fermions, the left-chiral and right-chiral fermions have different charges. The immediate consequence of this is that you can’t turn one into the other without violating the conservation of some charge so none of the fermions are allowed to have mass: the SM naively predicts that all fermion masses are zero!

The Higgs field was invented to fix this shortcoming. It is charged in such a way that some right-chiral and left-chiral fermions are allowed to interact with one another plus the Higgs field which, uniquely among all known fields, is thought to have been turned on everywhere since the phase transition that triggered electroweak symmetry breaking very early in the history of the universe. In other words, so long as the vacuum configuration of the Higgs field is not trivial, fermions acquire a mass thanks to these interactions.

This is not only a great idea; it is also at least mostly correct, as spectacularly confirmed by the discovery of the Higgs boson a little over a decade ago. It has many verifiable consequences. One is that the strength with which the Higgs boson couples to different particles is proportional to the particle ’s mass – the Higgs prefers to interact with the top quark or the Z or W bosons relative to the electron or the light quarks. Another consequence is that all masses are proportional to the value of the Higgs field in the vacuum (10¹¹ eV) and, in the SM, we naively expect all particle masses to be similar.

Neutrino masses are predicted to be zero because, in the SM, there are no right-chiral neutrino fields and hence none for the left-chiral neutrinos – the ones we know about – to “pair up” with. Neutrino masses therefore require the existence of new fields, and hence new particles, beyond those in the SM.

Wanted: new fields

The list of candidate new fields is long and diverse. For example, the new fields that allow for nonzero neutrino masses could be fermions or bosons; they could be neutral or charged under SM interactions, and they could be related to a new mass scale other than the vacuum value of the SM Higgs field (10¹¹ eV), which could be either much smaller or much larger. Finally, while these new fields might be “easy” to discover with the current and near-future generation of experiments, they might equally turn out to be impossible to probe directly in any particle-physics experiment in the foreseeable future.

Though there are too many possibilities to list, they can be classified into three very broad categories: neutrinos acquire mass by interacting with the same Higgs field that gives mass to the charged fermions; by interacting with a similar Higgs field with different properties; or through a different mechanism entirely.

At first glance, the simplest idea is to postulate the existence of right-chiral neutrino fields and further assume they interact with the Higgs field and the left-chiral neutrinos, just like right-chiral and left-chiral charged leptons and quarks. There is, however, something special about right-chiral neutrino fields: they are completely neutral relative to all local SM charges. Returning to the rules of quantum field theory, completely neutral chiral fermions are allowed to interact “amongst themselves” independent of whether there are other right-chiral or left-chiral fields around. This means the right-chiral neutrino fields should come along with a different mass that is independent from the vacuum value of the Higgs field of 10¹¹ eV.

To prevent this from happening, the right-chiral neutrinos must possess some kind of conserved charge that is shared with the left-chiral neutrinos. If this scenario is realised, there is some new, unknown fundamental conserved charge out there. This hypothetical new charge is called lepton number: electrons, muons, tau leptons and neutrinos are assigned charge plus one, while positrons, antimuons, tau antileptons and antineutrinos have charge minus one. A prediction of this scenario is that the neutrino and the antineutrino are different particles since they have different lepton numbers. In more technical terms, the neutrinos are massive Dirac fermions, like the charged leptons and the quarks. In this scenario, there are new particles associated with the right-chiral neutrino field, and a new conservation law in nature.

Accidental conservation

As of today, there is no experimental evidence that lepton number is not conserved, and readers may question if this really is a new conservation law. In the SM, however, the conservation of lepton number is merely “accidental” – once all other symmetries and constraints are taken into account, the theory happens to possess this symmetry. But lepton number conservation is no longer an accidental symmetry when right-chiral neutrinos are added, and these chargeless and apparently undetectable particles should have completely different properties if it is not imposed.

If lepton number conservation is imposed as a new symmetry of nature, making neutrinos pure Dirac fermions, there appears to be no observable consequence other than nonzero neutrino masses. Given the tiny neutrino masses, the strength of the interaction between the Higgs boson and the neutrinos is predicted to be at least seven orders of magnitude smaller than all other Higgs couplings to fermions. Various ideas have been proposed to explain this remarkable chasm between the strength of the neutrino’s interaction with the Higgs field relative to that of all other fermions. They involve a plurality of theoretical concepts including extra-dimensions of space, mirror copies of our universe and dark sectors.

A second possibility is that there are more Higgs fields in nature and that the neutrinos acquire a mass by interacting with a Higgs field that is different from the one that gives a mass to the charged fermions. Since the neutrino mass is proportional to the vacuum value of a different Higgs field, the fact that the neutrino masses are so small is easy to tolerate: they are simply proportional to a different mass scale that could be much smaller than 10¹¹ eV. Here, there are no right-chiral neutrino fields and the neutrino masses are interactions of the left-chiral neutrino fields amongst themselves. This is possible because, while the neutrinos possess weak-force charge they have no electric charge. In the presence of the nontrivial vacuum of the Higgs fields, the weak-force charge is effectively not conserved and these interactions may be allowed. The fact that the Higgs particle discovered at the LHC – associated with the SM Higgs field – does not allow for this possibility is a consequence of its charges. Different Higgs fields can have different weak-force charges and end up doing different things. In this scenario, the neutrino and the antineutrino are, in fact, the same particle. In more technical terms: the neutrinos are massive Majorana fermions.

Neutrino masses require the existence of new fields, and hence new particles, beyond those in the Standard Model

One way to think about this is as follows: the mass interaction transforms left-chiral objects into right-chiral objects. For electrons, for example, the mass converts left-chiral electrons into right-chiral electrons. It turns out that the antiparticle of a left-chiral object is right-chiral and vice versa, and it is tempting to ask whether a mass interaction could convert a left-chiral electron into a right-chiral positron. The answer is no: electrons and positrons are different objects and converting one into the other would violate the conservation of electric charge. But this is no barrier for the neutrino, and we can contemplate the possibility of converting a left-chiral neutrino into its right-chiral antiparticle without violating any known law of physics. If this hypothesis is correct, the hypothetical lepton-number charge, discussed earlier, cannot be conserved. This hypothesis is experimentally neither confirmed nor contradicted but could soon be confirmed with the observation of neutrinoless double-beta decays – nuclear decays which can only occur if lepton-number symmetry is violated. There is an ongoing worldwide campaign to search for the neutrinoless double-beta decay of various nuclei.

A new source of mass

In the third category, there is a source of mass different from the vacuum value of the Higgs field, and the neutrino masses are an amalgam of the vacuum value of the Higgs field and this new source of mass. A very low new mass scale might be discovered in oscillation experiments, while consequences of heavier ones may be detected in other types of particle-physics experiments, including measurements of beta and meson decays, charged-lepton properties, or the hunt for new particles at high-energy colliders. Searches for neutrinoless double-beta decay can reveal different sources for lepton-number violation, while ultraheavy particles can leave indelible footprints in the structure of the universe through cosmic collisions. The new physics responsible for nonzero neutrino masses might also be related to grand-unified theories or the origin of the matter–antimatter asymmetry of the universe, through a process referred to as leptogenesis. The range of possibilities spans 22 orders of magnitude (see “eV to ZeV” figure).

Challenging scenarios

Since the origin of the neutrino masses here is qualitatively different from that of all other particles, the values of the neutrino masses are expected to be qualitatively different. Experimentally, we know that neutrino masses are much smaller than all charged- fermion masses, so many physicists believe that the tiny neutrino masses are strong indirect evidence for a source of mass beyond the vacuum value of the Higgs field. In most of these scenarios, the neutrinos are also massive Majorana fermions. The challenge here is that if a new mass scale exists in fundamental physics, we know close to nothing about it. It could be within direct reach of particle-physics experiments, or it could be astronomically high, perhaps as large as 10¹² times the vacuum value of the SM’s Higgs field.

Searching for neutrinoless double-beta decay is the most promising avenue to reveal whether neutrinos are Majorana or Dirac fermions

How do we hope to learn more? We need more experimental input. There are many outstanding questions that can only be answered with oscillation experiments. These could provide evidence for new neutrino-like particles or new neutrino interactions and properties. Meanwhile, searching for neutrinoless double-beta decay is the most promising avenue to experimentally reveal whether neutrinos are Majorana or Dirac fermions. Other activities include high-energy collider searches for new Higgs bosons that like to talk to neutrinos and new heavy neutrino-like particles that could be related to the mechanism of neutrino mass generation. Charged-lepton probes, including measurements of the anomalous magnetic moment of muons and searches for lepton-flavour violation, may provide invaluable clues, while surveys of the cosmic microwave background and the distribution of galaxies could also reveal footprints of the neutrino masses in the structure of the universe.

We still know very little about the new physics uncovered by neutrino oscillations. Only a diverse experimental programme will reveal the nature of the new physics behind the neutrino mass puzzle.

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The conference highlighted the impressive progress and diversity of UPC physics, which goes far beyond the initial studies of exclusive pro­-cesses. UPC23 covered the latest results from experiments at RHIC and the LHC, and prospects for the future Electron-Ion Collider (EIC) at Brookhaven National Laboratory. Discussions delved into the intricacies of inelastic photo-nuclear events, including the exciting programme of open charm that is yet to be explored, and examined how UPCs serve as a novel lens for investigating the quark–gluon plasma and other final-state nuclear effects. Lots of attention was devoted to the physics of low-x parton densities – a fundamental aspect of protons and nuclei that photons can probe in a unique way.

Enriched understanding

Among the conference’s theoretical highlights, Farid Salazar (UCLA) showed how vector–meson photoproduction could be a powerful method to detect gluon saturation across different collision systems, from proton–nucleus to electron–nucleus to UPCs. Zaki Panjsheeri (Virginia) put forth innovative ideas to study double-parton correlations, linking UPC vector–meson studies to generalised parton distributions, enhancing our understanding of the proton’s structure. Ashik Ikbal (Kent State), meanwhile, introduced exciting proposals to investigate quantum entanglement through exclusive J/ψ photoproduction at RHIC.

The conference also provided a platform for discussing the active exploration of light-by-light scattering and two-photon processes for probing fundamental physics and searches for axion-like particles, and for putting constraints on the anomalous magnetic moment of the tau lepton (see CMS closes in on tau g–2).

Energy exploration

Physicists at the LHC have effectively repurposed the world’s most powerful particle accelerator into a high-energy photon collider. This innovative approach, traditionally the domain of electron beams in colliders like LEP and HERA, and anticipated at the EIC, allows the LHC to explore photon-induced interactions at energies never before achieved. David Grund (Czech Technical University in Prague), Georgios Krintiras (Kansas) and Cesar Luiz Da Silva (Los Alamos) shared the latest LHC findings on the energy dependence of UPC J/ψ events. These results are crucial for understanding the onset of gluon saturation – a state where gluons become so dense reaching saturation, the dynamical equilibrium where the emission and recombination occurs. However, the data also align with the nuclear phenomenon known as gluon shadowing, which arises from multiple-scattering processes. David Tlusty (Creighton) presented the latest findings from the STAR Collaboration, which has recently expanded its UPC programme, complementing the energy exploration at the LHC. Klaudia Maj (AGH University of Krakow) presented the latest results on two-photon interactions and photonuclear jets from the ATLAS collaboration, including measurements that may be probing the quark-gluon plasma. 

Delegates discussed the future opportunities for UPC physics with the large integrated luminosity expected for Runs 3 and 4 at the LHC

Carlos Bertulani (Texas A&M) paid tribute to Gerhard Baur, who passed away on June 16 last year. Bertulani and Baur co-authored “Electromagnetic processes in relativistic heavy ion collisions” – a seminal paper with more than 1000 citations. Bertulani invited delegates to consider the untapped potential of UPCs in the study of anti-atoms and exotic atoms.

Delegates also discussed the future opportunities for UPC physics with the large integrated luminosity expected for Run 3 and Run 4 at the LHC, with the planned detector upgrades for Run 4 such as FoCal, the recent upgrades by STAR, the sPHENIX programme and at the EIC. Delegates are expecting event selection and instrumentation close to the beam line, for example using “zero degree” calorimeters, to offer the greatest experimental opportunities in the coming years.

The next edition of the UPC conference will take place in Saariselka, Finland in June 2025.

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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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Alongside Robert Brout and François Englert, and building on the work of a generation of physicists, Higgs postulated the existence of the Brout–Englert–Higgs (BEH) field. Alone among known fundamental fields, the BEH field is “turned on” throughout the universe, rather than flickering in and out of existence and remaining localized. Its existence allowed matter to form in the early universe some 10^–11 s after the Big Bang, thanks to the interactions between elementary particles (such as electrons and quarks) and the ever-present BEH field. Higgs and Englert were awarded the Nobel Prize for Physics in 2013 in recognition of these achievements.

An immensely inspiring figure for physicists around the world

Fabiola Gianotti

“Besides his outstanding contributions to particle physics, Peter was a very special person, an immensely inspiring figure for physicists around the world, a man of rare modesty, a great teacher and someone who explained physics in a very simple yet profound way,” said CERN’s Director-General Fabiola Gianotti, expressing the emotion felt by the physics community upon his loss. “An important piece of CERN’s history and accomplishments is linked to him. I am very saddened, and I will miss him sorely.”

Peter Higgs’ scientific legacy will extend far beyond the scope of current discoveries. The Higgs boson – the observable “excitation” of the BEH field which he was the first to identify – is linked to some of most intriguing and crucial outstanding questions in fundamental physics. This still quite mysterious particle therefore represents a uniquely promising portal to physics beyond the SM. Since discovering it in 2012, the ATLAS and CMS collaborations have already made impressive progress in constraining its properties – a painstaking scientific study that will form a central plank of research at the LHC, high-luminosity LHC and future colliders for decades to come, promising insights into the many unanswered questions in fundamental science.

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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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For the tau lepton’s less massive cousins, measurements of magnetic moments offer exceptional sensitivity to beyond-the-Standard-Model (BSM) physics. In quantum electrodynamics (QED), quantum effects modify the Dirac equation, which predicts a gyromagnetic factor g precisely equal to two. The first-order correction, an effect of only α/2π, was calculated by Julian Schwinger in 1948. Taking into account higher orders too, the electron anomalous magnetic moment, a = (g–2)/2, is one of the most precisely measured quantities in physics and is in remarkable agreement with QED predictions. The g–2 of the muon has also been measured with high precision and shows a persistent discrepancy with certain theoretical predictions. By contrast, however, the tau lepton’s g–2 suffers from a lack of precision, given that its short lifetime makes direct measurements very challenging. If new-physics effects scale with the squared lepton mass, deviations from QED predictions in this measurement would be about 280 times larger than in the muon g–2 measurement. 

Experimental insights on g–2 can be indirectly obtained by measuring the exclusive production of tau–lepton pairs created in photon–photon collisions. As charged particles pass each other at relativistic velocities in the LHC beampipe, they generate intense electromagnetic fields, leading to photon–photon collisions. The production of tau lepton pairs in photon collisions was first observed by the ATLAS and CMS collaborations in Pb–Pb runs. The CMS collaboration has now observed the same process in proton–proton (pp) data. When photon collisions occur in pp runs, the protons can remain intact. As a result, final-state particles can be produced exclusively, with no other particles coming from the same production vertex. 

Tau–lepton tracks were isolated within just a millimetre around the interaction vertex

Separating these low particle multiplicity events from ordinary pp collisions is extremely challenging, as events “pile up” within the same bunch crossing. Thanks to the precise tracking capabilities of the CMS detector, tau–lepton tracks were isolated within just a millimetre around the interaction vertex. Figure 1 shows the resulting excess of ?? → ?? events rising above the estimated backgrounds when few additional tracks were observed within the selected 1 mm window.

This process was used to constrain a_? using an effective-field-theory approach. BSM physics affecting g–2 would modify the expected number of ?? → ?? events, with the effect increasing with the di-tau invariant mass. Compared to Pb–Pb collisions, the pp data sample provides a more precise g–2 value because of the larger number of events and of the higher invariant masses probed, thanks to the higher energy of the photons. Using the invariant-mass distributions collected in pp collisions during the full LHC Run 2, the CMS collaboration has not observed any statistically significant deviations from the Standard Model. The tightest constraint ever on a_? was set, as shown in figure 2. The uncertainty is only three times larger than the value of Schwinger’s correction.

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Experimental highlights focused on the latest results from CMS and ATLAS. CMS presented a new measurement of the associated production of a Higgs boson with top quarks decaying into b quarks, while ATLAS showed a new measurement of the associated production of a vector boson and a boosted Higgs boson in fully hadronic final states. A major highlight was a new CMS measurement of the Higgs-boson mass in the four-lepton decay channel, reaching the highest precision to date in a single decay channel as well as placing indirect constraints on the Higgs-boson width. Precision measurements were also shown in the framework of effective field theory, which allows potential subtle deviations with respect to the Standard Model to be probed. A small number of intriguing excesses observed, for instance, in the search for partners of the Higgs boson decaying into W-boson or photon pairs were also extensively discussed.

Following a historical talk on the “long and winding road” that led particle physicists from LEP to the discovery of the Higgs boson by Steve Myers, who was CERN director of accelerators and technology when the LHC started up, a dedicated session discussed Higgs-physics prospects at colliders beyond the High-Luminosity LHC (HL-LHC). Patrizia Azzi (INFN Padova) presented the experimental prospects at the proposed Future Circular Collider, and Daniel Schulte (CERN) described the status of muon colliders, highlighting the strong interest within the community and leading to a lively discussion.

The latest theory developments related to Higgs physics were discussed in detail, starting with state-of-the-art predictions for the various Higgs-boson production modes by Aude Gehrmann-De Ridder (ETH Zurich). Andrea Wulzer (CERN) overviewed the theory prospects relevant for future collider projects, while Raffaele Tito D’Agnolo (IPhT, Saclay) presented the connections between the properties of the Higgs boson and cosmology and Arttu Rajantie (Imperial College) focused on implications of the Higgs vacuum metastability on new physics. Finally, a “vision” talk by Matthew McCullough (CERN) questioned our common assumption that the Higgs boson discovered at the LHC is really compatible with Standard Model expectations, considering the current precision of the measurements of its properties.

During several experimental sessions, recent results covering a wide range of topics were presented – in particular those related to vector-boson scattering, since their high-energy behaviour is driven by the properties of the Higgs boson. The Higgs-boson self-coupling was another topic of interest. The best precision on this measurement is currently achieved by combining indirect constraints from processes involving a single Higgs boson together with direct searches for the rare production of a Higgs-boson pair. While the Run 3 data set will provide an opportunity to further improve the sensitivity to the latter, its observation is expected to take place towards the end of HL-LHC operations. Finally, Stéphanie Roccia (LPSC) presented the implications of experimental measurements of the neutron electron dipole moment on the CP-violating couplings of the Higgs boson to fermions, absent in the Standard Model. Concluding talks were given by Massimiliano Grazzini (University of Zurich) and Andrea Rizzi (University and INFN Pisa). The next Higgs Hunting workshop will be held in Orsay and Paris from 23 to 25 September 2024.

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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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History could have turned out differently, said Haidt, since both CERN and Brookhaven National Laboratory (BNL) were competing in the new era of high-energy neutrino physics: “The CERN beam was a flop initially, allowing BNL to snatch the muon-neutrino discovery in 1962, but a second attempt at CERN was better.” This led André Lagarrigue to dream of a giant bubble chamber, Gargamelle, financed and built by French institutes and operated by CERN with beams from the Proton Synchrotron (PS) from 1970 to 1976. Picking out the neutral-current signal from the neutron-cascade background was a major challenge, and a solution seemed hopeless until Haidt and his collaborators made a breakthrough regarding the meson component of the cascade.

The ten years between the discovery of neutral currents and the W and Z bosons are what took CERN from competent mediocrity to world leader

Lyn Evans

By early July 1973, it was realised that Gargamelle had seen a new effect. Paul Musset presented the results in the CERN auditorium on 19 July, yet by that autumn Gargamelle was “treated with derision” due to conflicting results from a competitor experiment in the US. ‘The Gargamelle claim is the worst thing to happen to CERN,’ Director-General John Adams was said to have remarked. Jack Steinberger even wagered his cellar that it was wrong. Following further cross checks by bombarding the detector with protons, the Gargamelle result stood firm. At the end of Haidt’s presentation, collaboration members who were present in the audience were recognised with a warm round of applause.

From the PS to the SPS
The neutral-current discovery and the subsequent Gargamelle measurement of the weak mixing angle made it clear not only that the electroweak theory was right but that the W and Z were within reach of the technology of the day. Moving from the PS to the SPS, Jean-Pierre Revol (Yonsei University) took the audience to the UA1 and UA2 experiments ten years later. Again, history could have taken a different turn. While CERN was working towards a e⁺e^– collider to find the W and Z, said Revol, Carlo Rubbia proposed the radically different concept of a hadron collider — first to Fermilab, which, luckily for CERN, declined. All the ingredients were presented by Rubbia, Peter McIntyre and David Cline in 1976; the UA1 detector was proposed in 1978 and a second detector, UA2, was proposed by CERN six months later. UA1 was huge by the standards of the day, said Revol. “I was advised not to join, as there were too many people! It was a truly innovative project: the largest wire chamber ever built, with 4π coverage. The central tracker, which allowed online event displays, made UA1 the crucial stepping stone from bubble chambers to modern electronic ones. The DAQ was also revolutionary. It was the beginning of computer clusters, with same power as IBM mainframes.”

First SppS collisions took place on 10 July 1981, and by mid-January 1983 ten candidate W events had been spotted by the two experiments. The W discovery was officially announced at CERN on 25 January 1983. The search for the Z then started to ramp up, with the UA1 team monitoring the “express line” event display around the clock. On 30 April, Marie Noelle Minard called Revol to say she had seen the first Z. Rubbia announced the result at a seminar on 27 May, and UA2 confirmed the discovery on 7 June. “The SppS was a most unlikely project but was a game changer,” said Haidt. “It gave CERN tremendous recognition and paved the way for future collaborations, at LEP then LHC.”

Former UA2 member Pierre Darriulat (Vietnam National Space Centre) concurred: “It was not clear at all at that time if the collider would work, but the machine worked better than expected and the detectors better than we could dream of.” He also spoke powerfully about the competition between UA1 and UA2: “We were happy, but it was spoiled in a way because there was all this talk of who would be ‘first’ to discover. It was so childish, so ridiculous, so unscientific. Our competition with UA1 was intense, but friendly and somewhat fun. We were deeply conscious of our debt toward Carlo and Simon [van der Meer], so we shared their joy when they were awarded the Nobel prize two years later.” Darriulat emphasised the major role of the Intersecting Storage Rings and the input of theorists such as John Ellis and Mary K Gaillard, reserving particular praise for Rubbia. “Carlo did the hard work. We joined at the last moment. We regarded him as the King, even if we were not all in his court, and we enjoyed the rare times when we saw the King naked!”

Our competition with UA1 was intense, but friendly and somewhat fun

Pierre Darriulat

The ten years between the discovery of neutral currents and the W and Z bosons are what took CERN “from competent mediocrity to world leader”, said Lyn Evans in his account of the SppS feat. Simon van der Meer deserved special recognition, not just for his 1972 paper on stochastic cooling, but also his earlier invention of the magnetic horn, which was pivotal in increasing the neutrino flux in Gargamelle. Evans explained the crucial roles of the Initial Cooling Experiment and the Antiproton Accumulator, and the many modifications needed to turn the SPS into a proton-antiproton collider. “All of this knowledge was put into the LHC, which worked from the beginning extremely well and continues to do so. One example was intrabeam scattering. Understanding this is what gives us the very long beam lifetimes at the LHC.”

Long journey
The electroweak adventure began long before CERN existed, pointed out Wolfgang Hollik, with 2023 also marking the 90^th anniversary of Fermi’s four-fermion model. The incorporation of parity violation came in 1957 and the theory itself was constructed in the 1960s by Glashow, Salam, Weinberg and others. But it wasn’t until ‘t Hooft and Veltman showed that the theory is renormalizable in the early 1970s that it became a fully-fledged quantum field theory. This opened the door to precision electroweak physics and the ability to search for new particles, in particular the top quark and Higgs boson, that were not directly accessible to experiments. Electroweak theory also drove a new approach in theoretical particle physics based around working groups and common codes, noted Hollik.

The afternoon session of the symposium took participants deep into the myriad of electroweak measurements at LEP and SLD (Guy Wilkinson, University of Oxford), Tevatron and HERA (Bo Jayatilaka, Fermilab), and finally the LHC (Maarten Boonekamp, Université Paris-Saclay and Elisabetta Manca, UCLA). The challenges of such measurements at a hadron collider, especially of the W-boson mass, were emphasised, as were their synergies with QCD in measurements in improving the precision of parton distribution functions.

The electroweak journey is far from over, however, with the Higgs boson offering the newest exploration tool. Rounding off a day of excellent presentations and personal reflections, Rebeca Gonzalez Suarez (Uppsala University) imagined a symposium 40 years from now when the proposed collider FCC-ee at CERN has been operating for 16 years and physicists have reconstructed nearly 10¹³ W and Z bosons. Such a machine would take the precision of electroweak physics into the keV realm and translate to a factor of seven increase in energy scale. “All of this brings exciting challenges: accelerator R&D, machine-detector interface, detector design, software development, theory calculations,” she said. “If we want to make it happen, now is the time to join and contribute!”

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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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Over five days of pronouncements, presentations and posters, topics included current and future prospects in detector technologies, advances in theoretical calculations (with a particular focus on effective field theories), and improving diversity and outreach in physics. Results from a large number of experiments were presented, many of which are building excitement for the next generation of measurements that seek to provide even more rigorous tests of the Standard Model (SM) and improved searches for physics beyond it (BSM).

The results presented were too numerous to review comprehensively. However, they tended to skew towards flavour physics, with a particular emphasis on searches for CP- and lepton flavour-violation and tests of lepton-flavour universality (LFU). Overall, tensions between the SM and experimental measurements of LFU remain. In particular, Kazuki Kojima (Nagoya University) presented a measurement of R(D^*), which is a test of LFU performed with B-meson decays, finding the ratio R(D^*) = 0.267 ^+0.041 _–0.039 (stat.) ^+0.028 _–0.033 (syst.). While compatible with the SM, it increases the tension with theory from 3.2σ to 3.3σ when all measurements of R(D) and R(D^*) are combined.

Not to be outdone, the LHC experiments presented a range of precision measurements of SM parameters, further reducing the available parameter space for BSM physics. In particular, Linda Finco (INFN Torino) from ATLAS presented the most precise measurement of the Higgs-boson mass: 125.11 ± 0.09 (stat.) ± 0.06 (syst.) GeV, using the full Run 1 and Run 2 datasets for both the H → ZZ → 4ℓ and H → γγ channels. This is one of the most precisely determined masses of any SM particle, a real achievement of precision physics.

Now that the available parameter space for BSM models is shrinking, more innovative approaches to particle physics are needed. One such approach, presented by Ling Sun (Australian National University), is to use the phenomenon of superradiance to search for ultralight bosons around rapidly rotating black holes. The boson clouds extract angular momentum from the black hole when the superradiance condition is met, producing gravitational radiation that could be measured by current and future gravitational-wave detectors. Such a method provides an avenue to measure particles that interact only through gravity, opening a novel avenue for exploring particles beyond the SM.

On the penultimate evening, Alan Duffy (Swinburne University) and Suzie Sheehy (University of Oxford and University of Melbourne) delivered a public lecture “How to discover a universe” to a mix of conference participants, high-school students and the interested public, stressing that science is cultural as well as technological. The best poster was awarded to Emily Filmer (University of Adelaide) for “Searches for BSM physics using challenging long-lived signatures with the ATLAS detector”, while the “people’s choice” was awarded to Eliot Walton (Monash University) for her poster “The Queer History of Physics”. Australia’s small but growing particle-physics community was extremely well represented, and the exposure of the global community to us made Lepton Photon 2023 a resounding success.

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The initial physics results from the Run 3 dataset collected in 2022 by ATLAS and CMS were shown, featuring the first measurement of the Higgs-boson production cross-section by ATLAS at 13.6 TeV. Clearly the Run 2 dataset is still a gold mine for the LHC experiments. The programme of precision measurements of Higgs-boson properties is continuing with improved accuracy from the full Run 2 dataset. In particular, ATLAS and CMS reported a new combined result targeting the rare decay H → Zγ, for which they found evidence at the level of 3.4σ and a measured rate slightly higher but comparable to that predicted by the Standard Model.

Innovative signatures

Searches for physics beyond the Standard Model (SM) remains a very active field of research at the LHC, with many innovative signatures explored, including those of long-lived particles. Some of these searches use new anomaly-detection techniques and explore potential lower-production cross sections. A new search of leptoquarks by CMS exploiting the leptonic tau content of the proton was reported, while ATLAS reported a search for stau production in supersymmetry models with much improved sensitivity. Many other searches were also presented, and while a few low-level excesses exist, more data will be required to check if these are statistical fluctuations or not.

The SM is under intense scrutiny but is still very successful at the high-energy frontier. A recent re-analysis of the W-boson mass by ATLAS with the 7 TeV dataset shows good agreement with SM predictions, unlike the CDF result released in 2022. Validating the model used for the ATLAS W-mass measurement, new precise measurements of the W and Z bosons’ transverse momentum distributions were reported by ATLAS using Run 2 data collected under lower pileup conditions. Vector-boson scattering processes are an important probe of the electroweak symmetry breaking mechanism, and most such processes are now observed at the LHC.

Exploring the top-quark sector, many recent results focused on rare top-production processes. Four-top production was observed recently by ATLAS and CMS. First evidence for the rare tWZ production mode was shown by CMS at LHCP 2023. Some of these rare production modes are seen with rates somewhat higher than predicted, and more data will be required to conclude if the differences are significant. Top production is also used to investigate more exotic scenarios. A new CMS result, measuring the tt– production cross section as a function of sidereal time, was reported. No indication of Lorentz invariance violation is observed.

Presentations covered the broad spectrum of physics at the LHC brilliantly

On the flavour-physics side, LHCb reported a new precise measurement of CP violation in the “golden” B → J/ψ K_s decay, with the most precise extraction of the beta angle of the CKM quark-mixing matrix (see p16). Recent LHCb results on the flavour “anomalies” no longer show an indication for lepton universality violation in B → Ke⁺e^– compared to B → Kμ⁺μ^– decay rates, but some puzzles remain and there is still some tension in the tau-to-muon ratio in the tree-level decays B → B^(*)τ(µ)ν. Lepton-flavour violation is investigated in a new CMS result searching for the forbidden τ → 3µ decays, where an upper limit close to the Belle result was reported.

Characterisation of the quark–gluon plasma is actively studied using PbPb collision data. New results from ALICE regarding investigations of jet-quenching properties as well as charm fragmentation studies were shown at the conference.

The recent detections of collider-produced neutrinos by the new FASER and SND experiments were also presented, marking the start of a new physics programme at the LHC.

Broad spectrum

Several theory presentations highlighted recent progress in SM predictions for a wide range of processes including the electroweak sector, top-quark and Higgs-boson productions, as well as linking LHC physics to lattice QCD computations – work that is vital to fully exploit the physics potential of the LHC. Open questions in the various sectors were summarised and prospects for new-physics searches in Run 3, including those related to the Higgs-boson sector, were discussed. Links between LHC physics and dark matter were also highlighted, with examples of light dark-matter models and feebly interacting particles. Effective field theories, which are key tools to probe new physics in a generic way, were described with emphasis on the complementarity with searches targeting specific models.

Overall, the presentations covered the broad spectrum of physics at the LHC brilliantly. Future data, including from the High-Luminosity LHC phase, should allow physicists to continue to address many of the field’s open questions. Next year’s LHCP conference will be held at Northeastern University in Boston.

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Since the discovery of the Higgs boson in 2012, its di-photon and four-lepton decays have played a crucial role in characterising its properties. Despite their small branching ratios, these decay channels are ideal for accurate measurements due to the excellent resolution and efficient identification of photons and leptons provided by the ATLAS detector.

The Higgs-boson mass (m_H) is a free parameter of the Standard Model (SM) that must be determined experimentally. Its value governs the coupling strengths of the Higgs boson with the other SM particles. It also enters as logarithmic corrections to the SM predictions of the W-boson mass and effective weak mixing angle, whose precise measurements allow the electroweak model to be tested. Moreover, the Higgs mass determines the shape and energy evolution of the Brout–Englert–Higgs potential and thus the stability of the electroweak vacuum. A precise measurement of m_H is therefore of paramount importance.

ATLAS has recently published a new result of the Higgs-boson mass in the H → γγ decay channel using proton–proton collision data from LHC Run 2 (2015–2018). The measurement requires a careful control of systematic uncertainties, primarily arising from the photon energy scale. The new analysis has achieved a substantial reduction by more than a factor of three of these uncertainties compared to the previous ATLAS result based on the 2015 and 2016 dataset. That improvement became possible after extensive efforts to refine the photon energy-scale calibration and associated uncertainties.

The calibration benefited from an improved understanding of the energy response across the longitudinal ATLAS electromagnetic calorimeter layers and of nonlinear electronics readout effects. A new correction was implemented in the extrapolation of the precisely measured electron-energy scale in Z → e⁺e^– events to photons, to account for differences in the lateral shower development between electrons and photons. These improvements reduced the systematic uncertainty in the mass measurement by about 40%. Moreover, the extrapolation of the electron energy scale from Z → e⁺e^– events to photons originating from the Higgs boson was further refined, and transverse-momentum dependent effects were corrected. Taken together, the improvements allowed ATLAS to measure the Higgs-boson mass in the di-photon channel with a precision of 1.1 per mille.

The new di-photon result was combined with the m_H measurement in the H → ZZ^* → 4ℓ decay using the full Run 2 dataset, published by ATLAS in 2022, and with the corresponding Run 1 (2011–2012) measurements (see figure 1). The resulting combined Higgs-boson mass m_H = 125.11 ± 0.11 GeV has a precision of 0.9 per mille and is dominated by statistical uncertainties that will further reduce with the Run 3 data.

The high level of readiness and excellent performance of the ATLAS detector also allowed first measurements of the fiducial Higgs-boson production cross-sections in the H → γγ and H → ZZ^* → 4ℓ decay channels using up to 31.4 fb^–1 of data collected in 2022. Their extrapolation to full phase space and combination gives σ(pp → H) = 58.2 ± 8.7 pb, which agrees with the SM prediction of 59.9 ± 2.6 pb (see figure 2).

With the continuation of Run 3 data taking, the precision of the 13.6 TeV cross-section measurements will improve and the combination with the Run 2 data will allow the exploration of Higgs-boson properties with growing sensitivity.

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The mass of the W boson, m_W, is important because the SM predicts its value to high precision, in contrast with the masses of the fermions or the Higgs boson. The mass of each fermion is determined by the strength of its interaction with the Brout–Englert–Higgs field, but this strength is currently only known to an accuracy of approximately 10% at best; future measurements from the High-Luminosity LHC and a future e⁺e^– collider are required to achieve percent-level accuracy. Meanwhile, m_W is predicted with an accuracy better than 0.01%. At tree level, this mass depends only on the mass of the Z boson and the weak and electromagnetic couplings. The first measurements of m_W by the UA1 and UA2 experiments at the SppS collider at CERN were in remarkable agreement with this prediction, within the large uncertainties. Further measurements at the Tevatron at Fermilab and the Large Electron Positron collider (LEP) at CERN achieved sufficient precision to probe the presence of higher-order electroweak corrections, such as from a loop containing top and bottom quarks.

Increasing sophistication

Measurements of m_W at the four LEP experiments were performed in collisions producing two W bosons. Hadron colliders, by contrast, can produce a single W-boson resonance, simplifying the measurement when utilising the decay to an electron or muon and an associated neutrino. However, this simplification is countered by the complication of the breakup of the hadrons, along with multiple simultaneous hadron–hadron interactions. Measurements at the Tevatron and LHC have required increasing sophistication to model the production and decay of the W boson, as well as the final-state lepton’s interactions in the detectors. The average time between the available datasets and the resulting published measurement have increased from two years for the first CDF measurement in 1991 to more than 10 years for the most recent CDF measurement announced last year (CERN Courier May/June 2022 p9). The latter benefitted from a factor of four more W bosons than the previous measurement, but suffered from a higher number of additional simultaneous interactions. The challenge of modelling these interactions while also increasing the measurement precision required many years of detailed study. The end result, m_W = 80433.5 ± 9.4 MeV, differs from the SM prediction of m_W = 80357 ± 6 MeV by approximately seven standard deviations (see “Out of order” figure).

The SM calculation of m_W includes corrections from single loops involving fermions or the Higgs boson, as well as from two-loop processes that also include gluons. The splitting of the W boson into a top- and bottom-quark loop produces the largest correction to the mass: for every 1 GeV increase in top-quark mass the predicted W mass increases by a little over 6 MeV. Measurements of the top-quark mass at the Tevatron and LHC have reached a precision of a few hundred MeV, thus contributing an uncertainty on m_W of only a couple of MeV. The calculated m_W depends only logarithmically on the Higgs-boson mass m_H, and given the accuracy of the LHC m_H measurements, it contributes negligibly to the uncertainty on m_W. The tree-level dependence of m_W on the Z-boson mass and on the electromagnetic coupling strength contribute an additional couple of MeV each to the uncertainty. The robust prediction of the SM allows an incisive test through m_W measurements, and it would appear to fail in the face of the recent CDF measurement.

Since the release of the CDF result last year, physicists have held extensive and detailed discussions, with a recurring focus on the measurement’s compatibility with the SM prediction and with the measurements of other experiments. Further discussions and workshops have reviewed the suite of Tevatron and LHC measurements, hypothesising effects that could have led to a bias in one or more of the results. These potential effects are subtle, as fundamentally the W-boson signature is strikingly unique and simple: a single charged electron or muon with no observable particle balancing its momentum. Any source of bias would have to lie in a higher-order theoretical or experimental effect, and the analysts have studied and quantified these in great detail.

Progress

In the spring of this year ATLAS contributed an update to the story. The collaboration re-analysed its data from 2011 to apply a comprehensive statistical fit using a profile likelihood, as well as the latest global knowledge of parton distribution functions (PDFs) – which describe the momentum distribution functions of quarks and gluons inside the proton. The preliminary result (m_W = 80360 ± 16 MeV) reduces the uncertainty and the central value of its previous result published in 2017, further increasing the tension between the ATLAS result and that of CDF.

Meanwhile, the Tevatron+LHC W-mass combination working group has carried out a detailed investigation of higher-order theoretical effects affecting hadron-collider measurements, and provided a combined mass value using the latest published measurement from each experiment and from LEP. These studies, due to be presented at the European Physical Society High-Energy Physics conference in Hamburg in late August, give a comprehensive and quantitative overview of W-boson mass measurements and their compatibilities. While no significant issues have been identified in the measurement procedures and results, the studies shed significant light on their details and differences.

LHC versus Tevatron

Two important aspects of the Tevatron and LHC measurements are the modelling of the momentum distribution of each parton in the colliding hadrons, and the angular distribution of the W boson’s decay products. The higher energy of the LHC increases the importance of the momentum distributions of gluons and of quarks from the second generation, though these can be constrained using the large samples of W and Z bosons. In addition, the combination of results from centrally produced W bosons at ATLAS with more forward W-boson production at LHCb reduces uncertainties from the PDFs. At the Tevatron, proton–antiproton collisions produced a large majority of W bosons via the valence up and down (anti)quarks inside the (anti)proton, and these are also constrained by measurements at the Tevatron. For the W-boson decay, the calculation is common to the LHC and the Tevatron, and precise measurements of the decay distributions by ATLAS are able to distinguish several calculations used in the experiments.

In any combination of measurements, the primary focus is on the uncertainty correlations. In the case of m_W, many uncertainties are constrained in situ and are therefore uncorrelated. The most significant source of correlated uncertainty is the PDFs. In order to evaluate these correlations, the combination working group generated large samples of events and produced simplified models of the CDF, DØ and ATLAS detectors. Several sets of PDFs were studied to determine their compatibility with broader W- and Z-boson measurements at hadron colliders. For each of these sets the correlations and combined m_W values were determined, opening a panorama view of the impact of PDFs on the measurement (see “Measuring up” figure).

The mass of the W boson is important because the SM predicts its value to high precision, in contrast with the masses of the fermions or the Higgs boson

The first conclusion from this study is that the compatibility of all PDF sets with W- and Z-boson measurements is generally low: the most compatible PDF set, CT18 from the CTEQ collaboration, gives a probability of only 1.5% that the suite of measurements are consistent with the predictions. Using this PDF set for the W-boson mass combination gives an even lower compatibility of 0.5%. When the CDF result is removed, the compatibility of the combined m_W value is good (91%), and when comparing this “N-1” combined value to the CDF value for the CT18 set, the difference is 3.6σ. The results are considered unlikely to be compatible, though the possibility cannot be excluded in the absence of an identified bias. If the CDF measurement is removed, the combination yields a mass of m_W = 80369.2 ± 13.3 MeV for the CT18 set, while including all measurements results in a mass of m_W = 80394.6 ± 11.5 MeV. The former value is consistent with the SM prediction, while the latter value is 2.6σ higher.

Two scenarios

The results of the preliminary combination clearly separate two possible scenarios. In the first, the m_W measurements are unbiased and differ due to large fluctuations and the PDF dependence of the W- and Z-boson data. In the second, a bias in one or more of the measurements produces the low compatibility of the measured values. Future measurements will clarify the likelihood of the first scenario, while further studies could identify effect(s) that point to the second scenario. In either case the next milestone will take time due to the exquisite precision that has now been reached, and to the challenges in maintaining analysis teams for the long timescales required to produce a measurement. The W boson’s midlife crisis continues, but with time and effort the golden years will come. We can all look forward to that.

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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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As dark matter (DM) search experiments increasingly constrain minimal models, more complex ones have gained importance, featuring a rich “dark sector” with additional particle states and often involving forces that cannot be directly felt by Standard Model (SM) particles. Nevertheless, the SM and dark sector are typically connected by a “portal” that can be experimentally probed.

The CMS collaboration recently presented the first dedicated collider search for inelastic dark matter (IDM) using the LHC Run 2 dataset. In IDM models, a small Majorana mass component is combined with a Dirac fermion field corresponding to the DM and added to the SM Lagrangian, resulting in two new DM mass eigenstates with a predominantly off-diagonal (inelastic) coupling and a small mass splitting. In addition, a dark photon (a gauge boson similar to the ordinary photon) serves as the portal to the SM. This means that at the LHC, the lighter (χ₁) and heavier (χ₂) DM states are simultaneously produced via a dark photon (A′). While the lighter state is stable and escapes the detector, the heavier one can travel a macroscopic distance before decaying to the lighter one and a pair of muons, which are produced away from the collision point.

This process can be probed by exploiting a striking signature: a pair of almost collinear, low-momentum and displaced muons from the χ₂ decay; significant missing transverse momentum (MET) from the χ₁; and an initial-state radiation jet that can be used for trigger purposes. The MET-dimuon system recoils against the high-momentum jet, so that the muons and MET are also almost collinear. This unique topology presents challenges, including the reconstruction of the displaced muons. This problem was addressed by using a dedicated reconstruction algorithm, which remains efficient even for muons produced several metres away from the collision point (figure 1, left).

The first dedicated collider search for IDM using the full dataset collected during LHC Run 2

After applying event-selection criteria targeting the expected IDM signal, the number of events is compared to the data-driven background prediction: no excess is observed. Upper limits are set on the product of the pp → A′ → χ₂χ₁ production cross-section and the branching fraction of the χ₂ → χ₁ μ⁺μ^– decay; they are shown in figure 1 (right) for a scenario with 10% mass splitting between the χ₁ and χ₂ states. The y variable is roughly proportional to the interaction strength between the SM and the DM sector. Values of y > 10^–7 to  10^–9 are excluded for masses between 3 and 80 GeV, when assuming that the fine structure constant has the same value in the dark sector and in the SM.

CMS physicists are looking forward to probing more complex and well-motivated DM models with novel and creative uses of the existing detector.

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Since the discovery of the W boson at the SppS 40 years ago, collider experiments at CERN and elsewhere have measured its mass ever more precisely. Such measurements provide a vital test of the Standard Model’s consistency, since the W mass is closely related to the strength of the electroweak interaction and to the masses of the Z boson, top quark and Higgs boson; higher experimental precision is needed to keep up with the most recent electroweak calculations. 

The latest experiment to weigh in on the W mass is ATLAS. Reanalysing a sample of 14 million W candidates produced in proton–proton collisions at 7 TeV, the collaboration finds M_w = 80.360 ± 0.005(stat) ± 0.015(syst) = 80.360 ± 0.016 GeV. The value, which was presented on 23 March at the Rencontres de Moriond, is in agreement with all previous measurements except one – the latest measurement from the CDF experiment at the former Tevatron collider at Fermilab.

In 2017 ATLAS released its first measurement of the W-boson mass, which was determined using data recorded in 2011 when the LHC was running at a collision energy of 7 TeV (CERN Courier January/February 2017 p10). The precise result (80.370 ± 0.019 GeV) agreed with the Standard Model prediction (80.354 ± 0.007 GeV) and all previous experimental results, including those from the LEP experiments. But last year, the CDF collaboration announced an even more precise measurement, based on an analysis of its full dataset (CERN Courier May/June 2022 p9). The result (80.434 ± 0.009 GeV) differed significantly from the Standard Model prediction and from the other experimental results (see figure), calling for more measurements to try to identify the source of the discrepancy. 

In its new study, ATLAS reanalysed its 2011 data sample using a more advanced fitting technique as well as improved knowledge of the parton distribution functions that describe how the proton’s momentum is shared amongst its constituent quarks and gluons. In addition, the collaboration verified the theoretical description of the W-production process using dedicated LHC proton–proton runs. The new result is 10 MeV lower than the previous ATLAS result and 15% more precise. 

“Due to an undetected neutrino in the particle’s decay, the W-mass measurement is among the most challenging precision measurements performed at hadron colliders. It requires extremely accurate calibration of the measured particle energies and momenta, and a careful assessment and excellent control of modelling uncertainties,” says ATLAS spokesperson Andreas Hoecker. “This updated result from ATLAS provides a stringent test and confirms the consistency of our theoretical understanding of electroweak interactions.” 

The LHCb collaboration reported a measurement of the W mass in 2021, while the results from CMS are keenly anticipated. In the meantime, physicists from the Tevatron+LHC W-mass combination working group are calculating a combined mass value using the latest measurements from the LHC, Tevatron and LEP. This involves a detailed investigation of higher-order theoretical effects affecting hadron-collider measurements, explains CDF representative Chris Hays from the University of Oxford: “The aim is to give a comprehensive and quantitative overview of W-boson mass measurements and their compatibilities. While no significant issues have been identified that significantly change the measurement results, the studies will shed light on their details and differences.”

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In a 1961 book, Richard Feynman describes the great satisfaction he and Murray Gell-Mann felt in formulating a theory that explained the close equality of the Fermi constants for muon and neutron-beta decay. These two physicists and, independently, Gershtein and Zeldovich, had discovered the universality of weak interactions. It was a generalisation of the universality of electric charge and strongly suggested the existence of a common origin of the two interactions, an insight that was the basis for unified theories developed later. 

Fermi’s description of neutron beta decay (n → p + e^– + ν_e) involved the product of two vector currents analogous to the electromagnetic current: a nuclear current transforming the neutron into a proton and a leptonic current creating the electron–antineutrino pair. Subsequent studies of nuclear decays and the discovery of parity violation complicated the description, introducing all possible kinds of relativistically invariant interactions that could be responsible for neutron beta decay. 

The decay of the muon (μ^– → ν_μ + e^– + ν_e) was also found to involve the product of two vector currents, one transforming the muon into its own neutrino and the other creating the electron–antineutrino pair. What Feynman and Gell-Mann, and Gershtein and Zeldovich, had found is that the nuclear and lepton vector currents have the same strength, despite the fact that the n → p transition is affected by the strong nuclear interaction while μ → ν_μ and e → ν_e transitions are not (we are anticipating here what was discovered only later, namely that the electron and muon each have their own neutrino). 

At the end of the 1950s, simplicity finally emerged. As proposed by Sudarshan and Marshak, and by Feynman and Gell-Mann, all known beta decays are described by the products of two currents, each a combination of a vector and an axial vector current. Feynman notes: after 23 years, we are back to Fermi! 

The book of 1961, however, also records Feynman’s dismay after the discovery that the Fermi constants of strange-particle beta decays, for example the lambda–hyperon beta decay: Λ → p+ e^– + ν_e were smaller by a factor of four or five than the theoretical prediction. In 1960 Gell-Mann, together with Maurice Lévy, had tried to solve the problem but, while taking a step in the right direction, they concluded that it was not possible to make quantitative predictions for the observed decays of the hyperons. It was up to Nicola Cabibbo, in a short article published in 1963 in Physical Review Letters, to reconcile strange-particle decays with the universality of weak interactions, paving the way to the modern unification of electromagnetic and weak interactions. 

Over to Frascati 

Nicola had graduated in Rome in 1958, under his tutor Bruno Touschek. Hired by Giorgio Salvini, he was the first theoretical physicist in the Electro-Synchrotron Frascati laboratories. There, Nicola met Raoul Gatto, five years his elder, who was coming back from Berkeley, and they began an extremely fruitful collaboration. 

These were exciting times in Frascati: the first e⁺ e^– collider, AdA (Anello di Accumulazione), was being realised, to be followed later by a larger machine, Adone, reaching up to 3 GeV in the centre of mass. New particles were studied at the electro-synchrotron, related to the newly discovered SU(3) flavour symmetry (e.g. the η meson). Cabibbo and Gatto authored an important article on e⁺ e^– physics and, in 1961, they investigated the weak interactions of hadrons in the framework of the SU(3) symmetry. Gatto and Cabibbo and, at the same time, Coleman and Glashow, observed that vector currents associated with the SU(3) symmetry by Noether’s theorem include a strangeness-changing current, V(ΔS = 1), that could be associated with strangeness-changing beta-decays in addition to the isospin current, V(ΔS = 0), responsible for strangeness-non-changing beta decays – the same considered by Feynman and Gell-Mann. For strange-particle decays, the identification implied that the variation of strangeness in the hadronic system has to be equal to the variation of the electric charge (in short: ΔS = ΔQ). The rule is satisfied in Λ beta decay (Λ: S = –1, Q = 0; p: S = 0, Q = +1). However, it conflicted with a single event allegedly observed at Berkeley in 1962 and interpreted as Σ⁺ → n + μ⁺ + ν_μ, which had ΔS = –ΔQ (Σ⁺: S = –1, Q = +1; n: S = Q = 0). In addition, the problem remained of how to correctly formulate the concept of muon-hadron universality in the presence of four vector currents describing the transitions e → ν_e, μ → ν_μ, n → p and Λ → p.

Cabibbo’s angle

In his 1963 paper, written while he was working at CERN, Nicola made a few decisive steps. First, he decided to ignore the evidence of a ΔS = –ΔQ component suggested by Berkeley’s Σ⁺ → n + μ⁺ + ν_μ event. Nicola was a good friend of Paolo Franzini, then at Columbia University, and the fact that Paolo, with larger statistics, had not yet seen any such event provided a crucial hint. Next, to describe both ΔS = 0 and ΔS = 1 weak decays, Nicola formulated a notion of universality between each leptonic vector current (electronic or muonic) and one, and only one, hadronic vector current. He assumed the current to be a combination of the two currents determined by the SU(3) symmetry that he had studied with Gatto in Frascati (also identified by Coleman and Glashow): V_hadron = aV(ΔS = 0) + bV(ΔS = 1), with a and b being numerical constants. By construction, V(ΔS = 0) and V(ΔS = 1) have the same strength of the electron or of the muon currents; for the hadronic current to have the same strength, one requires a² + b² = 1, that is a = cosθ, b = sinθ. 

Cabibbo obtained the final expression of the hadronic weak current, adding to these hypotheses the V–A formulation of the weak interactions. The angle θ became a new constant of nature, known since then as the Cabibbo angle. 

An important point is that the Cabibbo theory is based on the currents associated with SU(3) symmetry. For one, this means that it can be applied to the beta decays of all hadrons, mesons and baryons belonging to the different SU(3) multiplets. This was not the case for the precursory Gell-Mann–Lévy theory, which also assumed one hadron weak current but was formulated in terms of protons and lambdas, and could not be applied to the other hyperons or to the mesons. In addition, in the limit of exact SU(3) symmetry one can prove a non-renormalisation theorem for the ΔS = 1 vector current, which is entirely analogous to the one proved by Feynman and Gell-Mann for the ΔS = 0 isospin current. The Cabibbo combination, then, guarantees the universality of the full hadron weak current to the lepton current for any value of the Cabibbo angle, the suppression of the beta decays of strange particles being naturally explained by a small value of θ. Remarkably, a theorem derived by Ademollo and Gatto, and by Fubini a few years later, states that the non-renormalisation of the vector current’s strength is also valid to the first order in SU(3) symmetry breaking. 

Photons and quarks

In many instances, Nicola mentioned that a source of inspiration for his assumption for the hadron current was the passage of photons through a polarimeter, a subject he had considered in Frascati in connection with possible experiments of electron scattering through polarised crystals. Linearly polarised photons can be described via two orthogonal states, but what is transmitted is only the linear combination corresponding to the direction determined by the polarimeter. Similarly, there are two orthogonal hadron currents, V (ΔS = 0) and V (ΔS = 1), but only the Cabibbo combination couples to the weak interactions. 

An interpretation closer to particle physics came with the discovery of quarks. In quark language, V(ΔS = 0) induces the transition d → u and V(ΔS = 1) the transition s → u. The Cabibbo combination corresponds then to d_C = (cos θd + sin θs) → u. Stated differently, the u quark is coupled by the weak interaction only to one, specific, superposition of d and s quarks: the Cabibbo combination d_C. This is Cabibbo mixing, reflecting the fact that in SU(3) there are two quarks with the same charge –1/3. 

A first comparison between theory and meson and hyperon beta-decay data was done by Cabibbo in his original paper, in the exact SU(3) limit. Specifically, the value of θ was obtained by comparing K⁺ and π⁺ semileptonic decays. In baryon semileptonic decays, the matrix elements of vector currents are determined by the SU(3) symmetry, while axial currents depend upon two parameters, the so-called F and D couplings. Many fits have been performed in successive years, which saw a dramatic increase in the decay modes observed, in statistics, and in precision. 

Four decades after the 1963 paper, Cabibbo, with Earl Swallow and Roland Winston, performed a complete analysis of hyperon decays in the Cabibbo theory, then embedded in the three-generation Kobayashi and Maskawa theory, taking into account the momentum dependence of vector currents. In their words (and in modern notation):
“… we obtain V_us = 0.2250(27) (= sin θ). This value is of similar precision, but higher than the one derived from Kl3, and in better agreement with the unitarity requirement,
|V_ud |² + |V_us|² + |V_ub |² = 1. We find that the Cabibbo model gives an excellent fit of the existing form factor data on baryon beta decays (χ² = 2.96) for three degrees of freedom with F + D = 1.2670 ± 0.0030, F–D = –0.341±0.016, and no indication of flavour SU(3) breaking effects.” 

The Cabibbo theory predicts a reduction in the nuclear Fermi constant squared with respect to the muonic one by a factor cos² θ = 0.97. The discrepancy had been noticed by Feynman and S Berman, one of Feynman’s students, who estimated the possible effect of electromagnetic radiative corrections. The situation is much clearer today, with precise data coming from super-allowed Fermi nuclear transitions and radiative corrections under control.  

Closing up

From its very publication, the Cabibbo theory was seen as a crucial development. It indicated the correct way to embody lepton-hadron universality and it enjoyed a heartening phenomenological success, which in turn indicated that we could be on the right track for a fundamental theory of weak interactions. 

The idea of quark mixing had profound consequences. It prompted the solution of the spectacular suppression of strangeness-changing neutral processes by the GIM mechanism (Glashow, Iliopoulos and Maiani), where the charm quark couples to the combination of down and strange quarks orthogonal to the Cabibbo combination. Building on Cabibbo mixing and GIM, it has been possible to extend to hadrons the unified SU(2)_L ⊗ U(1) theory formulated, for leptons, by Glashow, and by Weinberg and Salam. 

There are very few articles in the scientific literature in which one does not feel the need to change a single word and Cabibbo’s is definitely one of them

CP symmetry violations observed experimentally had no place in the two-generation scheme (four quarks, four leptons) but found an elegant description by Makoto Kobayashi and Toshihide Maskawa in the extension to three generations. Quark mixing introduced by Cabibbo is now described by a three-by-three unitary matrix known in the literature as the Cabibbo–Kobayashi–Maskawa (CKM) matrix. In the past 50 years the CKM scheme has been confirmed with ever increasing accuracy by a plethora of measurements and impressive theoretical predictions (see “Testing quark mixing” figure). Major achievements have been obtained in the studies of charm- and beauty-particle decays and mixing. The CKM paradigm remains a great success in predicting weak processes and in our understanding of the sources of CP violation in our universe. 

Nicola Cabibbo passed away in 2010. The authoritative book by Abraham Pais, in its chronology, cites the Cabibbo theory among the most important developments in post-war particle physics. In the History of CERN, Jean Iliopoulos writes: “There are very few articles in the scientific literature in which one does not feel the need to change a single word and Cabibbo’s is definitely one of them. With this work, he established himself as one of the leading theorists in the domain of weak interactions.”

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The workshop programme covered current and future experimental projects to probe the Sakharov conditions: collider measurements of CP violation (LHCb, Belle II, FCC-ee), searches for electric dipole moments (PSI, FNAL), long-baseline neutrino experiments (NOvA, DUNE, T2K, Hyper-Kamiokande, ESSnuSB) and searches for baryon- and lepton-number violating processes such as neutrinoless double beta decay (GERDA, CUORE, CUPID-Mo, KamLAND-Zen, EXO-200) and neutron–antineutron oscillations (ESS). These were put in context with the different theoretical approaches to baryogenesis and leptogenesis.

With the workshop’s aim to provide a discussion forum for junior and senior scientists from various backgrounds, and following the tradition of the Ecole des Houches, a six-hour mini-school took place in parallel with more specialised talks. A first lecture by Julia Harz (University of Mainz) introduced the hypotheses related to baryogenesis, and another by Adam Falkowski (IJCLab) described how CP violation is treated in effective field theory. Each lecture provided both a common theoretical background, and an opportunity to discuss the fundamental motivation driving experimental searches for new sources of CP violation in particle physics.

In his summary talk, Mikhail Shaposhnikov (EPFL Lausanne) explained that it is impossible to identify which mechanism leads to the existing baryon asymmetry in the universe. He added that we live in exciting times and reviewed the vast number of opportunities in experiment and theory lying ahead.

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Studies of the Higgs boson by ATLAS and CMS have observed and measured a large spectrum of production and decay mechanisms. Its relatively long lifetime and low expected width (4.1 MeV, compared with the GeV-range decay widths of the W and Z bosons) make the Higgs boson a sensitive probe for small couplings to new states that may measurably distort its branching fractions. The search for invisible or yet undetected decay channels is thus highly relevant.

Dark-matter (DM) particles created in LHC collisions would have no measurable interaction with the ATLAS detector and thus would be “invisible”, but could still be detected via the observation of missing transverse momentum in an event, similarly to neutrinos. The Standard Model (SM) predicts the Higgs boson to decay invisibly via H → ZZ^* → 4ν in only 0.1% of cases. However, this value could be significantly enhanced if the Higgs boson decays into a pair of (light enough) DM particles. Thus, by constraining the branching fraction of Higgs-boson decays to invisible particles it is possible to constrain DM scenarios and probe other physics beyond the SM (BSM).

The ATLAS collaboration has performed comprehensive searches for invisible decays of the Higgs boson considering all its major production modes: vector-boson fusion with and without additional final-state photons, gluon fusion in association with a jet from initial-state radiation, and associated production with a leptonically decaying Z boson or a top quark–antiquark pair. The results of these searches have now been combined, including inputs from Runs 1 and 2 analyses. They yield an upper limit of 10.7% on the branching ratio of the Higgs boson to invisible particles at 95% confidence level, for an unprecedented expected sensitivity of 7.7%. The result is used to extract upper limits on the spin-independent DM-nucleon scattering cross section for DM masses smaller than about 60 GeV in a variety of Higgs-portal models (figure 1). In this range and for the models considered, invisible Higgs-boson decays are more sensitive than the results from DM-nucleon scattering detection experiments.

An alternative way to constrain possible undetected decays of the Higgs boson is to measure its total decay width Γ_H. Combining the observed value of the width with measurements of the branching fractions to observed decays allows the partial width for decays to new particles to be inferred. Directly measuring Γ_H at the LHC is not possible as it is much smaller than the detector resolution. However, Γ_H can be constrained by taking advantage of an unusual feature of the H → ZZ^(*) decay channel: the rapid increase in available phase space for the H → ZZ^(*) decay as m_H approaches the 2m_Z threshold counteracts the mass dependence of Higgs-boson production. Furthermore, this far “off-shell” production above 2m_Z has a negligible Γ_H dependence, unlike “on-shell” production near the Higgs-boson mass at 125 GeV. Comparing the Higgs-boson production rates in these two regions therefore allows an indirect measurement of Γ_H. Although some assumptions are required (e.g. that the relation between on-shell and off-shell production is not modified by BSM effects), the measurement is sensitive to the value of Γ_H expected in the SM. Recently, ATLAS measured the off-shell production cross-section using both the four-charged lepton (4l) and two-charged lepton plus two neutrino (2l2v) final states, finding evidence for off-shell Higgs-boson production with a significance of 3.3 σ (figure 2). By combining both the previously measured on-shell Higgs-boson production-cross section and the of-shell Higgs-boson production-cross section, Γ_H was found to be 4.5^+3.3_–2.5 MeV, which agrees with the SM prediction of 4.1 MeV but leaves plenty of room for possible BSM contributions.

This sensitivity will improve thanks to the new data to be collected in Run 3 of the LHC, which should more than triple the size of the Run 2 dataset.

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Neutrinos first
Neutrino masses and mixing provide a unique window on the only new physics so far seen beyond the Standard Model. The measured mass differences and mixing parameters provide a consistent picture suggesting the presence of a new scale potentially at approximately 10¹⁵ GeV. However, to complete this picture two fundamental elements are missing: the absolute mass scale of neutrinos and the determination, via neutrinoless double beta decay, of whether  neutrinos have a Majorana nature. Also of fundamental importance are the mass-squared ordering of  neutrinos, the maximality (or not) of atmospheric mixing, and the measurement of leptonic CP violation. All these questions were addressed by a range of new experimental results, many of which were presented for the first time.

NOvA and T2K presented a very consistent picture of the PMNS framework with a slight preference of the normal over the inverted ordering

The KATRIN collaboration reported an absolute upper limit on the electron-neutrino mass of 800 meV and is expected to reach a limit of 200 meV eventually. With a detailed analysis of their tritium decay spectrum, the team was also able to exclude rapid oscillations of electron neutrinos with potential sterile neutrinos and to set a limit on cosmic-neutrino local over-densities. The KamLandZEN, CUPID-Mo and Majorana Demonstrator experiments showed first results on neutrinoless double-beta decay searches in different systems.  KamLandZEN  had the largest number of radionuclei, providing upper limits on the effective electron neutrino mass between 36 and 156 meV (depending on model assumptions) and is expected to reach 20 meV with more data. CUPID-Mo and Majorana Demonstrator experiments are expected to eventually reach stronger limits down to approximately 10 meV. The latter experiment, based on germanium detectors, also reported interesting bounds on models for wave-function collapse.

The long-baseline ν_μ oscillation experiments NOvA and T2K presented analyses of their latest intermediate dataset, showing a very consistent picture of the PMNS framework with a slight preference (at the one or two standard-deviation level) of the normal over the inverted ordering and the upper over the lower octant for θ₂₃. Both experiments are sensitive to electron-neutrino appearance. NOvA, however, provided the first evidence for electron anti-neutrino appearance and a first long-baseline measurement of sin²θ₂₃, in very good agreement with the reactor neutrino data. Both experiments exclude CP conserving values of δ_CP of 0 or π at 90% confidence. IceCUBE with its DeepCORE extension also presented stunning atmospheric neutrino-oscillation results comparable with SuperKamiokande and long-baseline experiment sensitivities. All these experiments provide strong supporting evidence of the validity of the three neutrino-flavour paradigm.

Longstanding neutrino anomalies were discussed in detail. The reactor-neutrino deficit interpretation in terms of the existence of a sterile neutrino species is incompatible with several short baseline data. The significance of the LSND and MiniBooNE short-baseline low-energy excess was revisited in the light of new backgrounds. The long-standing gallium anomaly was further verified and confirmed by the independent experiment BEST. The BEST observations are, however, also not compatible with a simple sterile-neutrino oscillation pattern. The PROSPECT reactor-neutrino experiment also showed first results excluding the gallium anomaly in terms of an oscillation with a sterile neutrino. Finally, a peaking anomaly, in the range 5-7 MeV, was observed by several experiments (including RENO, DayaBay, NEOS, Chooz and PROSPECT). This anomaly cannot be easily interpreted in terms of fundamental neutrino physics. Instead, nuclear models have been discussed in detail and should be looked at carefully.

Finally, the results of CONUS, a Coherent neutrino scattering experiment based on high precision germanium detectors,  set limits on light vector mediators and the neutrino magnetic moment.

The three-neutrino paradigm is standing tall with some anomalies that  need to be further clarified, in particular the BEST gallium anomaly.

On the theoretical side, it was shown that leptogenesis is possible for any right-handed neutrino masses above about 0.1 GeV, which, if light enough, can be probed by the proposed SHiP experiment at CERN, as well as FCC-ee and HL-LHC. Neutrino experiments such as COHERENT were analysed in the framework of Standard Model Effective Field Theory.

The IceCUBE experiment also showed splendid multi-messenger results from high- and ultrahigh-energy neutrino observations and pointed out their ability to probe the Standard Model with ultrahigh-energy neutrinos that have travelled cosmic distances. These neutrinos are expected to be even mixtures of the three neutrino species; any deviation would be a clear sign of new physics. The cosmic-neutrino data also highlighted the missing data in neutrino-nucleon interactions in the range of a few 100 GeV to 10 TeV. At this year’s Moriond conference, the birth of collider neutrino physics was also presented, with the first results from the FASERν and SND experiments. FASERν showed the first unambiguous observation of neutrinos from proton-proton collisions at LHC point 1.

Overall the three neutrino paradigm is standing tall with some anomalies that still need to be further clarified, in particular the BEST gallium anomaly.

From neutrinos to quarks

From a theoretical point of view, neutrino and heavy-quark physics are two sides of the same coin: they provide information related to the flavour problem, namely the unexplained origin of quark and lepton families, masses and mixings. The fact that in the Standard Model fermion mass hierarchies arise from Yukawa couplings does not make it more satisfactory. The recently observed anomalies in semi-leptonic B decays exhibiting unexpected lepton-flavour patterns have raised numerous speculations and have in particular suggested that the flavour scale might be right around the corner at the TeV scale, motivating models discussed at the conference involving a new Z’ gauge boson or a scalar or a vector leptoquark from a twin Pati-Salam theory of flavour.

However, the recent results from LHCb on the main anomalies have shed new light on the question. LHCb discussed their recent reanalysis of the R(K) and R(K*) ratio of decay rates of B→K^(*)μμ /ee with the inclusion of an additional background from misidentified electrons are now in excellent agreement with the Standard Model. LHCb also presented a new result on the measurement of the R(D*) ratio of decay rates including fully hadronic τ decays and a new combined measurement of the R(D) and R(D*) ratios. With these new measurements from LHCb the R(D*) ratio agrees with the Standard Model predictions. A tension at the 3 standard deviations level is still observed, mostly due to the R(D) ratio.

Alternatively, D-meson decays were extensively discussed as a promising new playground for discovering new physics due to the richness of new data available, and the efficiency of the GIM mechanism for the charm quark and SU(3) flavour symmetry leading to easily verifiable null tests of the Standard Model.

Results of various rare decay and new resonance searches were presented by LHC experiments, with for example the ambitious searches of the extremely rare decay mode of the D meson in two muons, the observation by the CMS experiment of the decay of the η meson to four muons and the search for  states decaying to di-charmonium states as J/ψ/J/ψ or J/ψ/ψ_2S to four muons, which could correspond to four charm tetra-quark states.

Leaving no stone unturned, the LHC experiments have presented a whole host of new results of searches for new phenomena beyond the Standard Model

A highlight of the conference was the strong contribution from the Belle II experiment in all areas of heavy flavour physics, including: several measurements of b→s transitions, including a fully inclusive measurement; several time dependent CP-violation observables, which yield precisions on the CKM parameter sin(2β) on a par with the current world’s best measurements in those channels; as well as new input to the |V_ub| and |V_cb| puzzle (the tension between exclusive and inclusive measurements which suffer from different theoretical uncertainties), with an exclusive measurement in the golden B→πlν mode and an inclusive measurement of the B→D*lν decay.

LHCb presented nice new results in the b→sss transition in the φφ channel showing that no CP- violating effect is seen, with results separated in different polarisation modes. LHCb also presented a new measurement of the CKM angle γ in the B^±→D[K^∓π^±π^∓π^±]h^± (h = π, K) channel and an overall combination yielding a precision of approximately 3.7º.

Finally, a status report was given by the KOTO experiment which is searching for the extremely rare K_L→πνν process. The two first runs (starting in 2015 until 2018) have allowed the collaboration to identify two new backgrounds and provide methods to mitigate them since 2019.  With these improvements the KOTO experiment should reach sensitivities at the 10^-10 level, close to the expected branching fraction in the Standard Model of 3×10^-11. All measurements shown so far are compatible with the CKM paradigm.

Also in the quark sector, the latest measurements and the prospects in measurements of the neutron electric dipole moment were presented, providing strong constraints on new physics scenarios at high energy scales.

Lattice-QCD studies have made remarkable progress in recent years, with hadronic contributions to  muon g-2 being more or less under control, more so in the case of light-by-light contributions, which agree well with other results, and less so regarding the hadronic vacuum polarisation with  errors being driven down by the BMW collaboration, which by itself seems to lead to more consistency with the FNAL and BNL results. However, the BMW results are not yet fully confirmed either by other lattice groups or the R-ratio from experiment, with the recent VEPP data being out of line with previous experiments.

Higher precision from lattice calculations has also led to the so-called Cabibbo anomaly reported at Moriond, whereby the unitarity of the first row of the CKM matrix seems to be violated by 2.7σ. If confirmed by future experiments and lattice calculations, this could be a signal for new physics.

In addition, in the lepton flavour sector Belle II presented their first and already the world’s most precise tau-mass measurement, which agrees with previous measurements. With only approximately half the luminosity accumulated by the Belle experiment, Belle II presented measurements surpassing the Belle precision, thus displaying the excellent performance of the experiment.

Dark searches

A variety of dark-matter candidates were discussed including: primordial black hole with improved limits using 21 cm hydrogen astronomy; weakly interacting massive particles (WIMPs) from new electroweak fermion multiplets with heavier masses; heavy singlet dilaton-like scalars; keV neutrinos from an inverse seesaw model; axions or axion-like particles with an extended window of masses arising from non-standard cosmology; and ultralight dark matter such as dark photons whose interactions with the detector could be simulated by the software package DarkELF. An interesting proposal for axion detectors that can double up as high-frequency gravitational wave detectors was also discussed.

A flurry of results of searches for dark-sector particles at the LHC, Belle II, Babar, NA62, BES and PADME were shown.

The XENONnT collaboration presented new results, unblinded for the occasion, with an exposure of 95.1 days corresponding to 1.1 tonne-year. LZ also presented their latest results with a similar exposure. The two experiments, along with the PandaX xenon-based experiment, are now exploring new territory at low WIMP-nucleon cross sections.

These very low cross sections motivate further searches for the existence of a dark sector with dark photons or axion-like particles. A flurry of results of searches for dark-sector particles at the LHC, Belle II, Babar, NA62, BES and the PADME experiment were shown. PADME, a fixed-target e⁺e^– experiment, also presented their ability to directly probe an anomaly which was also seen in ¹²C and ⁴He.

Theories of new heavy particles were also discussed, ranging from an analysis of the minimal supersymmetric Standard Model which showed that gluinos of 1 TeV and stop squarks of 500 GeV could still have escaped detection, to theories of two Higgs-doublet models plus a Higgs singlet, which might be responsible for the 95 GeV diphoton events, to the observation that vector-like fermions (which come in opposite chirality pairs) have the right properties to avoid a metastable universe.

Electroweak searches at the LHC

The LHC experiments presented results from a host of searches for new phenomena beyond the Standard Model, leaving no stone unturned. These looked for signatures of models motivated by theories addressing the shortcomings of the Standard Model, astrophysical and cosmological observations such as dark matter that could be interpreted as the existence of a fundamental field, and experimental anomalies observed such as in the lepton-flavour or muon g-2 anomalies. These searches place very important limits on the presence of new phenomena up to the few-TeV scale. With 20 times more data, the High-Luminosity LHC (HL-LHC) will provide invaluable opportunities to significantly increase the search domain and bring potential for discoveries.

The LHC experiments also presented a series of new results based on W and Z production, coinciding very well with the 40th anniversary of the W and Z boson discoveries at the CERN SppS. The CMS collaboration showed a measurement of the τ polarisation. This measurement can be directly translated in terms of a measurement of the weak mixing angle with a precision of approximately 10%, which is close to the precision reached by e⁺e^– experiments. The CMS collaboration also presented a measurement of the invisible width of the Z boson that is more precise than the direct invisible-width measurements performed at LEP. ATLAS showed the precise measurement of the Z boson transverse momentum differential cross section integrated over the full phase space of leptons produced in the Z decay, and with it was able to provide the current most precise measurement of α_S with a precision comparable to the current world average or estimates using lattice QCD. ATLAS also presented a new measurement of the W-boson mass using a re-analysis of 7 TeV data collected in 2011, yielding a value slightly lower (by 10 MeV) and with a precision improved to 16 MeV, thus increasing the experimental tension with the recently published CDF measurement.

The LHC results have already obtained precision and sensitivity to processes that were thought to be unreachable prior to the start of operations.

ATLAS and CMS also showed results for more complex and rare processes equally highlighting the remarkable progresses made at the precision frontier. Both experiments showed an observation of the four top quarks production process and ATLAS presented the observation of two new tri-boson production processes, WZγ and Wγγ. ATLAS also presented a new measurement of the associated production of a W boson in association with a pair of top quarks which is a key background to numerous very important processes, as for instant the associated production of a Higgs boson with a pair of top quarks.

The results presented at this year’s Moriond elctroweak session show how LHC results have already obtained precision and sensitivity to processes that were thought to be unreachable prior to the start of operations. An outstanding example discussed in detail was the progress made in the search for di-Higgs production by ATLAS and CMS, a cornerstone of the HL-LHC physics programme to constrain the Higgs boson trilinear self-coupling. These results showed that combined, experiments should reach the sensitivity for the observation of this process at the LHC. Another example which was also discussed is the race to reach sensitivity to the Higgs-boson decays to charm quarks, where new methods based on deep learning techniques are making significant progress.

To further improve on the expected precision reach at the HL-LHC, intermediate goals at Run 3 are extremely important. Both ATLAS and CMS presented new results on measurements of Z boson, top, and Higgs boson production with LHC Run 3 data taken in 2022.

This year’s Moriond conference showed an extraordinary harvest of new results, giving an opportunity to take stock on the open questions and see the remarkable progress made since last year.

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Precision electroweak measurements are a powerful way to probe new physics, through the indirect effects predicted by quantum field theory. The electroweak mixing angle θ_W^eff is particularly sensitive to new phenomena related to electroweak symmetry breaking and the Brout–Englert–Higgs mechanism. It was measured at LEP in different processes; and at the LHC, thanks to the large number of collected events with Z-boson decays, the experiments can probe these effects with comparable sensitivity.

The CMS collaboration has reported a new measurement of the tau-lepton polarisation in the decay of Z bosons to a pair of tau leptons in proton–proton collisions at 13 TeV. The polarisation is defined as the asymmetry between the cross sections for the production of τ^– with positive and negative helicities, and is directly related to the electroweak mixing angle via the relation P_τ ≈ –2(1–4 sin²θ_W^eff). The polarisation of the tau lepton is determined from the angular distributions of the visible tau decay products, leptonic or hadronic, with respect to the τ flight direction or relative to each other. A so-called optimal polarisation observable is constructed using all of these angular properties of the tau decay products. Since the spin states in Z⁰ → τ^–τ⁺ are almost 100% anti-correlated, the sensitivity is improved by combining the spin observables of both τ leptons of the pair.

The average polarisation〈P_τ〉is obtained by a template fit to the observed optimal τ-polarisation observables, using tau-lepton pairs with an invariant mass in the range 75–120 GeV. As summarised in figure 1, the best sensitivity of P_τ is found in the channel where one tau decays to a muon and the other decays hadronically, thanks to the good selection efficiency and reconstruction of the spin observable in this channel. The fully hadronic final state suffers from higher trigger thresholds, which lead to fewer events and distortions of the templates.

The average τ polarisation is corrected to the value at the Z pole, P_τ (Z⁰) = –0.144 ± 0.006 (stat.) ± 0.014 (syst.), where the systematic uncertainty is dominated by the incorrect identification of the products of hadronically decaying tau leptons. The effective weak mixing angle is then determined as sin²θ_W^eff = 0.2319 ± 0.0019, in agreement with the Standard Model (SM) prediction. Figure 2 compares the tau– lepton asymmetry parameter (the negative of the polarisation) with results from previous experiments, demonstrating that the CMS measurement is nearly as precise as those of single LEP experiments.

This measurement shows that LHC collision events, although much more complex than those collected at LEP, can provide precise determinations of the polarisation of the τ lepton, as well as of spin correlations between τ-lepton pairs. Such measurements are crucial to probe the CP properties of the Higgs boson’s Yukawa coupling to τ leptons, which is an important step in the path to understand the Higgs sector of the SM.

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The 12^th Higgs Hunting workshop, which took place in Paris and Orsay from 12 to14 September, presented an overview of recent and new results in Higgs-boson physics. The results painted an increasingly detailed picture of Higgs-boson properties, thanks to the many analyses now reporting results based on the full LHC Run 2 dataset, with an integrated luminosity of about 140 fb^-1. Searches for phenomena beyond the Standard Model (BSM) were also presented.

Highlights included new results from CMS on decays of Higgs bosons to b quarks and to invisible final states, and a new limit from ATLAS on lepton-flavour violating decays of the Higgs boson. Events with two Higgs bosons in the final state were used to set limits on interactions involving three Higgs bosons and between two Higgs bosons and two weak vector bosons. All the results remain compatible with Standard Model expectations, except for a small number of intriguing tensions in some BSM searches, such as small excesses in a search for heavier partners of the Higgs boson decaying to W-boson pairs and in a search for resonances produced alongside a Z boson and decaying to a pair of Higgs bosons. These deviations from theory will be followed up by ATLAS and CMS in further analyses using Run 2 and Run 3 data.

This year’s workshop was special as the event marked the tenth anniversary of the Higgs-boson discovery in 2012. Two historical talks given by the former ATLAS and CMS spokespersons Peter Jenni (University of Freiburg & CERN) and Jim Virdee (Imperial College) highlighted the long-term efforts that laid the foundation for the Higgs-boson discovery in 2012.

The workshop also hosted an in-depth discussion on future accelerators and related detector R&D. It focused on future efforts in Europe, the US and Latin America, and featured presentations by Karl Jakobs (University of Freiburg and chair of the European Committee for Future Accelerators), Meenashi Narain (Brwon University and convener of the energy frontier group of the Snowmass process), Maria-Teresa Tova (National University of La Plata) and representative for the Latin American strategy effort) and Emmanuel Perez (CERN), who discussed recent improvements in physics analyses at future colliders.

Recent theory developments were also extensively covered, in particular recent developments in higher-order computations by Michael Spira (PSI), which highlighted the agreement between experimental results and predictions. A review of recent theory progress towards future colliders was also presented by Gauthier Durieux (CERN), while Carlos Wagner (Enrico Fermi Institute, & Kavli Institute for Cosmological Physics) discussed the new-physics that can be explored via precise measurements of Higgs-boson couplings. Finally, a “vision” presentation by Marcela Carena (Fermilab) highlighted new opportunities for the study of electroweak baryogenesis in relation to Higgs-boson measurements.

Many experimental sessions were held regarding recent results on a wide variety of topics, some which will be relevant in upcoming Run 3 measurements. This includes measurements related to potential CP-violating effects in the Higgs sector, as well as effective field theories (EFTs). This latter topic allows a general description of deviations from Standard Model  predictions in Higgs-boson measurements and beyond, and much improved measurements in this direction are expected in Run 3. The search for  Higgs-boson pair production was also an important focus at the Paris meeting. The latest Run 2 analyses showed greatly improved sensitivity compared to earlier rounds, and further improvements are expected in Run 3. While sensitivity to the Standard Model signal is not expected until the High-Luminosity LHC, these searches should set strong constraints on BSM effects in the Higgs sector.

Concluding talks were given by Fabio Maltoni (Louvain) and Giacinto Piacquadio (Stony Brook), and the next Higgs Hunting workshop will be held in Orsay and Paris from 11 to 13 September 2023.

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When the W and Z bosons were predicted in the mid-to-late 1960s, their masses were not known. Experimentalists therefore had no idea what energy they needed to produce them. That changed in 1973, when Gargamelle discovered neutral-current neutrino interactions and measured the cross-section ratio between neutral- and charged-current interactions. This ratio provided the first direct determination of the weak mixing angle, which, via the electroweak theory, predicted the W-boson mass to lie between 60 and 80 GeV, and the Z mass between 75 and 95 GeV – at least twice the energy of the leading accelerators of the day. 

By then, the world’s first hadron collider – the Intersecting Storage Rings (ISR) at CERN – was working well. Kjell Johnsen proposed a new superconducting ISR in the same tunnel, capable of reaching 240 GeV. A study group was formed. Then, in 1976, Carlo Rubbia, David Cline and Peter McIntyre suggested adding  an antiproton source to a conventional 400 GeV proton accelerator, either at Fermilab or at CERN, to transform it into a pp collider. The problem was that the antiprotons had to be accumulated
and cooled if the target luminosity (10²⁹ cm^–2s^–1, providing about one Z event per day) was to be reached. Two methods were proposed: stochastic cooling by Simon van der Meer at CERN and electron cooling by Gersh Budker in Novosibirsk. 

CERN Director-General John Adams wasn’t too happy that as soon as the SPS had been built, physicists wanted to convert it into a pp collider. But he accepted the suggestion, and the idea of a superconducting ISR was abandoned. Following the Initial Cooling Experiment, which showed that the luminosity target was achievable with stochastic cooling, the SppS was approved in May 1978 and the construction of the Antiproton Accumulator (AA) by van der Meer and collaborators began. Around that time, the design of the UA1 experiment was also approved. 

A group of us proposed a second, simpler experiment in another interaction region (UA2), but it was put on hold for financial reasons. Then, at the end of 1978, Sam Ting proposed an experiment to go in the same place. His idea was to surround the beam with heavy material so that everything would be absorbed except for muons, making it good at identifying Z → μ⁺μ^– but far from good for W bosons decaying to a muon and a neutrino. In a tense atmosphere, Ting’s proposal was turned down and ours was approved.

First sightings

The first low-intensity pp collisions arrived in late 1981. In December 1982 the luminosity reached a sufficient level, and by the following month UA1 had recorded six W candidates and UA2 four. The background was minimal; there was nothing else we could think of that would produce such events. Carlo presented the UA1 events and Pierre Darriulat the UA2 ones at a workshop in Rome on 12–14 January 1983. On 20 January, Carlo announced the W discovery at a CERN seminar, and the next day I presented the UA2 results, confirming UA1. In UA2 we never discussed priority, because we all knew that it was Carlo who had made the whole project possible. 

The same philosophy guided the discovery of the Z boson. UA2 had recorded a candidate Z → e⁺e^– event in December 1982, also presented by Pierre at the Rome workshop. One electron was perfectly clear, whereas the other had produced a shower with many tracks. I had shown the event to Jack Steinberger, who strongly suggested we publish immediately; however, we decided to wait for the first “golden” event with both electrons unambiguously identified. Then, one night in May 1983, UA1 found a Z. As with ours, only one electron satisfied all electron-identification criteria, but Carlo used the event to announce a discovery. The UA1 results (based on four Z → e⁺e^– events and one Z → μ⁺μ^–) were published that July, followed by the UA2 results (based on eight Z → e⁺e^– events, including the 1982 one) a month later. 

The SppS ran until 1990, when it became clear that Fermilab’s Tevatron was going to put us out of business. In 1984–1985 the energy was increased from 546 to 630 GeV and in 1986 another ring was added to the AA, increasing the luminosity 10-fold. Following the 1984 Nobel prize to Rubbia and van der Meer, UA1 embarked on an ambitious new electromagnetic calorimeter that never quite worked. UA2 went on to make a precise measurement of the ratio m_W/m_Z, which, along with the first precise measurement of m_Z at LEP, enabled us to determine the W mass with 0.5% precision and, via radiative corrections, to predict the mass of the top quark (160⁺⁵⁰_–60 GeV) several years before the Tevatron discovered it. 

Times have certainly changed since then, but the powerful interplay between theory, experiment and machine builders remains essential for progress in particle physics. 

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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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Lepton number is a quantum number that represents the difference in the number of leptons and antileptons participating in a process, while lepton flavour is a corresponding quantity that accounts for each generation of lepton (e, μ or τ) separately. Lepton number is always conserved but lepton flavour violation (LFV) is known to exist in nature, as this phenomenon has been observed in neutrino oscillations – the transition of a neutral lepton of a given flavour to one with a different flavour. This observation motivates searches for additional manifestations of LFV that may be the result of beyond-the-Standard Model (SM) physics, key among which is the search for LFV decays of the Higgs boson. 

The ATLAS collaboration has recently announced the results of searches for H → eτ and H → μτ decays based on the full Run 2 data set, which was collected at a centre-of-mass energy of 13 TeV. The unstable τ lepton decays to an electron or a muon and two neutrinos, or to one or more hadrons and one neutrino. Most of the background events in these searches arise from SM processes such as Z → ττ, the production of top–antitop and weak-boson pairs, as well as from events containing misidentified or non-prompt leptons (fake leptons). These fake leptons originate from secondary decays, for example of charged pions. Several multivariate analysis techniques were used for each final state to provide the maximum separation between signal and background events.

To ensure the robustness of the measurement, two background estimation methods were employed: a Monte Carlo (MC) template method in which the background shapes were extracted from MC and normalised to data, and a “symmetry method”, which used only the data and relied on an approximate symmetry between prompt electrons and prompt muons. Any difference between the branching fractions B(H → eτ_μ) and B(H → μτ_e), where the subscripts μ and e represent the decay modes of the τ lepton, would break this symmetry. In both cases, contributions from events containing fake leptons were estimated directly from the data.

The MC-template method enables the measurement of the branching ratios of the LFV decay modes. Searches based on the MC-template method for background estimation involve both leptonic and hadronic decays of τ leptons. A simultaneous measurement of the H → eτ and H → μτ decay modes was performed. For the H → μτ (H → eτ) search, a 2.5 (1.6) standard deviation upward fluctuation above the SM background prediction is observed. The observed (expected) upper limits on the branching fractions B(H → eτ) and B(H → μτ) at 95% confidence level are slightly below 0.2% (0.1%), which are the most stringent limits obtained by the ATLAS experiment on these quantities. The result of the simultaneous measurement of the H → eτ and H → μτ branching fractions is compatible with the SM prediction within 2.2 standard deviations (see figure 1).

The observed upper limits on the branching fractions are the most stringent limits obtained by the ATLAS experiment

The symmetry method is particularly sensitive to the difference in the two LFV decay branching ratios. For this measurement, only the fully leptonic final states were used. Special attention was paid to correctly account for asymmetries induced by the different detector response to electrons and muons, especially regarding the trigger and offline efficiency values for lepton reconstruction, identification and isolation, as well as regarding contributions from fake leptons. The measurement of the branching ratio difference indicates a small but not significant upward deviation for H → μτ compared to H → eτ. The best-fit value for the difference between B(H → μτ_e) and B(H → eτ_μ) is (0.25 ± 0.10)%. 

The expected twice-larger LHC Run 3 dataset at the higher centre-of-mass energy of 13.6 TeV will shed further light on these results.

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Marking 10 years since the discovery of the Higgs boson, a two-day workshop held at the University of Birmingham on 30 June and 1 July brought together ATLAS and CMS physicists who were involved in the discovery and subsequent characterisation of the Higgs boson. Around 75 physicists, in addition to members of the public who attended a colloquium, celebrated this momentous discovery together with PhD students, early-career researchers and members of IOP’s history of physics group. In an informal atmosphere, participants recalled and gave insights on what had taken place, spicing it with personal stories that placed the human dimension of science under the spotlight.

The story of the Higgs-boson search was traced from the times of LEP and the Tevatron. Participants were reminded of the uncertainty and excitement during the final days of LEP: the hints of an excess of events at around 115 GeV and the ensuing controversy surrounding the decision to either stop the machine or extend its data-taking further. For the Tevatron, the focus was more on the relentless race against time until the LHC could provide an overwhelming dataset. It was considered plausible that the Tevatron could observe the Higgs boson first, leading CERN to delay a scheduled break in LHC data-taking following its 2011 run.

The timeline of the design, construction and commissioning of the LHC experi­ments was presented, with a particular focus on the excellent performance achieved by ATLAS and CMS since the beginning of Run 1. The parallel role of theory and the collaboration among theorists and experimentalists was also discussed. Speakers from the experiments involved in the Higgs-discovery analyses provided personal perspectives on the events leading up to the 4 July 2012 announcement.

With his unique perspective, former CERN Director-General Chris Llewellyn-Smith described the early discussions and approval of the LHC project during a well-attended public symposium. He recalled his discussions with former UK prime minister Margaret Thatcher, the role of the ill-fated US Superconducting Super Collider and the “byzantine politics” that led to the LHC’s approval in 1994. Most importantly, he emphasised that the LHC was not inevitable: scientists had to fight to secure funding and bring it to reality. Former ATLAS spokesperson David Charlton reflected on the preparation of the experiments, the LHC startup in 2008 and subsequent magnet problems that delayed the physics runs until 2010, noting the excellent performance of the machine and detectors that enabled the discovery to be made much earlier than expected.

The workshop would not have been complete without a discussion on what happened after the discovery. Precision measurements of the Higgs-boson couplings, observation of new decay and production modes, as well as the search for Higgs-boson pair-production were described, always with a focus on the challenges that needed to be overcome. The workshop closed with a look to the future, both in terms of experimental prospects of the High-Luminosity LHC and theory.

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Peter Higgs winner of the 2013 Nobel Prize in Physics.

“It was an overwhelming time for us. It took time to understand what had happened. I especially remember the excitement among the young researchers.” 

Rolf Heuer former CERN Director-General. 

“It took 14 years to build the LHC. At one point we had 1000 dipoles, each costing a million Swiss francs, stored on the surface, throughout rain and snow.” 

Lyn Evans former LHC project director.

“The first two years of measuring Standard Model physics were essential to give us confidence in the readiness of the two experiments to search for new physics.” 

Peter Jenni founding ATLAS spokesperson.

“A key question for CMS was: can tracking be done in a congested environment with just a few points, albeit precise ones? It was a huge achievement requiring more than 200 m² of active silicon.” 

Michel Della Negra founding CMS spokesperson.

“I remember on 4 July 2012 a magnificent presentation of a historical discovery. I would also like to celebrate the life of Robert Brout, a great physicist and important man.” 

François Englert winner of the 2013 Nobel Prize in Physics. 

“The gist of the theory behind the Higgs boson would easily compete with the most far-fetched conspiracy theory, yet it seems nature chose it.” 

Eliezer Rabinovici president of the CERN Council.

“The structure of the vacuum is intimately connected to how the Higgs boson interacts with itself. To probe this phenomenon at the LHC we can study the production of Higgs-boson pairs.” 

André David CMS experimentalist (CERN).

“Collaboration between experiment and theory is even more necessary now to find any hints for BSM physics.” 

Reisaburo Tanaka ATLAS experimentalist (Université Paris-Saclay).

“Precision Higgs physics is a telescope to high-scale physics, so I’m looking forward to the next 10 years of discovery.” 

Sally Dawson theorist (BNL). 

“Theory accuracy will be even more important to make the best of the HL-LHC data, especially in the case in which no evidence of new physics will show up… This is also crucial for the Monte Carlo tools used in the analyses.”

Massimiliano Grazzini theorist (University of Zurich).

“After 10 years we’ve measured the five main production and five major decay mechanisms of the Higgs boson.” 

Kerstin Tackmann ATLAS experimentalist (DESY).

“What we know so far – Mass: known to 0.11%. Width: closing in on SM value of 3.2^+2.5_–1.7   MeV (plus evidence of off-shell Higgs production). Spin 0: spin 1 & 2 excluded at 99.9% CL. CP structure: in accordance with SM CP-even hypotheses.”

Marco Delmastro ATLAS experimentalist (CNRS/IN2P3 LAPP).

“We have learned much about the 125 GeV Higgs boson since its discovery. The LHC Run 3 starts tomorrow: ready for the next decade of Higgs-boson exploration!”

Adinda de Wit CMS experimentalist (University of Zurich).

“The Higgs boson is linked to profound structural problems in the Standard Model. It is therefore an extraordinary discovery tool that calls for a broad experimental programme at the LHC and beyond.” 

Fabiola Gianotti CERN Director-General.

“Elusive non-resonant pairs of Higgs bosons are the prime experimental signature of the Higgs-boson self-coupling. We are all eager to analyse Run 3 data to further probe HH events!”

Arnaud Ferrari ATLAS experimentalist (Uppsala University).

“New physics can affect differently the different fermion generations. We have to precisely measure the couplings if we want to understand the Higgs boson’s nature.”

Andrea Marini CMS experimentalist (CERN).

“From its potential invisible, forbidden, and exotic decays to the possible existence of scalar siblings, the Higgs boson plays a fundamental role in searches for physics beyond the Standard Model.”

Roberto Salerno CMS experimentalist (CNRS/IN2P3 – LLR & École polytechnique).

“An incredible collaborative effort has brought us this far. But there is much more to come, especially during Long Shutdown 3, with HL-LHC paving the way from Run 3 to ultimate performance. Interesting times ahead to say the least!”

Mike Lamont CERN director for accelerators and technology.

“The hard work and creativity in reconstruction and analysis techniques are already evident since the last round of projections. Imagine what we can do in the next 20 years!”

Elizabeth Brost ATLAS experimentalist (BNL).

“The Higgs is the first really new elementary particle we’ve seen. We need to study it to death!”  

Nima Arkani-Hamed theorist (IAS).

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Colliding particles at high energies is a tried and tested route to uncover the secrets of the universe. In a collider, charged particles are packed in bunches, accelerated and smashed into each other to create new forms of matter. Whether accelerating elementary electrons or composite hadrons, past and existing colliders all deal with matter constituents. Colliding force-carrying particles such as photons is more ambitious, but can be done, even at the Large Hadron Collider (LHC). 

The LHC, as its name implies, collides hadrons (protons or ions) into one another. In most cases of interest, projectile protons break up in the collision and a large number of energetic particles are produced. Occasionally, however, protons interact through a different mechanism, whereby they remain intact and exchange photons that fuse to create new particles (see “Photon fusion” figure). Photon–photon fusion has a unique signature: the particles originating from this kind of interaction are produced exclusively, i.e. they are the only ones in the final state along with the protons, which often do not disintegrate. Despite this clear imprint, when the LHC operates at nominal instantaneous luminosities, with a few dozen proton–proton interactions in a single bunch crossing, the exclusive fingerprint is contaminated by extra particles from different interactions. This makes the identification of photon–photon fusion challenging.

The sensitivity in many channels is expected to increase by a factor of four or five compared to that in Run 2

Protons that survive the collision, having lost a small fraction of their momentum, leave the interaction point still packed within the proton bunch, but gradually drift away as they travel further along the beamline. During LHC Run 2, the CMS collaboration installed a set of forward proton detectors, the Precision Proton Spectrometer (PPS), at a distance of about 200 m from the interaction point on both sides of the CMS apparatus. The PPS detectors can get as close to the beam as a few millimetres and detect protons that have lost between 2% and 15% of their initial kinetic energy (see “Precision Proton Spectrometer up close” panel). They are the CMS detectors located the farthest from the interaction point and the closest to the beam pipe, opening the door to a new physics domain, represented by central-exclusive-production processes in standard LHC running conditions.

Testing the Standard Model

Central exclusive production (CEP) processes at the LHC allow novel tests of the Standard Model (SM) and searches for new phenomena by potentially granting access to some of the rarest SM reactions so far unexplored. The identification of such exclusive processes relies on the correlation between the proton momentum loss measured by PPS and the kinematics of the central system, allowing the mass and rapidity of the central system in the interaction to be inferred very accurately (see “Tagging exclusive events” and “Exclusive identification” figures). Furthermore, the rules for exclusive photon–photon interactions only allow states with certain quantum numbers (in particular, spin and parity) to be produced. 

Precision Proton Spectrometer up close

PPS was born in 2014 as a joint project between the CMS and TOTEM collaborations (CERN Courier April 2017 p23), and in 2018 became a subsystem of CMS following an MoU between CERN, CMS and TOTEM. For the specialised PPS setup to work as designed, its detectors must be located within a few millimetres of the LHC proton beam. The Roman Pots technique – moveable steel “pockets” enclosing the detectors under moderate vacuum conditions with a thin wall facing the beam – is perfectly suited for this task. This technique has been successfully exploited by the TOTEM and ATLAS collaborations at the LHC and was used in the past by experiments at the ISR, the SPS, the Tevatron and HERA. The challenge for PPS is the requirement that the detectors operate continuously during standard LHC running conditions, as opposed to dedicated special runs with a very low interaction rate.

The PPS design for LHC Run 2 incorporated tracking and timing detectors on both sides of CMS. The tracking detector comprises two stations located 10 m apart, capable of reconstructing the position and angle of the incoming proton. Precise timing is needed to associate the production vertex of two protons to the primary interaction vertex reconstructed by the CMS tracker. The first tracking stations of the proton spectrometer were equipped with silicon-strip trackers from TOTEM – a precise and reliable system used since the start of the LHC. In parallel, a suitable detector technology for efficient operation during standard LHC runs was developed, and in 2017 half of the tracking stations (one per side) were replaced by new silicon pixel trackers designed to cope with the higher hit rate. The x, y coordinates provided by the pixels resolve multiple proton tracks in the same bunch crossing, while the “3D” technology used for sensor fabrication greatly enhances resistance against radiation damage. The transition from strips was completed in 2018, when the fully pixel-based tracker was employed.

In parallel, the timing system was set up. It is based on diamond pad sensors initially developed for a new TOTEM detector. The signal collection is segmented in relatively large pads, read out individually by custom, high-speed electronics. Each plane contributes to the time measurement of the proton hit with a resolution of about 100 ps. The design of the detector evolved during Run 2 with different geometries and set-ups, improving the performance in terms of efficiency and overall time resolution.

The most common and cleanest process in photon–photon collisions is the exclusive production of a pair of leptons. Theoretical calculations of such processes date back almost a century to the well-known Breit–Wheeler process. The first result obtained by PPS after commissioning in 2016 was the measurement of (semi-)exclusive production of e⁺e^– and μ⁺μ^– pairs using about 10 fb^–1 of CMS data: 20 candidate events were identified with a di-lepton mass greater than 110 GeV. This process is now used as a “standard candle” to calibrate PPS and validate its performance. The cross section of this process has been measured by the ATLAS collaboration with their forward proton spectrometer, AFP (CERN Courier September/October 2020 p15). 

An interesting process to study is the exclusive production of W-boson pairs. In the SM, electroweak gauge bosons are allowed to interact with each other through point-like triple and quartic couplings. Most extensions of the SM modify the strength of these couplings. At the LHC, electroweak self-couplings are probed via gauge-boson scattering, and specifically photon–photon scattering. A notable advantage of exclusive processes is the excellent mass resolution obtained from PPS, allowing the study of self-couplings at different scales with very high precision. 

During Run 2, PPS reconstructed intact protons that lost down to 2% of their kinetic energy, which for proton–proton collisions at 13 TeV translates to sensitivity for
central mass values above 260 GeV. In the production of electroweak boson pairs, WW or ZZ, the quartic self-coupling mainly contributes to the high invariant-mass tail of the di-boson system. The analysis searched for anomalously large values of the quartic gauge coupling and the results provide the first constraint on γγZZ in an exclusive channel and a competitive constraint on γγWW compared to other vector-boson-scattering searches.

Many SM processes proceeding via photon fusion have a relatively low cross section. For example, the predicted cross section for CEP of top quark–antiquark pairs is of the order of 0.1 fb. A search for this process was performed early this year using about 30 fb^–1 of CMS data recorded in 2017, with protons tagged by PPS. While the sensitivity of the analysis is not sufficient to test the SM prediction, it can probe possible enhancements due to additional contributions from new physics. Also, the analysis established tools with which to search for exclusive production processes in a multi-jet environment using machine-learning techniques. 

Uncharted domains 

The SM provides very accurate predictions for processes occurring at the LHC. Yet, it cannot explain the origin of several observations such as the existence of dark matter, the matter–antimatter asymmetry in the universe and neutrino masses. So far, the LHC experiments have been unable to provide answers to those questions, but the search is ongoing. Since physics with PPS mostly targets photon collisions, the only assumption is that the new physics is coupled to the electroweak sector, opening a plethora of opportunities for new searches. 

Photon–photon scattering has already been observed in heavy-ion collisions by the LHC experiments, for example by ATLAS (CERN Courier December 2016 p9). But new physics would be expected to enter at higher di-photon masses, which is where PPS comes into play. Recently, a search for di-photon exclusive events was performed using about 100 fb^–1 of CMS data at a di-photon mass greater than 350 GeV, where SM contributions are negligible. In the absence of an unexpected signal, a new best limit was set on anomalous four-photon coupling parameters. In addition, a limit on the coupling of axion-like particles to photon was set in the mass region 500–2000 GeV. These are the most restrictive limits to date.

A new, interesting possibility to look for unknown particles is represented by the “missing mass” technique. The exclusivity of CEP makes it possible, in two-particle final states, to infer the four-momentum of one particle if the other is measured. This is done by exploiting the fact that, if the protons are measured and the beam energy is known, the kinematics of the centrally produced final state can be determined: no direct measurements of the second particle are required, allowing us to “see the unseen”. This technique was demonstrated for the first time at the LHC this year, using around 40 and 2 fb^–1 of Run 2 data in a search for pp → pZXp and pp → pγXp, respectively, where X represents a neutral, integer-spin particle with an unspecified decay mode. In the absence of an observed signal, the analysis sets the first upper limits for the production of an unspecified particle in the mass range 600–1600 GeV.

Looking forward with PPS

For LHC Run 3, which began in earnest on 5 July, the PPS team has implemented several upgrades to maximise the physics output from the expected increase in integrated luminosity. The mechanics and readout electronics of the pixel tracker have been redesigned to allow remote shifting of the sensors in several small steps, which better distributes the radiation damage caused by the highly non-uniform irradiation. All timing stations are now equipped with “double diamond” sensors, and from 2023 an additional, second station will be added to each PPS arm. This will improve the resolution of the measured arrival time of protons, which is crucial for reconstructing the z coordinate of a possible common vertex, by at least a factor of two. Finally, a new software trigger has been developed that requires the presence of tagged protons in both PPS arms, thus allowing the use of lower energy thresholds for the selection of events with two particle jets in CMS.

The sensitivity in many channels is expected to increase by a factor of four or five compared to that in Run 2, despite only a doubling of the integrated luminosity. This significant increase is due to the upgrade of the detectors, especially of the timing stations, thus placing PPS in the spotlight of the Run 3 research programme. Timing detectors also play a crucial role in the planning for the high-luminosity LHC (HL-LHC) phase. The CMS collaboration has released an expression of interest to pursue studies of CEP at the HL-LHC with the ambitious plan of installing near-beam proton spectrometers at 196, 220, 234, and 420 m from the interaction point. This would extend the accessible mass range to the region between 50 GeV and 2.7 TeV. The main challenge here is to mitigate high “pileup” effects using the timing information, for which new detector technologies, including synergies with the future CMS timing detectors, are being considered.

PPS significantly extends the LHC physics programme, and is a tribute to the ingenuity of the CMS collaboration in the ongoing search for new physics.

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The cryogenic infrastructure of the Large Hadron Collider (LHC) at CERN is the most complex helium refrigeration system of all the world’s research facilities.

The operation of the LHC’s cryogenic system was initiated in 2008 after reception testing and a first cool down to 1.9 K. This webinar will cover information on the design, operational experiences and main challenges linked to the accelerator, along with the physics requirements.

During the first stage, the operation team had to learn about the responsivity and limitations of the system. They then had to manage stable operation by maintaining the necessary conditions for the superconducting magnets, RF cavities, electrical feed boxes, power links and detector devices, thus contributing to the physics programme and the discovery of the Higgs boson in 2012.

One of the most challenging parameters impacting the cryogenics was the beam-induced heat load that was taken up, beginning during the second operation period (Run 2) of the LHC in 2015 with increased beam parameters. A complicated optimisation of the configuration of the cryogenic system was successfully applied to cope with these requirements.

Run 3 (preparation for which started in 2020) required the handling of several hundred magnet training quenches towards the nominal beam energy for physics production.

Now, after several years of operational experience with steady state and transient handling, the cryogenic system is being optimised to provide the necessary refrigeration, whilst incorporating the all-important aspect of energy preservation.

In conclusion, there will be a brief discussion of the next four years of operation.

Krzysztof Brodzinski is a senior staff member in the cryogenics group at the technology department at CERN. He is a mechanical engineer with a specialisation in refrigeration equipment, and graduated from Cracow University of Technology in Poland. Krzysztof  joined the LHC cryogenic design team in 2001, has been a member of the cryogenic operation team since 2009 and in 2019 was mandated as a section leader of the cryogenic operation team for the LHC, ATLAS and CMS. He is also involved in the engineering of the cryogenic system for the HiLumi LHC RF deflecting cavities project, as well as participating in the ongoing FCC cryogenics study.

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It was March 1977 when the hypothetical Higgs boson first made its way onto the pages of this magazine. Reporting on a talk by Steven Weinberg at the Chicago Meeting of the American Physical Society, the editors noted the dramatic success of gauge theories in explaining recent discoveries at the time — beginning with the observation of the neutral current at CERN in 1973 and the “new physics” following the J/ψ discovery at Brookhaven and Stanford the following year, observing: “The theories also postulate a set of scalar particles in a similar mass range… If Higgs bosons exist, they will affect particle behaviour at all energies. However, their postulated interactions are even weaker than the normal weak interactions. The effects would only be observable on a very small scale and would usually be drowned out by the stronger interactions.”

The topic clearly drew the attention of readers, as just a few issues later, in September 1977, the editors delved deeper into the origins of the Higgs boson and its role in spontaneous symmetry breaking, offering Abdus Salam’s “personal picture” to communicate this abstruse concept: “Imagine a banquet where guests sit at round tables. A bird’s eye view of the scene presents total symmetry, with serviettes alternating with people around each table. A person could equally well take a serviette from his right or from his left. The symmetry is spontaneously broken when one guest decides to pick up from his left and everyone else follows suit.”

Within a year, CERN Courier was on the trail of how the Higgs boson might show itself experimentally. Reporting on a “Workshop on Producing High Luminosity Proton–Antiproton Storage Rings” held at Berkeley, the April 1978 issue stated: “As well as the intermediate boson, the proton–antiproton colliders could give the first signs of the Higgs parti­cles or of other unexpected states. While the discovery of weak neutral currents and charm provided impres­sive evidence for the gauge-theory pic­ture that unifies electromagnetic and weak interactions, one prediction of this picture is the existence of spinless Higgs bosons. If these are not found at higher energies, some re-thinking might be required.” In the December 1978 issue, with apologies to Neil Armstrong, the Courier ran a piece titled “A giant LEP for mankind”. The hope was that with LEP, physicists had the tool to explore in depth the details of the symmetry breaking mechanism at the heart of weak interaction dynamics.

The award of the 1979 Nobel Prize in Physics to Weinberg, Glashow and Salam for the electroweak theory received full coverage in December that year, with the Courier expressing confidence in the Higgs: “Another vital ingredient of the theory which remains to be tested are the Higgs particles of the spon­taneous symmetry breaking me­chanism. Here the theory is still in a volatile state and no firm predictions are possible. But this mechanism is crucial to the theory, and something has to turn up.”

A Higgs for the masses

To many people, wrote US theorist Sam Treiman in November 1981, the Higgs particle looks somewhat artifi­cial — “a kind of provisional stand-in for deeper effects at a more funda­mental level”. Four years later, “with several experiments embark­ing on fresh Higgs searches”, Ri­chard Dalitz and Louis Lyons organised a neatly titled workshop “Higgs for the masses” to review the theoretical and experimental status. Another oddity of the Higgs, wrote Lyons, is that unless it is very light (less than 10^–17 eV), the Higgs should make the uni­verse curved, “contributing more to the cosmological constant than the known limit permits”. Lower limits (from spontaneous sym­metry breaking) and higher limits (from the unitarity requirement) open up a wide range of masses for the Higgs to man­oeuvre — between 7 and 1000 GeV, he noted. “From time to time, new ‘bumps’ and effects are tentatively put for­ward as candidate Higgs, but so far none are convincing.”

LEP’s electroweak adventure reached a dramatic climax in the summer of 2000, with hints that a light Higgs boson was showing itself. In October, the machine was granted a stay of Higgs execution. Alas, the signal faded, and the final curtain fell on LEP in November — a “LEPilogue” heralding the beginning of a new era: the LHC.

Discussions about a high-energy hadron collider were ongoing long before: ICFA’s Future Perspectives meeting at Brookhaven in October 1987 noted two major hadron collider pro­jects on the market: “the US Superconducting Supercollider, with collision energies of 40 TeV in an 84 kilometre ring, and the CERN Large Hadron Collider, with up to 17 TeV colli­sion energies”. In December 1994, shortly after CERN turned 40, Council provided the lab with “The ultimate birthday present“: the unanimous approval of the LHC. A quarter of a century later, the LHC started up and brought particle physics to the world.

Together with LEP data, Fermilab’s CDF and DØ experiments and the LHC 2011 measurement campaign narrowed down the possible mass range for the Higgs boson to be between 115 and 127 GeV. First tantalising hints of the Higgs boson were presented on 13 December 2011. The quest remained open for another half a year, until Director-General Rolf Heuer, following the famous talks by ATLAS and CMS spokespersons Fabiola Gianotti and Joe Incandela, concluded: “As a layman I would say: I think we have it” on 4 July 2012. It was a day to remember: a breakthrough discovery rooted in decades of work by thousands of individuals that rocked the CERN auditorium and reverberated around the world. A new chapter in particle physics had begun…

To mark the 10^th anniversary of this momentous event, from Monday 4 July the Courier will be exploring the theoretical and experimental effort behind the Higgs-boson discovery, the immense progress made by ATLAS and CMS in our understanding of this enigmatic particle, and the deep connections between the Higgs boson and some of the most profound open questions in fundamental physics.

Wherever the Higgs boson leads, CERN Courier  will be there to report!

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Ten years ago, a few small bumps in ATLAS and CMS data confirmed a 48 year-old theoretical prediction, and particle physics hasn’t been the same since. Behind those sigmas was the hard work, dedication, competence and team spirit of thousands of experimentalists and accelerator physicists worldwide. Naturally it was a triumph for theory, too. Peter Higgs, François Englert, Carl Hagen and Gerald Guralnik received a standing ovation in the CERN auditorium on 4 July 2012, although Higgs insisted it was a day to celebrate experiment, not theory. The Nobel prize for Englert and Higgs came a year later. Straying from tradition for elementary-particle discoveries, the citation explicitly acknowledged the experimental effort of ATLAS and CMS, the LHC and CERN. 

The implications of the Higgs-boson discovery are still being understood. Ten years of precision measurements have shown the particle to be consistent with the minimal version required by the Standard Model. Combined with the no-show of non-Standard Model particles that were expected to accompany the Higgs, theorists are left scratching their heads. As we celebrate the collective effort of high-energy physicists in discovering the Higgs boson and determining its properties, another intriguing journey has opened up.

Marvelously mysterious 

As “a fragment of vacuum” with the barest of quantum numbers, the Higgs boson is potentially connected to many open questions in fundamental physics. The field from which it hails governs the nature of the electroweak phase transition in the early universe, which might be connected with the observed matter–antimatter asymmetry; as the only known elementary scalar particle, it could serve as a portal to other, hidden sectors relevant to dark matter; its couplings to matter particles — representing a new interaction in nature — may hold clues to the puzzling hierarchy of fermion masses; and its interactions with itself have implications for the ultimate stability of the universe. 

Nobody knows what the Higgs boson has in store

With the LHC and its high-luminosity upgrade, physicists have 20 years of Higgs exploration to look forward to. But to fully understand the shape of the Brout–Englert–Higgs potential, the couplings of the Higgs boson to Standard Model particles and its possible connections to new physics, a successor collider will be needed. It is fascinating to picture future generations of particle physicists working as one with astroparticle physicists, cosmologists, quantum technologists and others to fill out the details of this potential new vista, with colliders driving progress alongside astrophysical, cosmological and gravitational-wave observatories. Future colliders aren’t just about generating knowledge, argues Anna Panagopoulou of the European Commission, but are “moonshots” delivering a competitive edge in technology, innovation, education and training — opening adventures that inspire young people to enter science in the first place.

Nobody knows what the Higgs boson has in store. Perhaps further studies will confirm the scenario of a Standard-Model Higgs and nothing else. The sheer number and profundity of known unknowns in the universe would suggest otherwise, think theorists. The good news is that, in the Higgs boson, physicists have clear measurement targets – and in principle the necessary theoretical and experimental machinery – to explore such mysteries, building upon the events of 4 July 2012 to reach the next level of understanding in fundamental physics. 

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Future colliders are vital to push the precision Higgs programme to the next level

The scalar sector of the SM may therefore be seen as a messenger of a more fundamental theory that replaces the SM at energies beyond the EW scale and turns apparent arbitrariness into logical consequences. After all, the mechanism of EW symmetry breaking as realised in the SM via the Brout–Englert–Higgs (BEH) field is just the simplest possible way to generate massive EW gauge bosons and fermions while preserving gauge symmetry. The scalar potential could be more complicated, for example involving multiple scalar fields, as is common in many beyond-the-SM (BSM) theories. This would result in a richer pattern of stable and metastable minima and influence the nature of the EW phase transition. A first-order phase transition, together with extra sources of CP violation beyond what is implied by the SM, could explain the origin of the matter–antimatter asymmetry of the universe via EW baryogenesis (see Electroweak baryogenesis). Understanding the origin of the EW scale is thus key to connecting very different realms of particle physics and cosmology, and the question we face while we look into the future of collider physics. 

Game changer

The discovery of the Higgs boson during Run 1 of the LHC has been a game changer in the exploration of new physics beyond the EW scale. The measurement of the Higgs-boson mass has added the last missing input parameter to precision global fits of the SM, which now provide a very powerful tool to constrain BSM scenarios. Thanks to an unprecedented level of precision reached in both theory and experiment, the measurement of Higgs-boson couplings to EW gauge bosons (W, Z) and to the first two generations of quarks and leptons (t, b, τ, µ) from Run 2 data has already constrained their deviations from SM expectations to within 5–20%, with the best accuracy reached for the couplings to the gauge bosons. Based on these results, the High-Luminosity LHC (HL-LHC) is projected to constrain the effects of new physics on Higgs-boson couplings to EW gauge bosons to 1–2%, and to heavy quarks and fermions to 3–5%. If no anomalies are found, this level of accuracy will push the lower bound on the scale of new physics into the TeV ballpark. Vice versa, the detection of possible anomalies may point to the presence of new physics at the TeV scale, possibly just around the corner.

On the other hand, testing the SM scalar potential will still be challenging even during the HL-LHC era. The shape of the BEH potential can be tested by measuring the Higgs-boson self-interactions corresponding to its cubic and quartic terms. In the SM, these interactions are strictly proportional to the Higgs-boson mass via the vacuum expectation value of the BEH field. Deviations from the SM are searched for via Higgs pair production and radiative corrections to single-Higgs measurements. Although the LHC and HL-LHC promise to provide evidence for di-Higgs production, the extraction of the Higgs self-coupling from such measurements will be statistically limited.

Future colliders are vital to push the precision Higgs programme to the next level. While the type and concept of the next collider is yet to be decided, all proposed facilities would deliver a huge number of Higgs bosons over their lifetime, operating at different and well targeted centre-of-mass energies (see “At a glance” figure). They can complement one another and, staggered over a period of the next few decades, provide the missing elements of the EW puzzle.

Among future lepton colliders under study, circular e⁺e^– colliders (CEPC, FCC-ee) are expected to operate at lower energies between 90–350 GeV with very high luminosities, while linear e⁺e^– colliders (ILC, C³, CLIC) offer both low- and high-energy phases generally with slightly lower luminosities. Combined with data from the HL-LHC, these “Higgs factories” would enable the SM, including most Higgs couplings, to be stress-tested below the per-cent level and in cases at or below the per-mille level. In particular, FCC-ee operating at the s-channel Higgs resonance (125 GeV) has the capability to provide bounds on couplings as small as the electron Yukawa coupling, while linear e⁺e^– colliders operating at 550–600 GeV and above could substantially improve on the top-quark Yukawa coupling with respect to the HL-LHC. A possible muon collider, operated either as a Higgs factory at 125 GeV or as a high-energy discovery machine at 3–10 TeV, is estimated to reach similar precisions on Higgs couplings to other particles as e⁺e^– machines. 

Finally, high-energy lepton colliders (ILC 1000, CLIC 3000 and a 3–30 TeV muon collider) and very high-energy hadron colliders (FCC-hh at 100 TeV) would reach enough statistics and energy to measure the Higgs self-coupling and investigate the nature of the BEH potential, either via di-Higgs or single-Higgs production (see “Self-coupling” figure). With an aggressive Higgs physics programme they may also reach enough sensitivity to probe the cubic and quartic terms in the BEH potential separately. 

Almost half a century after it was predicted, the LHC delivered the Higgs boson in spectacular style on 4 July 2012. Over the next 15–20 years, the machine and its luminosity upgrade will continue to enable ATLAS and CMS to make great strides in understanding the Higgs boson’s properties. But to fully exploit the discovery of the Higgs boson and explore its mysterious relation to new physics beyond the EW scale, we will need a successor collider.

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The Higgs particle is the only portal connecting normal matter to such phantom fields

The other contributions to T_μν, all of which involve the Higgs particle, do not yet reach that standard. We can aspire to do better! They are of three kinds. First, there are the many Yukawa-like terms from which quark and lepton masses and mixings arise. Then there is the Higgs self-coupling and finally a term representing its mass. These contributions to T_μν contain almost two dozen dimensionless coupling parameters that present-day theory does not enable us to calculate or even much constrain. It is therefore important to investigate experimentally, through quantitative studies of Higgs-particle properties and interactions, whether this ramshackle structure describes nature accurately. 

Higgs potential

The Higgs boson is special among the elementary particles. As the quantum of a condensate that fills all space, it is metaphorically “a fragment of vacuum”. Speaking more precisely, the Higgs particle has no spin, no electric or colour charge and, at the level of strong and electromagnetic interactions, normal charge conjugation and parity. Thus, it can be emitted singly and without angular momentum barriers, and it can decay directly into channels free of colour and electromagnetically charged particles, which might otherwise be difficult to access. For these and other, more technical, reasons, the Higgs particle has the potential to reveal new physical phenomena of several kinds. 

A unique aspect of the Higgs mass term is especially promising for revealing possible shortcomings in the SM. In quantum field theory, an important property of an interaction is the “mass dimension” of the operator that implements it – a number that in an important sense indicates its complexity. Scalar and gauge fields have mass dimension 1 as do space–time derivatives, whereas fermion fields have mass dimension 3/2. More complicated operators are built up by multiplying these, and the mass dimension of a product is the sum of the mass dimensions of its factors. Interactions associated with operators whose mass dimension is greater than 4 are problematic because they lead to violent quantum fluctuations and mathematical divergences. Whereas all the other terms in the SM Lagrangian arise from operators of mass dimension 4, the Higgs mass term has mass dimension 2. Thus it is uniquely open to augmentation by couplings to hypothetical new SU(3) × SU(2) × U(1) singlet scalar fields, because the mass dimension of the augmented interaction can be 3 or 4 – i.e. still “safe”. The Higgs particle is the only portal connecting normal matter to such phantom fields.

Why is this an interesting observation? There are three main reasons: two broadly theoretical, one pragmatic. First of all, the particles that are generally considered part of the SM carry a variety of charge assignments under the gauge groups SU(3) × SU(2) × U(1) that govern the strong and electroweak interactions. For example, the left-handed up quark is charged under all three groups, while the right-handed electron carries only U(1) hypercharge. Thus it is not only logically possible, but reasonably plausible, that there could be particles that are neutral under all three groups. Such phantom particles might easily escape detection, since they do not participate in the strong or electroweak interactions. Indeed, there are several examples of well-motivated candidate particles of that kind. Axions are one. Since they are automatically “dark” in the appropriate sense, phantom particles could contribute to the astronomical dark matter, and might even dominate it, as model-builders have not failed to notice. Also, many models of unification bring in scalar fields belonging to representations of a unifying gauge group that contains SU(3) × SU(2) × U(1) singlets, as do models with supersymmetry. Only phantom scalars are directly accessible through the Higgs portal, but phantoms of higher spin, including right-handed neutrinos, could cascade from real or virtual scalars.

Mysterious values

Second, the empirical value of the Higgs mass term is somewhat mysterious and even problematic, given that quantum corrections should push it to a value many orders of magnitude higher. This is the notorious “hierarchy problem” (see Naturalness after the Higgs). Given this situation, it seems appropriate to explore the possibility that part (or all) of the effective mass-term of the SM Higgs particle arises from more fundamental couplings upon condensation of SU(3) × SU(2) × U(1) singlet scalar fields, i.e. the emergence of a non-zero space-filling field, as occurs in the Brout–Englert–Higgs mechanism.

The portal idea leads to concrete proposals for directions of experimental exploration

Third, the portal idea leads to concrete proposals for directions of experimental exploration. These are of two basic kinds: one involves the observed strength of conventional Higgs couplings, the other the kinematics of Higgs production and decay. Couplings of the Higgs field to singlets that condense will lead to mixing, altering numerical relationships among Higgs-particle couplings and masses of gauge bosons, and of fermions from their minimal SM values. Also, the Higgs-field couplings to gauge bosons and fermions will be divided among two or more mass eigenstates. Since existing data indicates that deviations from the minimal model are small, the coupling of normal matter to the “mostly but not entirely” singlet pieces could be quite small, perhaps leading to very long lifetimes (as well as small production rates) for those particles. Whether or not the phantom particles contribute significantly to cosmological dark matter, they will appear as missing energy or momentum accompanying Higgs particle decay or, through Bremsstrahlung-like processes, when they are produced. 

We introduced the term “Higgs portal” to describe this circle of ideas in 2006, triggering a flurry of theoretical discussion. Now that the portal is open for business, and with larger data samples in store at the LHC, we can think more concretely about exploring it experimentally.

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At around 10:30 a.m. on 4 July 2012, two remarkable feats of theoretical and experimental physics reached an apex in the CERN auditorium. One was the work of a few individuals using the most rudimentary of materials, the other a global endeavour involving thousands of people and the world’s most powerful collider. Forty-eight years after it was predicted, the CMS and ATLAS collaborations presented conclusive evidence for the existence of a new elementary particle, the Higgs boson, the cornerstone of the electroweak Standard Model. 

“It took us several years to recover,” says CMS experimentalist Chiara Mariotti, who was co-convener of the collaboration’s Higgs group at the time. “For me there was a strong sense of ‘Higgs blues’ afterwards! On the other hand, the excitement was also productive. Immediately after the discovery we managed to invent a new method to measure the Higgs width, with a precision more than 200 times better than what we were thinking – a real breakthrough.”

Theoretically, the path to the Higgs boson had been paved by the early 1970s, building on foundations laid by the pioneers of quantum field theory and superconductivity. When Robert Brout and François Englert, and independently Peter Higgs, published their similarly titled papers on broken symmetry and the mass of gauge bosons in 1964, nobody took much notice. One of Higgs’s manuscripts was even rejected by an editor based at CERN. The profound consequences of the Brout–Englert–Higgs (BEH) mechanism – that the universe is pervaded by a scalar field responsible for breaking electroweak symmetry and giving elementary particles their mass (see “The Higgs, the universe and everything” panel) – only caught wider attention after further Nobel-calibre feats by Steven Weinberg, who incorporated the BEH mechanism into electroweak theory developed also by Abdus Salam and Sheldon Glashow, and by Gerard ’t Hooft and Martinus Veltman, who proved that the unified theory was mathematically consistent and capable of making testable predictions (see A triumph for theory). 

Over to CERN 

The first bridge linking the BEH mechanism to the real world was sketched out in CERN’s theory corridors in the form of a 50-page-long phenomenological profile of the Higgs boson by John Ellis, Mary Gaillard and Dimitri Nanopoulos published in 1976. The discovery of neutral currents in 1973 by Gargamelle at CERN, and of the charm quark at Brookhaven and SLAC in 1974, had confirmed that the Standard Model was on the right track. Despite their conviction that something like the Higgs boson had to exist, however, Ellis et al. ended their paper on a cautionary, somewhat tongue-in-cheek note: “We apologise to experimentalists for having no idea what is the mass of the Higgs boson… and for not being sure of its couplings to other particles, except that they are probably all very small. For these reasons we do not want to encourage big experimental searches for the Higgs boson, but we do feel that people performing experiments vulnerable to the Higgs boson should know how it may turn up”. 

As it turned out, discovering and measuring the electroweak bosons would drive three major projects at CERN spanning three decades: the SPS proton–antiproton collider, LEP and the LHC. Following Carlo Rubbia and Simon van der Meer’s ingenious modification of the SPS to collide protons and antiprotons, greatly increasing the available energy, the UA1 and UA2 collaborations confirmed the existence of the W boson on 25 January 1983. The discovery of the slightly heavier Z boson came a few months later. The discoveries made the case for the Higgs boson stronger, since all three bosons hail from the same scalar field (see panel). 

The Higgs, the universe and everything

The Higgs boson is the excitation of a featureless condensate that fills all space – a complex scalar field with a shape resembling a Mexican hat. The universe is pictured as being born in a symmetric state at the top of the hat: the electromagnetic and weak forces were one, and particles moved at the speed of light. A fraction of a nanosecond later, the universe transitioned to a less symmetric but more stable configuration in the rim of the hat, giving the universe a vacuum expectation value of 246 GeV. 

During this electroweak symmetry- breaking process, three of the BEH field’s components were absorbed to generate polarisation states, and thus masses, for the W and Z bosons; the other component, corresponding to a degree of freedom “up and down” the rim of the hat, is the Higgs boson (see “Lifting the lid” image). The masses of the fermions are generated via Yukawa couplings to the BEH field, implying that mass is not an intrinsic property of elementary particles.

The roots of the BEH mechanism lie in the phenomenon of spontaneous symmetry breaking, which is inherent in superconductivity and superfluidity. In 1960, Yoichiro Nambu and then Jeffrey Goldstone introduced spontaneous symmetry breaking into particle physics, paving the way for taming the weak interaction using gauge theory, like electromagnetism before it. Four years later, Robert Brout and Franҫois Englert and, independently, Peter Higgs, showed that a mathematical obstacle called the Goldstone theorem, which implied the existence of unobserved massless particles, is a blessing rather than a curse for gauge theories: the degrees of freedom responsible for the troublesome massless states generate masses for the heavy gauge bosons that mediate the short-range weak interaction (see A triumph for theory).

LEP, along with the higher energy Tevatron collider at Fermilab, offered Higgs hunters their first serious chance of a sighting. Dedicated analysis groups formed in the  experiments. For a decade they saw nothing. Then, on 14 June 2000, LEP’s final year of scheduled running, ALEPH reported a Higgs candidate at around 114–115 GeV, followed soon by a second and third event. LEP was granted a one-month extension. On 16 October, L3 announced a candidate. By 3 November ALEPH had notched up a 2.9σ excess. A request to extend LEP by one year was made, but there was deadlock at CERN. Five days later, Director-General Luciano Maiani announced that LEP had closed for the last time, so as not to delay the LHC. In addition to determining the properties of the W and Z bosons in detail and confirming the existence of electroweak radiative corrections, LEP had planted a flag in energy below which the Higgs would not be found.

Muscling a discovery 

In 1977, CERN Director-General John Adams had the foresight to make the LEP tunnel large enough to accommodate a TeV hadron collider capable of probing the scale of electroweak symmetry breaking. Spurred on by the W and Z discoveries, finding or ruling out the Higgs boson became the central goal of the LHC, greatly influencing the designs of the ATLAS and CMS detectors during the 1990s. Tens of millions of people worldwide watched as the first proton beams were threaded through the machine on 10 September 2008. While the LHC had other goals, the quest for the Higgs boson and the origin of mass resonated with non-experts and brought particle physics to the world. 

It was a bumpy start (see The bumpy ride to the bump), but high-energy LHC data began to flood in on 10 March 2010. By the time of the European Physical Society high-energy physics conference in Grenoble in July 2011, ATLAS and CMS were ready to offer a peek of their results. Practically, the search for the Higgs came down to a process of excluding mass ranges in which no signal had been seen. ATLAS and CMS had shrunk the allowed range and found a number of events hinting at a Higgs boson with a mass of about 142 GeV. “We both saw a bump at the same place, and we had champagne after the talks,” recalls Kyle Cranmer, co-coordinator of the ATLAS Higgs combination group at the time. “We weren’t confident then, but we were optimistic.” Fermilab’s Tevatron collider was also sensitive to a Higgs in the upper mass range and its CDF and D0 experiments pioneered many of the analysis methods that were used in ATLAS and CMS. Just four years earlier, they had hinted at a possible signal at 160 GeV, only for it to disappear with further data. Was the US machine about to make a last-gasp discovery and scoop the LHC? 

The media were hot on the sigma trail. On 13 December 2011, the LHC experiments updated their findings: ATLAS constrained the Higgs to lie in the range 116-130 GeV, and CMS to lie in the range 115-127 GeV. For some, a light Higgs boson was in the bag. Others were hesitant. “There was a three-sigma excess when combining all the channels, but there were also less significant excesses in other mass regions,” recalls Mariotti. “I maybe also wanted not to believe it, in order not to be biased when analysing the data in 2012. And maybe because somehow if the Higgs was not there, it would have been really thrilling, much more challenging for us all.”

The following year, with the LHC running at a slightly higher energy, the collaborations knew that they would soon be able to say something definitive about the low-mass excess of events. From that moment, CMS decided not to look at the data and instead to redesign its analyses on simulated events “blinded”. On the evening of 14 June, all the analysis groups met separately to “open the box”. The next day, they shared their results with the collaboration. The two-photon and four-lepton channels had a beautiful peak at the same place. “It was like a very strong punch in the stomach,” says Mariotti. “From that moment it was difficult to sleep, and it was hard not to smile!”

The quest for the Higgs boson and the origin of mass resonated with non-experts and brought particle physics to the world

Members of both collaborations were under strict internal embargoes concerning the details. ATLAS unblinded its di-photon results late on 31 May, revealing a roughly 2σ excess. By 19 June it had grown to 3.3σ. The four-lepton group saw a similar excess. “My student Sven Kreiss was the first person in ATLAS to combine the channels and see the curve cross the 5σ threshold,” says Cranmer. “That was on 24 June, and it started to sink in that we had really found it. But it was still not clear what we would claim or how we would phrase things.” Amazingly, he says, he was not aware of the CMS results. “I was also not going out of my way to find out. I was relishing the moment, the excitement, and the last days of uncertainty. I also had more important things to do in preparation for the talk.” 

With the rumour mill in overdrive, a seminar at CERN was called for 4 July, also the first day of the ICHEP conference in Melbourne. Peter Higgs and François Englert, and Carl Hagan and Gerald Guralnik (who, with Tom Kibble, also arrived at the mass-generating mechanism), were to be there. The collaborations were focused only on their presentations. It had to be a masterpiece, says Mariotti. The day before, the CMS and ATLAS Higgs conveners met for coffee. They revealed nothing. “It was really hard not to know. We knew we had it, but somehow if ATLAS did not have it or had it but at a different mass, it all would have been a big disillusion.”

Many at CERN decided to spend the night of 3 July in front of the auditorium so as not to miss the historic moment. CMS spokesperson Joe Incandela was first to guide the audience through the checks and balances behind the final plots. Fabiola Gianotti followed for ATLAS. When it was clear that both had seen a 5σ excess of events at around 125 GeV, the room erupted. Was is it really the Higgs? All that was certain was that the particle was a boson, with a mass where the Standard Model expected it. Seizing the moment, and the microphone, Director-General Rolf Heuer announced: “As a layman, I would now say ‘I think we have it’, do you agree?” It was a spontaneous decision, he says. “For a short period between the unblindings and the seminar, I was one of the few people in the world, just with research director Sergio Bertolucci, in fact, who was aware of both results. We would not have announced a discovery had one experiment not come close to that threshold.”  

The summer of 2012 produced innumerable fantastic memories, says Marumi Kado, ATLAS Higgs-group co-convener at the time and now a deputy spokesperson. “The working spirit in the group was exceptional. Each unblinding, each combination of the channels was an incredible event. Of course, the 4 July seminar was among the greatest.” In CMS, says Mariotti, there was a “party-mood” for months. “Every person thought, correctly, that they had played a role in the discovery, which is important, otherwise very large experiments cannot be done.” 

The path from here 

Ten years later, ATLAS and CMS measurements have shown the Higgs boson to be consistent with the minimal version required by the Standard Model. Its couplings to the gauge bosons and the heaviest three fermions (top, bottom and tau) have been confirmed, evidence that it couples to a second-generation fermion (the muon) obtained, and first studies of Higgs–charm and Higgs–Higgs couplings reported (see The Higgs boson under the microscope). However, data from Run 3, the High-Luminosity LHC and a possible Higgs-factory to follow the LHC, are needed to fully test the Standard-Model BEH mechanism (see The Higgs after LHC). 

Every person thought, correctly, that they had played a role in the discovery, which is important, otherwise very large experiments cannot be done

Events on 4 July 2012 brought one scientific adventure to a close, but opened another, fascinating chapter in particle physics with fewer theoretical signposts. What is clear is that precision measurements of the Higgs boson open a new window to explore several pressing mysteries. The field from which the Higgs boson hails governs a critical phase transition that might be linked to the cosmic matter–antimatter asymmetry (see Electroweak baryogenesis); as an elementary scalar, it offers a unique “portal” to dark or hidden sectors which might include dark matter (see Through the Higgs portal); as the arbiter of mass, it could hold clues to the puzzling hierarchy of fermion masses (see The origin of particle masses); and its interactions govern the ultimate stability of the universe (see The Higgs and the fate of the universe). The very existence of a light Higgs boson in the absence of new particles to stabilise its mass is paradoxical (see Naturalness after the Higgs). Like the discovery of the accelerating universe, Nima Arkani-Hamed told the Courier in 2019, it is profoundly “new” physics: “Both discoveries are easily accommodated in our equations, but theoretical attempts to compute the vacuum energy and the scale of the Higgs mass pose gigantic, and perhaps interrelated, theoretical challenges. While we continue to scratch our heads as theorists, the most important path forward for experimentalists is completely clear: measure the hell out of these crazy phenomena!”

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Often in physics, experimentalists observe phenomena that theorists had not been able to predict. When the muon was discovered, theoreticians were confused; a particle had been predicted, but not this one. Isidor Rabi came with his famous outcry: “who ordered that?” The J/ψ is another special case. A particle was discovered with properties so different from the particles that were expected, that the first guesses as to what it was were largely mistaken. Soon it became evident that it was a predicted particle after all, but it so happened that its features were more exotic than was foreseen. This was an experimental discovery requiring new twists in the theory, which we now understand very well. The Higgs particle also has a long and interesting history, but from my perspective, it was to become a triumph for theory. 

From the 1940s, long before any indications were seen in experiments, there were fundamental problems in all theories of the weak interaction. Then we learned from very detailed and beautiful measurements that the weak force seemed to have a vector-minus axial-vector (V-A) structure. This implied that, just as in Yukawa’s theory for the strong nuclear force, the weak force can also be seen as resulting from an exchange of particles. But here, these particles had to be the energy quanta of vector and axial-vector fields, so they must have spin one, with positive and negative parities mixed up. They also must be very heavy. This implied that, certainly in the 1960s, experiments would not be able to detect these intermediate particles directly. But in theory, we should be able to calculate accurately the effects of the weak interaction in terms of just a few parameters, as could be done with the electromagnetic force. 

Electromagnetism was known to be renormalisable – that is, by carefully redefining and rearranging the mass and interaction parameters, all observable effects would become calculable and predictable, avoiding meaningless infinities. But now we had a difficulty: the weak exchange particles differed from the electromagnetic ones (the photons) because they had mass. The mass was standing in the way when you tried to do what was well understood in electromagnetism. How exactly a correct formalism should be set up was not known, and the relationship between renormalisability and gauge invariance was not understood at all. Indeed, today we can say that the first hints were already there by 1954, when C N Yang and Robert Mills wrote a beautiful paper in which they generalised the principle of local gauge invariance to include gauge transformations that affect the nature of the particles involved. In its most basic form, their theory described photons with electric charge.

Thesis topic

In 1969 I began my graduate studies under the guidance of Martinus J G Veltman. He explained to me the problem he was working on: if photons were to have mass, then renormalisation would not work the same way. Specifically, the theory would fail to obey unitarity, a quantum mechanical rule that guarantees probabilities are conserved. I was given various options for my thesis topic, but they were not as fundamental as the issues he was investigating. “I want to work with you on the problem you are looking at now,” I said. Veltman replied that he had been working on his problem for almost a decade; I would need lots of time to learn about his results. “First, read this,” he said, and he gave me the Yang–Mills paper. “Why?” I asked. He said, “I don’t know, but it looks important.”

That, I could agree  with. This was a splendid idea. Why can’t you renormalise this? I had convinced myself that it should be possible, in principle. The Yang–Mills theo­­ry was a relativistic quantised field theory. But Veltman explained that, in such a theory, you must first learn what the Feynman rules are. These are the prescriptions that you have to follow to get the amplitudes generated by the theory. You can read off whether the amplitudes are unitary, obey dispersion relations, and check that everything works out as expected.

Many people thought that renormalisation – even quantum field theory – was suspect. They had difficulties following Veltman’s manipulations with Feynman diagrams, which required integrations that do not converge. To many investigators, he seemed to be sweeping the difficulties with the infinities under the rug. Nature must be more clever than this! Yang–Mills seemed to be a divine theory with little to do with reality, so physicists were trying all sorts of totally different approaches, such as S-matrix theory and Regge trajectories. Veltman decided to ignore all that.

Solid-state inspiration

Earlier in the decade, some investigators had been inspired by results from solid-state physics. Inside solids, vibrating atoms and electrons were described by nonrelativistic quantum field theories, and those were conceptually easier to understand. Philip Anderson had learned to understand the phenomenon of superconductivity as a process of spontaneous symmetry breaking; photons would obtain a mass, and this would lead to a remarkable rearrangement of the electrons as charge carriers that would no longer generate any resistance to electric currents. Several authors realised that this procedure might apply to the weak force. In the summer of 1964, Peter Higgs submitted a manuscript to Physical Review Letters, where he noted that the mechanism of making photons massive should also apply to relativistic particle systems. But there was a problem. Jeffrey Goldstone had sound mathematical arguments to expect the emergence of massless scalar particles as soon as a continuous symmetry breaks down spontaneously. Higgs put forward that this theorem should not apply to spontaneously broken local symmetries, but critics were unconvinced.

The journal sent Higgs’s manuscript out to be peer reviewed. The reviewer did not see what the paper would add to our understanding. “If this idea has anything to do with the real world, would there be any possibility to check it experimentally?” The correct question would have been what the paper would imply for the renormalisation procedure, but this question was in nobody’s mind. Anyway, Higgs gave a clear and accurate answer: “Yes, there is a consequence: this theory not only explains where the photon mass comes from, but it also predicts a new particle, a scalar particle (a particle with spin zero), which unlike all other particles, forms an incomplete representation of the local gauge symmetry.” In the meantime, other papers appeared about the photon mass-generation process, not only by François Englert and Robert Brout in Brussels, but also by Tom Kibble, Gerald Guralnik and Carl Hagen in London. And Sheldon Glashow, Abdus Salam and Steven Weinberg were formulating their first ideas (all independently) about using local gauge invariance to create models for the weak interaction. 

I started to study everything from the ground up

At the time spontaneous symmetry breaking was being incorporated into quantum field theory, the significance of renormalisation and the predicted scalar particles were hardly mentioned. Certainly, researchers were not able to predict the mass of such particles. Personally, although I had heard about these ideas, I also wasn’t sure I understood what they were saying. I had my own ways of learning how to understand things, so I started to study everything from the ground up. 

If you work with quantum mechanics, and you start from a relativistic classical field theory, to which you add the Copenhagen procedure to turn that into quantum mechanics, then you should get a unitary theory. The renormalisation procedure amounts to transforming all expressions that threaten to become infinite due to divergence of the integrals, to apply only to unobservable qualities of particles and fields, such as their “bare mass” and “bare charge”. If you understand how to get such things under control, then your theory should become a renormalised description of massive particles. But there were complications.

The infinities that require a renormalisation procedure to tame them originate from uncontrolled behaviour at very tiny distances, where the effective energies are large and consequently the effects of mass terms for the particles should become insignificant. This revealed that you first have to renormalise the theory without any masses in them, where also the spontaneous breakdown of the local symmetry becomes insignificant. You had to get the particle book-keeping right. A massless photon has only two observable field components (they can be left- or right-rotating), whereas a massive particle with the same spin can rotate in three different ways. One degree of freedom did not match. This was why an extra field was needed. If you wanted massive photons with electric charges +, 0 or –, you would need a scalar field with four components; one of these would represent the total field strength, and would behave as an extra, neutral, spin-0 particle – the observable particle that Higgs had talked about – but the others would turn the number of spinning degrees of freedom of the three other bosons from two to three each (see “Dynamical” figure).

One question

In 1970 Veltman sent me to a summer school organised by Maurice Lévy in a new science institute at Cargèse on the French island of Corsica. The subject would be the study of the Gell–Mann–Lévy model for pions and nucleons, in particular its renormalisation and the role of spontaneous symmetry breaking. Will renormalisation be possible in this model, and will it affect its symmetry? The model was very different from what I had just started to study: Yang–Mills theory with spontaneous breaking of its symmetry. There were quite a few reputable lecturers besides Lévy himself: Benjamin Lee and Kurt Symanzik had specialised in renormalisation. Shy as I was, I only asked one question to Lee, and the same to Symanzik: does your analysis apply to the Yang–Mills case?

Both gave me the same answer: if you are Veltman’s student, ask him. But I had, and Veltman did not believe that these topics were related. I thought that I had a better answer, and I fantasised that I was the only person on the planet who knew how to do it right. It was not obvious at all; I had two German roommates at the hotel where I had been put, who tried to convince me that renormalisation of Feynman graphs where lines cross each other would be unfathomably complicated.

Veltman had not only set up detailed, fully running machinery to handle the renormalisation of all sorts of models, but he had also designed a futuristic computer program to do the enormous amount of algebra required to handle the numerous Feynman diagrams that appear to be relevant for even the most basic computations. I knew he had those programs ready and running. He was now busy with some final checks: if his present attempts to check the unitarity of his renormalised model still failed, we should seriously consider giving this up. Yang–Mills theories for the weak interactions would not work as required.

But Veltman had not thought of putting a spin-zero, neutral particle in his model, certainly not if it wasn’t even in a complete representation of the gauge symmetry. Why should anyone add that? After returning from Cargèse I went to lunch with Veltman, during which I tried to persuade him. Walking back to our institute, he finally said, “Now look, what I need is not an abstract mathematical idea, what I want is a model, with a Lagrangian, from which I can read off the Feynman diagrams to check it with my program…”. “But that Lagrangian I can give you,” I said. Next, he walked straight into a tree! A few days after I had given him the Lagrangian, he came to me, quite excited. “Something strange,” he said, “your theory isn’t right because it still isn’t unitary, but I see that at several places, if the numbers had been a trifle different, it could have worked out.” Had he copied those factors ¼ and ½ that I had in my Lagrangian, I wondered? I knew they looked odd, but they originated from the fact that the Higgs field has isospin ½ while all other fields have isospin one.

No, Veltman had thought that those factors came from a sloppy notation I must have been using. “Try again,” I asked. He did, and everything fell into place. Most of all, we had discovered something important. This was the beginning of an intensive but short collaboration. My first publication “Renormalization of massless Yang–Mills fields”, published in October 1971, concerned the renormalisation of the Yang–Mills theory without the mass terms. The second publication that year, “Renormalizable Lagrangians for massive Yang–Mills fields,” where it was explained how the masses had to be added, had a substantial impact. 

There was an important problem left wide open, however: even if you had the correct Feynman diagrams, the process of cancelling out the infinities could still leave finite, non-vanishing terms that ruin the whole idea. These so-called “anomalies” must also cancel out. We found a trick called dimensional renormalisation, which would guarantee that anomalies cancel except in the case where particles spin preferentially in one direction. Fortunately, as charged leptons tend to rotate in opposite directions compared to quarks, it was discovered that the effects of the quarks would cancel those of the leptons. 

The fourth component

Within only a few years, a complete picture of the fundamental interactions became visible, where experiment and theory showed a remarkable agreement. It was a fully renormalisable model where all quarks and all leptons were represented as “families” that were only complete if each quark species had a leptonic counterpart. There was an “electroweak force”, where electromagnetism and the weak force interfere to generate the force patterns observed in experiments, and the strong force was tamed at almost the same time. Thus the electroweak theory and quantum chromodynamics were joined into what is now known as the Standard Model.

Be patient, we are almost there, we have three of the four components of this particle’s field

This theory agreed beautifully with observations, but it did not predict the mass of the neutral, spin-0 Higgs particle. Much later, when the W and the Z bosons were well-established, the Higgs was still not detected. I tried to reassure my colleagues: be patient, we are almost there, we have three of the four components of this particle’s field. The fourth will come soon.

As the theoretical calculations and the experimental measurements became more accurate during the 1990s and 2000s, it became possible to derive the most likely mass value from indirect Higgs-particle effects that had been observed, such as those concerning the top-quark mass. On 4 July 2012 a new boson was directly detected close to where the Standard Model said the Higgs  would be. After these first experimental successes, it was of utmost importance to check whether this was really the object we had been expecting. This has kept experimentalists busy for the past 10 years, and will continue to do so for the foreseeable future. 

The discovery of the Higgs particle is a triumph for high technology and basic science, as well as accurate theoretical analyses. Efforts spanning more than half a century paid off in the summer of 2012, and a new era of understanding the particles, their masses and interactions began.

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The above description suggests that “all” that is required to understand the basic structure of matter is to understand the origin of the electron mass and to study quantum chromodynamics. But this misses the bigger picture revealed by the Standard Model (SM). Protons, neutrons and other light, long-lived baryons are the lightest excitations of the pion field, which is constructed from the ultra-light u and d quarks, and perhaps also s quarks. This reveals the profound importance of the values of the fermion masses: increasing the u and d mass difference by less than 10 MeV (that is, about 1% of the proton mass), for instance, would make hydrogen and its isotopes unstable, thereby preventing the formation of almost all the elements in the early universe. Indeed, there are only certain regions in the vast quark-mass and Λ_QCD parameter space that enable the universe as we know it to form.

Having established that the structure of the masses of the elementary particles is an existential issue, what does this have to do with the discovery of the Higgs boson? While the Higgs boson carries a cosmological background value called the vacuum expectation value (VEV), which is associated with the spontaneous breaking of the electroweak symmetry, the VEV is not necessarily the source of the actual value and/or the pattern of fermion masses. The reason is that, in addition to baryonic charge (or number), all the elementary charged particles carry “chiral charge” – they are either left- or right-handed – which is conserved in the absence of the Brout–Englert–Higgs (BEH) field. What is fascinating about the BEH mechanism is that with the appropriate choice of coupling, the product of the field and its coupling-strength to the fermions effectively becomes a source of chiral charge, allowing the fermions to interact with it; the VEV is merely the constant of proportionality that induces the masses of the fermions (and of the weak-force mediators). This is a very minimal setup! In other known symmetry-breaking frameworks – for instance models based on technicolour/QCD-like dynamics or on superconductivity, where the electromagnetic symmetry inside a superconductor is broken by a condensate of electrons denoted Cooper pairs – there is no direct link to the generation of fermion masses. 

Standard Model couplings

The BEH mechanism might be minimal, but it still involves many parameters. The origin of fundamental masses requires switching on nine trilinear-couplings, which are broken into three generations of fundamental particles: three involving the u-type left- and right-handed quarks (u, c, t), three involving the d-type left- and right-handed quarks (d, s, b) and three involving the left- and right-handed charged leptons (e, µ, τ). Each coupling is associated with a linear “Yukawa” coupling of the Higgs boson to fermions, which implies that all the charged fermions acquire a mass proportional to the VEV of the BEH field. In other words, there is a linear relation between the Yukawa coupling and the fermion masses. Strikingly, the observed fermion masses encoded in the Yukawa couplings span some five orders of magnitude, with all but some members of the third generation being extremely small – leading to the fermion mass-hierarchy puzzle.

The coupling between the Higgs boson and the fermions can be pictured as a new force – one that is radically different to the SM gauge forces. Given that this force only works between two particles that are closer than around 10^–18 m – i.e. 1000 times smaller than the proton radius – it is not relevant to any experimental setup. The Higgs–Yukawa couplings do, however, conceal two interesting aspects related to our existence. The first is that increasing the VEV by a few factors would increase the neutron–proton mass splitting to the point where all nuclei are unstable. The second, pointed out by Giuseppe Degrassi and co-workers in 2013, is that the top-quark Yukawa interaction is close to its maximal size: increasing it by as little as 10% would push the VEV to fantastically large values, rendering our current universe unstable (see The Higgs and the fate of the universe). 

Massive alternatives

The minimal BEH mechanism is not the only way to understand the fermion mass hierarchy. This is illustrated by two radically different options. In the first, proposed in 2008 by Gian Giudice and Oleg Lebedev, the Yukawa couplings are assumed to depend on the BEH field, therefore avoiding hierarchies in the Yukawa couplings. The idea postulates a variation of chiral symmetry (in which the lighter the fermion the more chiral charge it carries) that forbids lighter particles from coupling to the Higgs linearly, but instead generates their masses through appropriate powers of the VEV (see “In line” figure, blue curve). The other extreme possibility, discussed more recently by the present author and colleagues, is where the masses of the light fermions instead come from their interaction with a subdominant additional source of electroweak symmetry breaking, similar to the technicolour framework. This new source replaces the Higgs boson’s role as the carrier of the light-generation chiral-charge, causing the light fermion-Higgs couplings to vanish (see figure, red curve). Both cases lead to an alternative understanding of the mass hierarchy puzzle and to the establishment of new physics.

The conclusion is that measuring the fermion-Higgs couplings at higher levels of precision will significantly improve our understanding of the origin of masses in nature. It took a few years after the Higgs-boson discovery, around 2018, for ATLAS and CMS to establish that the standard BEH mechanism is behind the third-generation fermion masses. This is a legacy result from the LHC experiments that is sometimes overlooked by our community (CERN Courier September/October 2020 p41). While significant, however, it told us little about the origin of the matter in the universe, which is almost exclusively made out of first-generation fermions with extremely small couplings to the Higgs boson. So far, we only have indirect information, via Higgs-boson couplings to the gauge bosons, about the origin of mass of the first and second generations. But breakthroughs are imminent. In the past two years, ATLAS and CMS have found signs that the Higgs boson contributes to both the second-generation muon and charm masses, which would exclude models leading to both the blue and red curves in the figure. Measuring the smallest electron Yukawa coupling is only possible at a future collider, whereas for the u and d quarks there is no clear experimental pathway.

Experimental novelties

A recent, unexpected way to tackle the mystery of fermion masses involves dark matter, specifically a class of models in which the dark-matter particle is ultra-light and its field-value oscillates with time. Such particles would couple to fermions in a way that echoes the Higgs–Yukawa coupling, though with an extremely low interaction strength, and lead to a variation in the masses of the fundamental fermions with time. This feeble effect cannot be searched for at colliders, but it can be probed with quantum sensors such as atomic clocks or future nuclear clocks that reach sensitivity of one part in 10¹⁹ or more. The strongest sensitivity of these tabletop experiments is the one to the electron mass.

It is now a priority to directly test the mass-generating mechanism of the first two generations

The discovery of the Higgs boson has opened a new window on the origin of masses, and consequently the structure of the basic blocks of nature, with profound links to our existence. ATLAS and CMS have made several breakthroughs, including the observation that the third-generation masses originate from the SM minimal BEH mechanism, and also providing evidence for part of the second-generation fermions. It is now a priority to directly test the mass-generating mechanism of the first two generations, and to determine all the Higgs couplings at higher precision, in search of possible chinks in the SM armour. 

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A vacuum is ordinarily pictured as an empty region containing no particles, atoms or molecules of matter, as in outer space. To a particle physicist, however, it is better defined as the lowest energy state that can be attained when no physical particles are present. Even in empty space there are fields that are invisible to the naked eye but nevertheless influence the behaviour of matter, while quantum mechanics ensures that, even if particles are not physically present, they continually fluctuate spontaneously in and out of existence. 

In the Standard Model (SM), in addition to the familiar gravitational and electromagnetic fields, there is the Brout–Englert–Higgs (BEH) field that is responsible for particle masses. It is usually supposed to have a constant value throughout the universe, namely the value that it takes at the bottom of its “Mexican hat” potential (see “New depths” figure). However, as was first pointed out by several groups in 1979, and revisited by many theorists subsequently, the shape of the Mexican hat is subject to quantum effects that change its shape. For example, the BEH field has self-interactions that tend to curl the brim of the hat upwards, but there are additional quantum effects that tend to curl the brim downwards, due to the interactions with the fundamental particles to which the BEH field gives mass. The most important of these is the heaviest matter particle: the top quark.

Push and pull

The upward push of the Higgs boson’s self-interaction and the downward pressure of the top quark are very sensitive to their masses, and also to the strong interactions, which modify the effect of the top quark. Experiments at the LHC have already determined the mass of the Higgs boson with a precision approaching 0.1%, and CMS recently measured the mass of the top quark with an accuracy of almost 0.2%, while the strong coupling strength is known to better than 1%. The latest calculations of the quantum effects of the Higgs boson and the top quark indicate that the brim of the Mexican hat turns down when the BEH field exceeds its value today by 10 orders of magnitude, implying that the current value is not the lowest energy and hence not the true vacuum of the SM. A consequence is that the current BEH value is not stable, because quantum fluctuations would inevitably cause it to decay into a lower-energy state. The universe as we know it would be doomed (see “On the cusp” figure).

However, there is no immediate need to panic. First, the universe is metastable with an estimated lifetime before it decays that is many, many orders of magnitude longer than its age so far. Second, one could perhaps cling to the increasingly forlorn hope that the prediction of a lower-energy state of the SM vacuum is somehow mistaken. Perhaps an experimental measurement going into the calculation has an unaccounted uncertainty, or perhaps there is some ingredient that is missing from the theoretical calculation of the shape of the Mexican hat? 

If you simply take the calculation at face value and humbly accept the eventual demise of the universe as we know it, however, a further problem arises. Since quantum and thermal fluctuations in the BEH field were probably much larger when the universe was young and much hotter than today, the overwhelming majority of the universe would have been driven into the lower-energy state. Only an infinitesimal fraction would be in the metastable state we find ourselves in today, where the value of the BEH field is relatively small. Of course, one could argue anthropically that this good luck was inevitable, as we could not live in any other “vacuum” state. 

To me, this argument reeks of special pleading. Instead, my instinct is to argue that some physics beyond the SM must appear below the turn-down scale and stabilise the vacuum that we live in. This argument is not specific about the type of new physics or the scale at which it appears. One extension of the SM that fits the bill is supersymmetry, but the stability argument offers no guarantee that this or any other extension of the SM is within reach of current experiments.

It used to be said that the nightmare scenario for the LHC would be to discover the Higgs boson and nothing else. However, the measured masses of the Higgs boson and the top quark may be hinting that there must be physics beyond the SM that stabilises the vacuum. Let us take heart from this argument, and keep looking for new physics, even if there is no guarantee of immediate success.

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The discovery was made mainly by detecting decays of the new particle into two photons or two Z bosons (each of which decay into a pair of electrons or muons), for which the invariant mass can be reconstructed with high resolution. The search for the Higgs boson was also performed in other channels, and all results were found to be consistent with the SM expectations. A peculiar feature of the Higgs boson is that it has zero spin. At the time of the discovery, it was already excluded that the particle was a standard vector boson: a spin-1 particle cannot decay into two photons, leaving only spin-0 or spin-2 as the allowed possibilities. 

Ten years ago, the vast majority of high-energy physicists were convinced that a Higgs boson had been detected. The only remaining question was whether it was the boson predicted by the SM or part of an extended Higgs sector.

Basic identity  

The mass of the Higgs boson is the only parameter of the Higgs sector that is not predicted by the SM. A high-precision measurement of the mass is therefore crucial because, once it is known, all the couplings and production cross sections can be predicted in the SM and then compared with experimental measurements. The mass measurement is carried out using the H → γγ and H → ZZ → 4ℓ channels, with a combined ATLAS and CMS measurement based on Run 1 data obtaining a value of 125.09 ± 0.24 GeV. More precise results with a precision at the level of one part per thousand have been obtained by ATLAS and CMS using partial datasets from Run 2.

The width of the Higgs boson, unlike its mass, is well predicted at approximately 4 MeV. Since this is much smaller than the ATLAS and CMS detector resolutions, a precise direct measurement can only be carried out at future electron–positron colliders. At the LHC it is possible to indirectly constrain the width by studying the production of di-boson pairs (ZZ or WW) via the exchange of off-shell Higgs bosons: under some reasonable assumptions, the off-shell cross section at high mass relative to the on-shell cross section increases proportionally to the width. A recent result from CMS constrains the Higgs-boson width to be between 0.0061 and 2.0 times the SM prediction at 95% confidence level. Finding the width to be smaller than the SM would mean that some of the couplings are smaller than predicted, while a larger measured width could reflect additional decay channels beyond the SM, or a larger branching fraction of those predicted by the SM.

This is the first strong suggestion that the Higgs boson also couples to fermions from generations other than the third

The spin and charge-parity (CP) properties of the Higgs boson are other key quantities. The SM predicts that the Higgs boson is a scalar (spin-0 and positive CP) particle, but in extended Higgs models it could be a superposition of positive and negative CP states, for example. The spin and CP properties can be probed using angular distributions of the Higgs-boson decay products, and several decay channels were exploited by ATLAS and CMS: H → γγ, ZZ, WW and ττ. All results to date indicate consistency with the SM and exclude most other models at more than 3σ confidence level, including all models with spin different from zero. 

Couplings to others 

One of the main tools for characterising the Higgs boson is the measurement of its production processes and decays. Thanks to growing datasets, improved analysis techniques, more accurate theoretical tools and better modeling of background processes, ATLAS and CMS have made remarkable progress in this crucial programme over the past decade. 

Using Run 1 data recorded between 2010 and 2012, the gluon-fusion and vector-boson fusion production processes were established, as were the decays to pairs of bosons (γγ, WW^* and ZZ^*) and to a τ-lepton pair from the combination of ATLAS and CMS data. With Run 2 data (2015–2018), both ATLAS and CMS observed the decay to a pair of b quarks. Although the preferred decay mode of the Higgs boson, this channel suffers from larger backgrounds and is mainly accessible in the associated production of the Higgs boson with a vector boson. The rarer production mode of the Higgs boson in association with a t-quark pair was also observed using a combination of different decay modes, providing a direct proof of the Yukawa coupling between the Higgs boson and top quark. The existence of the Yukawa couplings between the Higgs boson and third-generation fermions (t, b, τ) is thus established.

The collaborations also investigated the coupling of the Higgs boson to the second-generation fermions, in particular the muon. With the full Run 2 dataset, CMS reported evidence at the level of 3σ over the background-only hypothesis that the Higgs boson decays into μ⁺μ^–, while ATLAS supported this finding with a 2σ excess. This is the first strong suggestion that the Higgs boson also couples to fermions from generations other than the third, again in accordance with the SM. Research is also ongoing to constrain the Higgs’s coupling to charm quarks via the decay H → cc. This is a much more difficult channel but, thanks to improved detectors and analysis methods, including extensive use of machine learning, ATLAS and CMS recently achieved a sensitivity beyond expectations and excluded a branching fraction of H → cc relative to the SM prediction larger than O(10). The possibility that the Higgs-boson’s coupling to charm is at least as large as the coupling to bottom quarks is excluded by a recent ATLAS analysis at 95% confidence level.

The accuracy of the production cross-section times decay branching-fraction measurements in the bosonic decay channel (diphoton, ZZ and WW) with the full Run 2 dataset is around 10%, allowing measurements in a more restricted kinematical region that can be sensitive to physics beyond the SM. In all probed phase-space regions, the measured cross sections are compatible with the SM expectations (Data used for some of the measurements are shown in the “Mass spectra” figure). 

Ten years after the discovery of a new elementary boson, considerable progress has been made toward understanding this particle

The combination of all measurements in the different production and decay processes can be used to further constrain the measured couplings between the Higgs boson and the other particles. The production cross section for vector-boson-fusion production, for example, is directly proportional to the square of the coupling strengths between the Higgs boson and W or Z bosons. A modification of these couplings will also affect the rate at which the Higgs boson decays to various final states. Assuming no contribution beyond the SM to Higgs decays and that only SM particles contribute to Higgs-boson vertices involving loops, couplings to t, b and τ are currently determined with uncertainties of around 10%, and couplings to W and Z bosons with uncertainties of about 5%. 

The relation between the mass of a particle and its coupling to the Higgs boson is as expected from the SM, in which the particle masses originate from their coupling to the Brout–Englert–Higgs field (see “Couplings” figure). These measurements thus set bounds on specific new-physics models that predict deviations of the Higgs-boson couplings from the SM. The impact of new physics at a high energy scale is also probed in effective-field-theory frameworks, introducing all possible operators that describe couplings of the Higgs boson to SM particles. No deviations from predictions are observed. 

New physics 

The Higgs boson is the only elementary particle with spin-0. However, an extended Higgs sector is a minimal extension of the SM and is predicted by many theories, such as those based on supersymmetry. These extensions predict several neutral or charged spin-0 particles: one is the observed 125 GeV Higgs boson; the others would preferentially couple to heavier SM particles. Searches for heavier scalar (or pseudo-scalar) particles have been carried out in a variety of final states, but no evidence for such particles is found. For example, the search for heavy scalar or pseudo-scalar particles decaying to a pair of τ leptons excludes masses up to 1–1.5 TeV. The extended Higgs sector can also include lighter scalar or pseudo-scalar particles into which the observed Higgs boson could decay. A wide range of final states have been investigated but no evidence found, setting stringent constraints on the corresponding Higgs-boson decay branching fractions.

The Higgs sector could also play a role linking the SM to new physics that explains the presence of dark matter in the form of new neutral, weakly interacting particles. If their mass is less than half that of the Higgs boson, the Higgs boson could decay to a pair of these neutral particles. Since the particles would be invisible in the detector, this process can be detected by observing the presence of missing transverse momentum from the Higgs-boson recoiling against visible particles. The most sensitive processes are those in which the Higgs boson is produced in association to other particles: vector boson fusion, and the associated productions with a vector boson or with a top quark pair. No evidence of such decay has been found, setting upper limits on the invisible decay branching fraction of the Higgs boson at the level of 10%, and providing complementary constraints to those from direct dark-matter detection experiments.

Self-interaction

In addition to its couplings to other bosons and to fermions, the structure of the Brout–Englert–Higgs potential predicts a self-coupling of the Higgs boson that is related to electroweak symmetry breaking (see Electroweak baryogenesis). By studying Higgs-boson pair production at the LHC, it is possible to directly probe this self-coupling. 

The two main challenges of this measurement are the tiny cross section for Higgs-boson pair production (about 1000 times smaller than the production of a single Higgs boson) and the interference between processes that involve the self-coupling and those that do not. Final states with a favourable combination of the expected signal yield and signal-over-background ratio are exploited. 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. Upper limits of approximately three times the predicted cross section have been obtained with the Run 2 dataset. These searches can also be used to set constraints on the Higgs boson self-coupling relative to its SM value. 

The sensitivities achieved for Higgs-boson pair production searches with the Run 2 dataset are significantly better than expected before the start of Run 2, thanks to several improvements in object reconstruction and analysis techniques. These searches are mostly limited by the size of the dataset and thus will improve further with the Run 3 and much larger High-Luminosity LHC (HL-LHC) datasets.

Going further

Ten years after the discovery of a new elementary boson, considerable progress has been made toward understanding this particle. All measurements so far point to properties that are very consistent with the SM Higgs boson. All main production and decay modes have been observed by ATLAS and CMS, and the couplings to vector bosons and third-generation fermions are probed with 5 to 10% accuracy, confirming the pattern expected from the Brout–Englert–Higgs mechanism for electroweak symmetry breaking and the generation of the masses of elementary particles. Still, there is ample room for improvement in the forthcoming Run 3 and HL-LHC phases, to reduce the uncertainty in the coupling measurements down to a few per cent, to establish couplings to second-generation fermions (muons) and to investigate the Higgs-boson self-coupling. Improved measurements will also significantly expand the sensitivity to a possible extended Higgs sector or new dark sector. 

To reach the ultimate accuracy in the measurements of all Higgs-boson properties (including its self-coupling), to remove the assumptions in the determination of the Higgs couplings at the LHC, and to considerably extend the search for new physics in the Higgs sector, new colliders – such as an e⁺e^– collider and a future hadron collider – will be required.

The post The Higgs boson under the microscope appeared first on CERN Courier.

When Victor Weisskopf sat down in the early 1930s to compute the energy of a solitary electron, he had no way of knowing that he’d ultimately discover what is now known as the electroweak hierarchy problem. Revisiting a familiar puzzle from classical electrodynamics – that the energy stored in an electron’s own electric field diverges as the radius of the electron is taken to zero (equivalently, as the energy cutoff of the theory is taken to infinity) – in Dirac’s recently proposed theory of relativistic quantum mechanics, he made a remarkable discovery: the contribution from a new particle in Dirac’s theory, the positron, cancelled the divergence from the electron itself and left a quantum correction to the self-energy that was only logarithmically sensitive to the cutoff. 

The same cancellation occurred in any theory of charged fermions. But when Weisskopf considered the case for charged scalar particles in 1939, the problem returned. To avoid the need for finely-tuned cancellations between this quantum correction and other contributions to a scalar’s self-energy, he posited that the cutoff energy for scalars should be close to their observed self-energy, heralding the appearance of new features that would change the calculation and render the outcome “natural”. 

Nearly 30 years would pass before Weisskopf’s prediction about scalars was put to the test. The charged pion, a pseudoscalar, suffered the very same divergent self-energy that he had computed. As the neutral pion is free from this divergence, Weisskopf’s logic suggested that the theory of charged and neutral pions should change at around 800 MeV, the cutoff scale suggested by the observed difference in their self-energies. Lo and behold, the rho meson appeared at 775 MeV. Repeating the self-energy calculation with the rho meson included, the divergence in the charged pion’s self-energy disappeared. 

This same logic would predict something new. It had been known for some time that the relative self-energy between the neutral kaons K_L and K_S diverged due to contributions from the weak interactions in a theory containing only the known up, down and strange quarks. Matching the observed difference suggested that the theory should change at around 3 GeV. Repeating the calculation with the addition of the recently proposed charm quark in 1974, Mary K Gaillard and Ben Lee discovered that the self-energy difference became finite, which allowed them to predict that the charm quark should lie below 1.5 GeV. The discovery at 1.2 GeV later that year promoted Weisskopf’s reasoning from an encouraging consistency check to a means of predicting new physics.

Higgs, we have a problem

Around the same time, Ken Wilson recognised that the coupling between the Higgs boson and other particles of the Standard Model (SM) leads to yet another divergent self-energy, for which the logic of naturalness implied new physics at around the TeV scale. Thus the electroweak hierarchy problem was born – not as a new puzzle unique to the Higgs, but rather the latest application of Weisskopf’s wildly successful logic (albeit one for which the answer is not yet known). 

History suggested two possibilities. As a scalar, the Higgs could only benefit from the sort of cancellation observed among fermions if there is a symmetry relating bosons and fermions, namely supersymmetry. Alternatively, it could be a light product of compositeness, just as the pions and kaons are light bound states of the strong interactions. These solutions to the hierarchy problem came to dominate expectations for physics beyond the SM, with a sharp target – the TeV scale – motivating successive generations of collider experiments. Indeed, when the physics case for the LHC was first developed in the mid-1980s, it was thought that new particles associated with supersymmetry or compositeness would be much easier to discover than the Higgs itself. But while the Higgs was discovered, no signs of supersymmetry or compositeness were to be found.

In the meantime, other naturalness problems were brewing. The vacuum energy – Einstein’s infamous cosmological constant – suffers a divergence of its own, and even the finite contributions from the SM are many orders of magnitude larger than the observed value. Although natural expectations for the cosmological constant fail, an entirely different set of logic seems to succeed in its place. To observe a small cosmological constant requires observers, and observers can presumably arise only if gravitationally-bound structures are able to form. As Steven Weinberg and others observed in the 1980s, such anthropic reasoning leads to a prediction that is remarkably close to the value ultimately measured in 1998. To have predictive power, this requires a multitude of possible universes across which the cosmological constant varies; only the ones with sufficiently small values of the cosmological constant produce observers to bear witness.

An analogous argument might apply to the electroweak hierarchy problem: the nuclear binding energy is no longer sufficient to stabilise the neutron within typical nuclei if the Higgs vacuum expectation value (VEV) is increased well above its observed value. If the Higgs VEV varies across a landscape of possible universes while its couplings to fermions are kept fixed, only universes with sufficiently small values of the Higgs VEV would lead to complex atoms and, presumably, observers. Although anthropic reasoning for the hierarchy problem requires stronger assumptions than for the cosmological-constant problem, its compatibility with null results at the LHC is enough to raise questions about the robustness of natural reasoning. 

Amidst all of this, another proposed scalar particle entered the picture. The observed homogeneity and isotropy of the universe point to a period of exponential expansion of spacetime in the early universe driven by the inflaton. While the inflaton may avoid naturalness problems of its own, the expansion of spacetime and the quantum fluctuations of fields during inflation lead to qualitatively new effects that are driving new approaches to the hierarchy problem at the intersection of particle physics, cosmology and gravitation.

Perhaps the most prominent of these new approaches came, surprisingly enough, from a failed solution to the cosmological constant problem. Around the same time as the first anthropic arguments for the cosmological constant were taking form, Laurence Abbott proposed to “relax” the cosmological constant from a naturally large value by the evolution of a scalar field in the early universe. Abbot envisioned the scalar evolving along a sloping, bumpy potential, much like a marble rolling down a wavy marble run. As it did so, this scalar would decrease the total value of the cosmological constant until it reached the last bump before the cosmological constant turned negative. Although the universe would crunch away into nothingness if the scalar evolved to negative values of the cosmological constant, it could remain poised at the last bump for far longer than the age of the observed universe. 

Despite the many differences among the new approaches, they share a common tendency to leave imprints on the Higgs boson

While this fails for the cosmological constant (the resulting metastable universe is largely devoid of matter), analogous logic succeeds for the hierarchy problem. As Peter Graham, David Kaplan and Surjeet Rajendran pointed out in 2015, a scalar evolving down a potential in the early universe can also be used to relax the Higgs mass from naturally large values. Of course, it needs to stop close to the observed mass. But something interesting happens when the Higgs mass-squared passes from positive values to negative values: the Higgs acquires a VEV, which gives mass to quarks, which induces bumps in the potential of a particular type of scalar known as an axion (proposed to explain the unreasonably good conservation of CP symmetry by the strong interactions). So if the relaxing scalar is like an axion – a relaxion, you might say – then it will encounter bumps in its potential when it relaxes the Higgs mass to small values. If the relaxion is rolling during an inflationary period, the expansion of spacetime can provide the “friction” necessary for the relaxion to stop when it hits these bumps and set the observed value of the weak scale. The effective coupling between the relaxion and the Higgs that induces bumps in the relaxion potential is large enough to generate a variety of experimental signals associated with a new, light scalar particle that mixes with the Higgs.

The success of the relaxion hypothesis in solving the hierarchy problem hinges on an array of other questions involving gravity. Whether the relaxion potential can remain sufficiently smooth over the vast trans-Planckian distances in field space required to set the value of the weak scale is an open question, one that is intimately connected to the fate of global symmetries in a theory of quantum gravity (itself the target of active study in what is known as the Swampland programme).

Models abound 

In the meantime, the recognition that cosmology might play a role in solving the hierarchy problem has given rise to a plethora of new ideas. For instance, in Raffaele D’Agnolo and Daniele Teresi’s recent paradigm of “sliding naturalness”, the Higgs is coupled to a new scalar whose potential features two minima. In the true minimum, the cosmological constant is large and negative, and the universe would crunch away into oblivion if it ended up in this vacuum. In the second, local minimum, the cosmological constant is safely positive (and can be made compatible with the small observed value of the cosmological constant by Weinberg’s anthropic selection). The Higgs couples to this scalar in such a way that a large value of the Higgs VEV destabilises the “safe” minimum. During the inflationary epoch, only universes with suitably small values of the Higgs VEV can grow and expand, while those with large values of the Higgs VEV crunch away. A second scalar coupled analogously to the Higgs can explain why the VEV is small but non-zero. Depending on how these scalars are coupled to the Higgs, experimental signatures range from the same sort of axion-like signals arising from the relaxion, to extra Higgs bosons at the LHC.

Alternatively, in the paradigm of “Nnaturalness” proposed by Nima Arkani-Hamed and others, the multitude of SMs over which the Higgs mass varies occur in one universe, rather than many. The fact that the universe is predominantly composed of one copy of the SM with a small Higgs mass can be explained if inflation ends and reheats the universe through the decay of a single particle. If this particle is sufficiently light, it will preferentially reheat the copy of the SM with the smallest non-zero value of the Higgs VEV, even if it couples symmetrically to each copy. The sub-dominant energy density deposited in other copies of the SM leaves its mark in the form of dark radiation susceptible to detection by the Simons Observatory or upcoming CMB-S4 facility. 

Finally, Gian Giudice, Matthew Mccullough and Tevong You have recently shown that inflation can help to understand the electroweak hierarchy problem by analogy with self-organised criticality. Just as adding individual grains of sand to a sandpile induces avalanches over diverse length scales – a hallmark of critical behaviour, obtained without tuning parameters – so too can inflation drive scalar fields close to critical points in their potential. This may help to understand why the observed Higgs mass lies so close to the boundary between the unbroken and broken phases of electroweak symmetry without fine tuning.

Going the distance 

Underlying Weisskopf’s natural reasoning is a long-standing assumption about relativistic theories of quantum mechanics: physics at short distances (the ultraviolet, or UV) is decoupled from physics at long distances (the infrared, or IR), making it challenging to apply a theory involving a large energy scale to a much smaller one without fine tuning. This suggests that loopholes may be found in theories that mix the UV and the IR, as is known to occur in quantum gravity. 

While the connection between this type of UV/IR mixing and the mass of the Higgs remains tenuous, there are encouraging signs of progress. For instance, Panagiotis Charalambous, Sergei Dubovsky and Mikhail Ivanov recently used it to solve a naturalness problem involving so-called “Love numbers” that characterise the tidal response of black holes. The surprising influence of quantum gravity on the parameter space of effective field theories implied by the Swampland programme also has a flavour of UV/IR mixing to it. And UV/IR mixing may even provide a new way to understand the apparent violation of naturalness by the cosmological constant.

We have come a long way since Weisskopf first set out to understand the self-energy of the electron. The electroweak hierarchy problem is not the first of its kind, but rather the one that remains unresolved. The absence of supersymmetry or compositeness at the TeV scale beckons us to search for new solutions to the hierarchy problem, rather than turning our backs on it. In the decade since the discovery of the Higgs, this search has given rise to a plethora of novel approaches, building new bridges between particle physics, cosmology and gravity along the way. Despite the many differences among these new approaches, they share a common tendency to leave imprints on the Higgs boson. And so, as ever, we must look to experiment to show the way. 

The post Naturalness after the Higgs appeared first on CERN Courier.

With the boson confirmed, speculation inevitably grew about the 2012 Nobel Prize in Physics. The prize is traditionally announced on the Tuesday of the first full week in October, at about midday in Stockholm. As it approaches, a highly selective epidemic breaks out: Nobelitis, a state of nervous tension among scientists who crave Nobel recognition. Some of the larger egos will have previously had their craving satisfied, only perhaps to come down with another fear: will I ever be counted as one with Einstein? Others have only a temporary remission, before suffering a renewed outbreak the following year.

Three people at most can share a Nobel, and at least six had ideas like Higgs’s in the halcyon days of 1964 when this story began. Adding to the conundrum, the discovery of the boson involved teams of thousands of physicists from all around the world, drawn together in a huge cooperative venture at CERN, using a machine that is itself a triumph of engineering. 

The 2012 Nobel Prize in Physics was announced on Tuesday 9 October and went to Serge Haroche and David Wineland for taking the first steps towards a quantum computer. Two days later, I went to Edinburgh to give a colloquium and met Higgs for a coffee beforehand. I asked him how he felt now that the moment had passed, at least for this year. “I’m enjoying the peace and quiet. My phone hasn’t rung for two days,” he remarked. 

That the sensational discovery of 2012 was indeed of Higgs’s boson was, by the summer of 2013, beyond dispute. That Higgs was in line for a Nobel prize also seemed highly likely. Higgs himself, however, knew from experience that in the Stockholm stakes, nothing is guaranteed. 

Back in 1982, at dawn on 5 October in the Midwest and the eastern US, preparations were in hand for champagne celebrations in three departments at two universities. At Cornell, the physics department hoped they would be honouring Kenneth Wilson, while over in the chemistry department their prospect was Michael Fisher. In Chicago, the physicists’ hero was to be Leo Kadanoff. Two years earlier the trio had shared the Wolf Prize, the scientific analogue of the Golden Globes to the Nobel’s Oscars, for their work on critical phenomena connected with phase transitions, fuelling speculation that a Nobel would soon follow. At the appointed hour in Stockholm, the chair of the awards committee announced that the award was to Wilson alone. The hurt was especially keen in the case of Michael Fisher, whose experience and teaching about phase transitions, illuminating the subtle changes in states of matter such as melting ice and the emergence of magnetism, had inspired Wilson, five years his junior. The omission of Kadanoff and Fisher was a sensation at the time and has remained one of the intrigues of Nobel lore.

Fisher’s agony was no secret to Peter Higgs. As undergraduates they had been like brothers and remained close friends for more than 60 years. Indeed, Fisher’s influence was not far away in July 1964, for it was while examining how some ideas from statistical mechanics could be applied to particle physics that Higgs had the insight that would become the capstone to the theory of particles and forces half a century later. For this he was to share the 2004 Wolf Prize with Robert Brout (who sadly died in 2011) and François Englert – just as Fisher, Kadanoff and Wilson had shared this prize in 1980. Then as October approached in 2013 Higgs became a hot favourite at least to share the Nobel Prize in Physics, and the bookmakers would only take bets at extreme odds-on. 

Time to escape 

In 2013, 8 October was the day when the Nobel decision would be announced. Higgs’s experiences the year before had helped him to prepare: “I decided not to be at home when the announcement was made with the press at my door; I was going to be somewhere else.” His first plan was to disappear into the Scottish Highlands by train, but he decided it was too complicated, and that he could hide equally well in Edinburgh. “All I would have to do is go down to Leith early enough. I knew the announcement would be around noon so I would leave home soon after 11, giving myself a safe margin, and have an early lunch in Leith about noon.” 

Richard Kenway, the Tait Professor of Mathematical Physics at Edinburgh and one of the university’s vice principals, confirmed the tale. “That was what we were all told, and he completely convinced us. Right up to the actual moment when we were sitting waiting for the [Nobel] announcement, we thought he had disappeared off somewhere into the Highlands.” Some newspapers got the fake news from the department, and one reporter even went up into the Highlands to look for him.

As scientists and journalists across the world were glued to the live broadcast, the Nobel committee was still struggling to reach the famously reclusive physicist. The announcement of his long-awaited crown was delayed by about half an hour until they decided they could wait no longer. Meanwhile, Peter Higgs sat at his favourite table in The Vintage, a seafood bar in Henderson Street, Leith, drinking a pint of real ale and considering the menu. As the committee announced that it had given the prize to François Englert and Peter Higgs “for the theoretical discovery of a mechanism that contributes to our understanding of the origin of mass of subatomic particles, and which recently was confirmed through the discovery of the predicted fundamental particle, by the ATLAS and CMS experiments at CERN’s Large Hadron Collider”, phones started going off in the Edinburgh physics department. 

Higgs finished his lunch. It seemed a little early to head home, so he decided to look in at an art exhibition. At about three o’clock he was walking along Heriot Row in Edinburgh, heading for his flat nearby, when a car pulled up near the Queen Street Gardens. “A lady in her 60s, the widow of a high-court judge, got out and came across the road in a very excited state to say, ‘My daughter phoned from London to tell me about the award’, and I said, ‘What award?’ I was joking of course, but that’s when she confirmed that I had won the prize. I continued home and managed to get in my front door with no more damage than one photographer lying in wait.” It was only later that afternoon that he finally learned from the radio news that the award was to himself and Englert. 

Suited and booted 

On arrival in Stockholm in December 2013, after a stressful two-day transit in London, Higgs learned that one of the first appointments was to visit the official tailor. The costume was to be formal morning dress in the mid-19th-century style of Alfred Nobel’s time, including elegant shoes adorned with buckles. As Higgs recalled, “Getting into the shirt alone takes considerable skill. It was almost a problem in topology.” The demonstration at the tailor’s was hopeless. Higgs was tense and couldn’t remember the instructions. On the day of the ceremony, fortunately, “I managed somehow.” Then there were the shoes. The first pair were too small, but when he tried bigger ones, they wouldn’t fit comfortably either. He explained, “The problem is that the 19th-century dress shoes do not fit the shape of one’s foot; they were rather pointy.” On the day of the ceremony both physics laureates had a crisis with their shoes. “Englert called my room: ‘I can’t wear these shoes. Can we agree to wear our own?’ So we did. We were due to be the first on the stage and it must have been obvious to everyone in the front row that we were not wearing the formal shoes.” 

Robert Brout in spirit completed a trinity of winners

On the afternoon of 10 December, nearly 2000 guests filled the Stockholm Concert Hall to see 12 laureates receive their awards from King Gustav of Sweden. They had been guided through the choreography of the occasion earlier, but on the day itself, performing before the throng in the hall, there would be first-night nerves for this once-in-a-lifetime theatre. Winners of the physics prize would be called to receive their awards first, while the others watched and could see what to expect when they were named. The scenery, props and supporting cast were already in place. These included former winners dressed in tail suits and proudly wearing the gold button stud that signifies their membership of this unique club. Among them were Carlo Rubbia, discoverer of the W and Z particles, who instigated the experimental quest for the boson and won the prize in 1984; Gerard ’t Hooft, who built on Higgs’s work to complete the theoretical description of the weak nuclear force and won in 1999; and 2004 winner Frank Wilczek, who had built on his own prize-winning work to identify the two main pathways by which the Higgs boson had been discovered.

After a 10-minute oration by the chair of the Nobel Foundation and a musical interlude, Lars Brink, chairman of the Nobel Committee for Physics, managed to achieve one of the most daunting challenges in science pedagogy, successfully addressing both the general public in the hall and the assembled academics, including laureates from other areas of science. The significance of what we were celebrating was beyond doubt: “With discovery of the Higgs boson in 2012, the Standard Model of physics was complete. It has been proved that nature follows precisely that law that Brout, Englert and Higgs created. This is a fantastic triumph for science,” Brink announced. He also introduced a third name, that of Englert’s collaborator, Robert Brout. In so doing, he made an explicit acknowledgement that Brout in spirit completed a trinity of winners. 

Brink continued with his summary history of how their work and that of others established the Standard Model of particle physics. Seventeen months earlier the experiments at the LHC had confirmed that the boson is real. What had been suspected for decades was now confirmed forever. The final piece in the Standard Model of particle physics had been found. The edifice was robust. Why this particular edifice is the one that forms our material universe is a question for the future. Brink now made the formal invitation for first Englert and then Higgs to step forward to receive their share of the award.

Higgs, resplendent in his formal suit, and comfortable in his own shoes, rose from his seat and prepared to walk to centre-stage. Forty-eight years since he set out on what would be akin to an ascent of Everest, Higgs had effectively conquered the Hillary step – the final challenge before reaching the peak – on 4 July 2012 when the existence of his boson was confirmed. Now, all that remained while he took nine steps to reach the summit was to remember the choreography: stop at the Nobel Foundation insignia on the carpet; shake the king’s hand with your right hand while accepting the Nobel prize and diploma with the other. Then bow three times, first to the king, then to the bust of Alfred Nobel at the rear of the stage, and finally to the audience in the hall.

Higgs successfully completed the choreography and accepted his award. As a fanfare of trumpets sounded, the audience burst into applause. Higgs returned to his seat. The chairman of the chemistry committee took the lectern to introduce the winners of the chemistry prize. To his relief, Higgs was no longer in the spotlight.

All in a name 

The saga of Higgs’s boson had begun with a classic image – a lone genius unlocking the secrets of nature through the power of human thought. The fundamental nature of Higgs’s breakthrough had been immediately clear to him. However, no one, least of all Higgs, could have anticipated that it would take nearly half a century and several false starts to get from his idea to a machine capable of finding the particle. Nor did anyone envision that this single “good idea” would turn a shy and private man into a reluctant celebrity, accosted by strangers in the supermarket. Some even suggested that the reason why the public became so enamoured with Higgs was the solid ordinariness of his name, one syllable long, unpretentious, a symbol of worthy Anglo-Saxon labour. 

In 2021, nine years after the discovery, we were reminiscing about the occasion when, to my surprise, Higgs suddenly remarked that it had “ruined my life”. To know nature through mathematics, to see your theory confirmed, to win the plaudits of your peers and join the exclusive club of Nobel laureates: how could all this equate with ruin? To be sure I had not misunderstood, I asked again the next time we spoke. He explained: “My relatively peaceful existence was ending. I don’t enjoy this sort of publicity. My style is to work in isolation, and occasionally have a bright idea.”   

• This is an edited extract from Elusive: How Peter Higgs Solved the Mystery of Mass, by Frank Close, published on 14 June (Basic Books, US) and 7 July (Allen Lane, UK)

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Precision measurements of the Higgs boson open the possibility to explore the moment in cosmological history when electroweak symmetry broke and elementary particles acquired mass. Ten years after the Higgs-boson discovery, it remains a possibility that the electroweak phase transition happened as a rather violent process, with a large departure from thermal equilibrium, via Higgs-bubble nucleations and collisions. This is a fascinating scenario for three reasons: it provides a framework for explaining the matter–antimatter asymmetry of the universe; it predicts the existence of at least one new weak-scale scalar field and thus is testable at colliders; and it would leave a unique signature of gravitational waves detectable by the future space-based interferometer LISA.

One major failure of the Standard Model (SM) is its inability to explain the baryon-to-photon ratio in the universe: η ≈ 6 × 10^–10. Measurements of this ratio from two independent approaches – anisotropies in the cosmic microwave background and the abundances of light primordial elements – are in beautiful agreement. In a symmetric universe, however, the prediction for η is a billion times smaller; big-bang nucleosynthesis could not have occurred and structures could not have formed. This results from strong annihilations between nucleons and antinucleons, which deplete their number densities very efficiently. Only in a universe with a primordial asymmetry between nucleons and antinucleons can these annihilations be prevented. There are many different models to explain such “baryogenesis”. Interestingly, however, the Higgs boson plays a key role in essentially all of them. 

Accidental symmetry

It is worth recalling how baryon number B gets violated by purely SM physics. B is an “accidental” global symmetry in the SM. There are no B-violating couplings in the SM Lagrangian. But the chiral nature of electroweak interactions, combined with the non-trivial topology of the SU(2) gauge theory, results in non-perturbative, B-violating processes. Technically, these are induced by extended gauge-field configurations called sphalerons, whose energy is proportional to the value of the Brout–Englert–Higgs (BEH) field. The possibility of producing these configurations is totally suppressed at zero temperature, such that B is an extremely good symmetry today. However, at high temperature, and in particular at 100 GeV or so, when the electroweak symmetry is unbroken, the baryon number is violated intensively as there is no energy cost. Since both baryons and antibaryons are created by sphalerons, charge–parity (CP) violation is needed. Indeed, as enunciated by Sakharov in 1967, a theory of baryogenesis requires three main ingredients: B violation, CP violation and a departure from equilibrium, otherwise the baryon number will relax to zero. 

The conclusion is that baryogenesis must take place either from a mechanism occurring before the electroweak phase transition (necessitating new sources of B violation beyond the SM) or from a mechanism where B-violation relies exclusively on SM sphalerons and occurring precisely at the electroweak phase transition (provided that it is sufficiently out-of-equilibrium and CP-violating). The most emblematic example in the first category is leptogenesis, where a lepton asymmetry is produced from the decay of heavy right-handed neutrinos and “reprocessed” into a baryon asymmetry by sphalerons. This is a popular mechanism motivated by the mystery of the origin of neutrino masses, but is difficult to test experimentally. The second categ­ory, electroweak baryogenesis, involves electroweak-scale physics only and is therefore testable at the LHC.

Electroweak baryogenesis requires a first-order electroweak phase transition to provide a large departure from thermal equilibrium, otherwise the baryon asymmetry is washed out. A prime example of this type of phase transition is boiling water, where bubbles of gas expand into the liquid phase. During a first-order electroweak phase transition, symmetric and broken phases coexist until bubbles percolate and the whole universe is converted into the broken phase (see “Bubble nucleation” image). Inside the bubble, the BEH field has a non-zero vacuum expectation value; outside the bubble, the electroweak symmetry is unbroken. As the wall is passing, chiral fermions in the plasma scatter off the Higgs at the phase interface. If some of these interactions are CP-violating, a chiral asymmetry will develop inside and in front of the bubble wall. The resulting excess of left-handed fermions in front of the bubble wall can be converted into a net baryon number by the sphalerons, which are unsuppressed in the symmetric phase in front of the bubble. Once inside the bubble, this baryon number is preserved as sphalerons are frozen there. In this picture, the baryon asymmetry is determined by solving a diffusion system of coupled differential equations.

New scalar required

The nature of the electroweak phase transition in the SM is well known: for a 125 GeV Higgs boson, it is a smooth crossover with no departure from thermal equilibrium. This prevents the possibility of electroweak baryogenesis. It is, however, easy to modify this prediction to produce a first-order transition by adding an electroweak-scale singlet scalar field that couples to the Higgs boson, as predicted in many SM extensions. Notably, this is a general feature of composite-Higgs models, where the Higgs boson emerges as a “pseudo Nambu–Goldstone” boson of a new strongly-interacting sector. 

An important consequence of such models is that the BEH field is generated only at the TeV scale; there is no field at temperatures above that. In the minimal composite Higgs model, the dynamics of the electroweak phase transition can be entirely controlled by an additional scalar Higgs-like field, the dilaton, which has experimental signatures very similar to the SM Higgs boson. In addition, we expect modifications of the Higgs boson’s couplings (to gauge bosons and to itself) induced by its mixing with this new scalar. LHC Run 3 thus has excellent prospects to fully test the possibility of a first-order electroweak phase transition in the minimal composite Higgs model.

The properties of the additional particle required to modify the electroweak phase transition also suggest new sources of CP violation, which is welcome as CP-violating SM processes are not sufficient to explain the baryon asymmetry. In particular, this would generate non-zero electric dipole moments (EDMs). The most recent bounds on the electron EDM from the ACME experiment in the US placed stringent constraints on a large number of electroweak baryogenesis models, in particular two-Higgs-doublet models. This is forcing theorists to consider new paths such as dynamical Yukawa couplings in composite Higgs models, a higher temperature for the electroweak phase transition, or the use of dark particles as the new source of CP violation. Here, there is a tension. To evade the stringent EDM bounds, the new scalar has to be heavy. But if it is too heavy, it reheats the universe too much at the end of the electroweak phase transition and washes out the just-produced baryon asymmetry. During the next decade, precise measurements of the Higgs boson at the LHC will enable a definitive test of the electroweak baryogenesis paradigm. 

Gravitational waves 

There is a further striking consequence of a first-order electroweak phase transition: fluid velocities in the vicinity of colliding bubbles generate gravitational waves (GWs). Today, these would appear as a stochastic background that is homogeneous, isotropic, Gaussian and unpolarised – the superposition of GWs generated by an enormous number of causally-independent sources, arriving at random times and from random directions. It would appear as noise in GW detectors with a frequency (in the mHz region) corresponding to the typical inverse bubble size, redshifted to today (see “Primordial peak” figure). There has been a burst of activity in the past few years to evaluate the chances of detecting such a peaked spectrum at the future space interferometer LISA, opening the fascinating possibility of learning about Higgs physics from GWs. 

The results from the LHC so far have pushed theorists to question traditional assumptions about where new physics beyond the SM could lie. Electroweak baryogenesis relies on rather conservative and minimal assumptions, but more radical approaches are now being considered, such as the intriguing possibility of a cosmological interplay between the Higgs boson and a very light and very weakly-coupled axion-like particle. Through complementarity of studies in theory, collider experiments, EDMs, GWs and cosmology, probing the electroweak phase transition will keep us busy for the next two decades. There are exciting times ahead.

The post Electroweak baryogenesis appeared first on CERN Courier.

What impact did the discovery of the Higgs boson have on your work? 

It was huge because before then it was possible that maybe there was no Higgs. You could have some kind of dynamical symmetry breaking, or maybe a heavy Higgs, at 400 GeV say, which would be extremely interesting but completely different. So once you knew that the Higgs was at the same mass scale as the W and the Z, our thinking changed because that comes out of only a certain kind of model. And of course once you had it, everyone, including myself, was motivated to calculate everything we could. 

I am working on how you tease out new physics from the Higgs boson. It’s the idea that even if we don’t see new particles at the LHC, precision measurements of the Higgs couplings are going to tell us something about what is happening at very high energy scales. I’m using what’s called an effective field theory approach, which is the standard these days for trying to find out what we can learn from combining Higgs measurements with other types of measurements, such as gauge-boson pair production and top-quark physics. 

Aside from the early formal work, what was the role of Standard Model calculations in the discovery of the Higgs boson?

You had to know what you were looking for, because there’s so many events at the LHC. Otherwise, it would be like looking for a needle in a haystack. The Higgs was discovered, for example, by its decay to two photons and there are millions of two-photon events at the LHC that have nothing to do with the Higgs. Theory told you how to look for this particle, and I think it was really important that a trail was set out to follow. This involves calculating how often you make a Higgs boson and what the background might look like. It wasn’t until the late 1980s that people began taking this seriously. It was really the Superconducting Super Collider that started us thinking about how to observe a Higgs at a hadron collider. And then there were the LEP and Tevatron programmes that actively searched for the Higgs boson. 

To what order in perturbation theory were those initial calculations performed?

For the initial searches you didn’t need the complicated calculations because you weren’t looking for precision measurements such as those required at the Z-pole, for example. You really just needed the basic rate and background information. We weren’t inspired to do higher order calculations until later in the game. When I was a postdoc at Berkeley in 1986, that’s when I really started to calculate things about the Higgs. But there was a long gap between the time when the Brout–Englert–Higgs mechanism was proposed and when people really started doing some hard calculations. There’s the famous paper in 1976 by Ellis, Gaillard and Dimopoulos that calculated how the Higgs might be observed, but in essence it said: why bother looking for this thing, we don’t know where it is! So people were thinking we could see the Higgs in kaon decays, if it was very light, and in other ways, and were looking at the problem in a global kind of way. 

Was this what drove your involvement with The Higgs Hunter’s Guide in 1990?

We were further along in terms of calculating things precisely by then, and I suppose there was a bit of a generation gap. It was a wonderful collaboration to produce the guide. We still went through the idea of how you would find the Higgs at different energy scales because we still had no idea where it was. The calculations went into high gear around that time, which was well before the Higgs was discovered. Partly it was the motivation that we were pretty sure we would see it at the LHC. But partly it was developments in theory which meant we could calculate things that we never would have imagined was possible 30 years earlier. The capability of theorists to calculate has grown exponentially. 

What have these improvements been?

It’s what they call the next-to-next-to-leading order (NNLO) revolution – a new frontier in perturbative QCD where diagrams with two extra emissions of real or extra loops of virtual partons are accounted for. These were new mathematical techniques for evaluating the integrals that come into the quantum field theory, so not just turning the crank computationally but really an intellectual advance in understanding the structure of these calculations. It started with Bern, Dixon and Kosower, who understood the needed amplitudes in a formal way. This enabled all sorts of calculations, and now we have N³LO calculations for certain Higgs-boson production modes. 

What is driving greater precision on Higgs calculations today?

Actually it’s really exciting because at the high-luminosity LHC (HL-LHC), experimentalists will be limited in their understanding of the Higgs boson by theory – the theory and experimental uncertainties will be roughly the same. This is truly impressive. You might think that these higher order corrections, which have quite small errors, are enough but they need to be even smaller to match the expected experimental precision. As theorists we have to keep going and do even better, which from my point of view is wonderful. It’s the synergy between experiment and theory that is the real story. We’re co-dependent. Even now, theory is not so different from ATLAS and CMS in terms of precision. Theory errors are hard things to pin down because you never really know what they are. Unlike an absolute statistical uncertainty, they’re always an estimate. 

How do the calculations look for measurements beyond the LHC? 

It’s a very different situation at e⁺e^– colliders compared to hadron colliders. The LHC runs with protons containing gluons, so that’s why you need the higher order corrections. At a future e⁺e⁺ collider, you need higher-order corrections but they are much more straightforward because you don’t have parton distribution functions to worry about. We know how to do the calculations needed for an e⁺e^– Future Circular Collider, for example, but there is not a huge community of people working on them. That’s because they are really hard: you can’t just sit down and do them as a hobby, they really need a lot of skills. 

You are currently leading the Higgs properties working group of the current Snowmass planning exercise. What has been the gist of discussions? 

This is really exciting because our job has essentially been to put together the pieces of the puzzle after the European strategy update in 2020. That process did a very careful job of looking at the future Higgs programme, but there have been developments in our understanding since then. For example, the muon collider might be able to measure the Higgs couplings to muons very precisely, and there has been some good work on how to measure the couplings to strange quarks, which is very hard to do. 

I would like to see an e⁺e^– collider built somewhere, anywhere. In point of fact, when you look at the proposals they’re roughly the same in terms of Higgs physics. This was clear from the European strategy report and will be clear from the upcoming Snowmass report. Personally, I don’t much care whether there is a precision of 1% or 1.5% on some coupling. I care that you can get down to that order of magnitude, and that e⁺e^– machines will significantly improve on the precision of HL-LHC measurements. The electroweak programme of large circular e⁺e^– colliders is extremely interesting. At the Z-pole you get some very precise measurements of Standard Model quantities that feed into the whole theory because everything is connected. And at the WW threshold you get very precise measurements in the effective field theory of things that connect the Higgs and WW pairs. As a theorist, it doesn’t make sense to think of the Higgs in a vacuum. The Higgs is part of this whole electroweak programme. 

What are the prospects for finding new physics via the Higgs?

The fact that we haven’t seen anything unexpected yet is probably because we haven’t probed enough. I’m absolutely convinced we are going to see something, I just don’t know what (or where) it is. So I can’t believe in the alternative “nightmare” scenario of a Standard-Model Higgs and nothing else because there are just so many things we don’t know. You can make pretty strong arguments that we haven’t yet reached the precision where we would expect to see something new in precision measurements. It’s a case of hard work.  

What’s next in the meantime?

The next big thing is measuring two Higgs bosons at a time. That’s what theorists are super excited about because we haven’t yet seen the production of two Higgses and that’s a fundamental prediction of our theory. If we don’t see it, and it’s extremely difficult to do so experimentally, it tells us something about the underlying model. It’s a matter of getting the statistics. If we actually saw it, then we would do more calculations. For the trilinear Higgs coupling we now have a complete calculation at next-to-leading order, which is a real tour de force. The calculations are sufficient for a discovery, and because it’s so rare it’s unlikely we will be doing precision measurements, so it is probably okay for the foreseeable future. For the quartic coupling there are some studies that suggest you might see it at a 100 TeV hadron collider.

With all the Standard Model particles in the bag, does theory take more of a back seat from here? 

The hope is that we will see something that doesn’t fit our theory, which is of course what we’re really looking for. We are not making these measurements at ever higher precisions for the sake of it. We care about measuring something we don’t expect, as an indicator of new physics. The Higgs is the only tool we have at the moment. It’s the only way we know how to go.

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The CMS collaboration has substantially improved on its measurement of the top-quark mass. The latest result, 171.77 ± 0.38 GeV, presented at CERN on 5 April, represents a precision of about 0.22% – compared to the 0.36% obtained in 2018 with the same data. The gain comes from new analysis methods and improved procedures to consistently treat uncertainties in the measurement simultaneously.

As the heaviest elementary particle, precise knowledge of the top-quark mass is of paramount importance to test the internal consistency of the Standard Model. Together with accurate knowledge of the masses of the W and Higgs bosons, the top-quark mass is no longer a free parameter but a clear prediction of the Standard Model. Since the top-quark mass dominates higher-order corrections to the Higgs-boson mass, a precise measurement of the top mass also places strong constraints on the stability of the electroweak vacuum (see The Higgs and the fate of the universe). 

Since its discovery at Fermilab in 1995, the mass of the top quark has been measured with increasing precision using the invariant mass of different combinations of its decay products. Measurements by the Tevatron experiments resulted in a combined value of 174.30 ± 0.65 GeV, while the ATLAS and CMS collaborations measured 172.69 ± 0.48 GeV and 172.44 ± 0.48 GeV, respectively, from the combination of their most precise results from LHC Run 1 recorded at a centre-of-mass energy of 8 TeV. The latter measurement achieved a relative precision of about 0.28%. In 2019, the CMS collaboration also experimentally investigated the running of the top quark mass – a prediction of QCD that causes the mass to vary as a function of energy – for the first time at the LHC. 

The LHC produces top quarks predominantly in quark–antiquark pairs via gluon fusion, which then decay almost exclusively to a bottom quark and a W boson. Each tt event is classified by the subsequent decay of the W bosons. The latest CMS analysis uses semileptonic events – where one W decays into jets and the other into a lepton and a neutrino – selected from 36 fb^–1 of Run 2 data collected at a centre-of-mass energy of 13 TeV. Five kinematical variables, as opposed to up to three in previous analy­ses, were used to extract the top-quark mass. While the extra information in the fit improved the precision of the measurement in a novel and unconventional way, it made the analysis significantly more complicated. In addition, the measurement required an extremely precise calibration of the CMS data and an in-depth understanding of the remaining experimental and theoretical uncertainties and their interdependencies. 

The final result, 171.77 ± 0.38 GeV, which includes 0.04 GeV statistical uncertainty, is a considerable improvement compared to all previously published top-quark mass measurements and supersedes the previously published measurement in this channel using the same data set. 

“The cutting-edge statistical treatment of uncertainties and the use of more information have vastly improved this new measurement from CMS,” says Hartmut Stadie of the University of Hamburg, who contributed to the result. “Another big step is expected when the new approach is applied to the more extensive dataset recorded in 2017 and 2018.”

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Due to its connection to the process of electroweak symmetry breaking, the Higgs boson plays a special role in the Standard Model (SM). Its properties, such as its mass and its couplings to fermions and bosons, have been measured with increasing precision. For these reasons, the Higgs boson has become an ideal tool to conduct new-physics searches. Prominent examples are direct searches for new heavy particles decaying into Higgs bosons or searches for exotic decays of the Higgs boson. Such phenomena have been predicted in many extensions of the SM motivated by long-standing open questions, including the hierarchy problem, dark matter and electroweak baryogenesis. Examples of new particles that couple to the Higgs boson are heavy vector bosons (as in models with Higgs compositeness or warped extra dimensions) and additional scalar particles (as in supersymmetric models or axion models).

Searches for resonances

The ATLAS collaboration recently released results of a search for a new heavy particle decaying into a Higgs and a W boson. The search was performed by probing for a localised excess in the invariant mass distribution of the ℓνbb final state. As no such excess was found, upper limits at 95% confidence level were set on the production-cross section times branching ratio of the new heavy resonance (figure 1). The results were also interpreted in the context of the heavy vector triplet (HVT) model, which extends the SM gauge group by an additional SU(2) group, to constrain the coupling strengths of heavy vector bosons to SM particles. In two HVT benchmark models, W′ masses below 2.95 and 3.15 TeV are excluded.

Rare or exotic decays are excellent candidates to search for weakly coupled new physics. The Higgs boson is particularly sensitive to such new physics owing to its narrow total width, which is three orders of magnitude smaller than that of the W and Z bosons and the top quark. Several searches for exotic decays of the Higgs boson have been carried out by ATLAS, and they may be broadly classified as those scenarios where the possible new daughter particle decays promptly to SM particles, and those where it would be long-lived or stable.

A recent search from ATLAS targeted exotic decays of the Higgs boson into a final state into four electrons or muons, which benefit from a very clean experimental signature. Although a signal was not observed, the search put stringent constraints on decays to new light scalar bosons – particularly in the low mass range of a few GeV – and to new vector bosons, dubbed dark Z bosons or dark photons, in the mass range up to a few tens of GeV. Depen­ding on the new-physics model, this search can exclude branching ratios of the Higgs boson to new particles as low as O(10^–5).

Invisibles

Another interesting possibility is the case where the Higgs boson decays to particles that are invisible in the detector, such as dark-matter candidates. To select such events, different strategies are pursued depending on the particles produced in association with the Higgs boson. The most powerful channel for such a search is the vector-boson fusion production process, where two energetic jets from quarks are produced with large angular separation along­side the invisibly decaying Higgs boson (figure 2). Another sensitive channel is the associated production of a Higgs boson with a Z boson that decays to a pair of leptons. Improvements in background predictions have made it possible to reach a sensitivity down to 10% on the branching ratio of invisible Higgs-boson decays, while the corresponding observed limit amounts to 15%.

These searches will greatly benefit from the large datasets expected in Run 3 and later High-Luminosity LHC runs, and will enable searches for even more feeble couplings of new particles to the Higgs boson.

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This webinar is focused on the technology of the superconducting magnets used in the LHC. After reviewing the equations for an electromagnet, we show how superconductivity enables much larger magnetic fields in very compact devices, thanks to the possibility of increasing the current density in the windings by more than two order of magnitudes with respect to resistive conductors. We then outline the development of superconducting accelerator magnets from the ISR quadrupoles, up to the LHC and beyond.

We conclude by describing the successive increases of LHC energy since 2008 up to the 6.8 TeV per beam recently achieved, and show how the control of field imperfections has been an essential element for reaching the ultimate luminosity.

Ezio Todesco was born in Bologna Italy, where he got a PhD in physics. In the 90’s, after a master thesis at CERN, he worked at the Italian national institute of nuclear physics (INFN) on topics related to nonlinear dynamics of particle accelerators, and long-term stability in the planned Large Hadron Collider. He joined the magnet group at CERN in 1998, and has been in charge of the field quality follow-up of the LHC main dipoles and quadrupole during the five-year-long magnet production. After the completion of the production phase, he has been in charge of the magnetic field model of the LHC, following the initial commissioning and the successive energy increases up to 13 TeV centre of mass. Then, he has been involved in the studies of the LHC luminosity upgrade, and he leads the interaction region magnets for HL-LHC since the beginning of the project in 2015.

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Within the Standard Model (SM), the Higgs boson is predicted to interact with (or couple to) quarks with a strength proportional to their mass. By measuring these interaction strengths, physicists can test this prediction and gain insight into possible physics beyond the SM, where such couplings can be modified. In a new analysis exploiting the full Run-2 dataset, the ATLAS collaboration experimentally excludes new-physics scenarios which predict that decays of the Higgs boson to a pair of charm quarks (H → cc) are as frequent as those to bottom quarks (H → bb). 

The search for H → cc is hampered by abundant background processes. In order to identify charm–quark signatures, a new multivariate classification method was developed to identify charm hadrons within jets, while simultaneously reducing the probability of misidentifying jets originating from a bottom quark. To maximise the sensitivity to the signal, events with one or two charm-tagged jets were selected. Background processes were further suppressed by selecting Higgs-boson events produced together with a weak boson, VH(cc), where the weak boson (V = W or Z) decays to 0, 1 or 2 electrons or muons. In total, 44 regions were fitted simultaneously to measure the H → cc process. 

In the SM, the H → cc process accounts for only 3% of all Higgs-boson decays. The ATLAS analysis found no significant sign for this process in the data, setting an upper limit on the rate of the VH(cc) process 26 times the SM rate at 95% confidence level. This limit constrains the Higgs-to-charm coupling strength to less than 8.5 times the predicted SM value. The analysis strategy is validated by measuring events with two vector bosons that contain the decay of a W boson to one charm quark, VW(cq), or the decay of a Z boson to two charm quarks, VZ(cc), whose rates are found to agree with the predictions. The combined dijet-mass distribution, after subtraction of the backgrounds, is shown in figure 1.

Since H → cc and H → bb decays lead to very similar signatures in the ATLAS detector, a combined analysis of both processes is key to a common interpretation. The multivariate classification method is used to identify jets as originating from a bottom quark, a charm quark or lighter quarks. Since a fraction of the H → bb events passes the selection criteria of the H → cc analysis and vice versa, the individual analyses are designed to ensure that no collision events are counted twice. This orthogonality between the analyses enabled a simultaneous measurement of the two processes for the first time.

Within the SM, the ratio of the couplings of bottom and charm quarks to the Higgs boson is given by their mass ratio: m_b/m_c = 4.578 ± 0.008, obtained from lattice-QCD calculations. With its novel combination of H → cc and H → bb decays, the ATLAS analysis excludes the hypothesis that the Higgs-boson interaction with charm quarks is stronger than or equal to the interaction with bottom quarks at 95% confidence level (figure 2). For the first time, this measurement establishes that the Higgs-boson coupling is smaller for charm quarks than for bottom quarks.

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Around 140 physicists convened for one of the first in-person international particle-physics conferences in the COVID-19 era. The Moriond conference on electroweak interactions and unified theories, which took place from 12 to 19 March on the Alpine slopes of La Thuile in Italy, was a wonderful chance to meet friends and colleagues, to have spontaneous exchanges, to listen to talks and to prolong discussions over dinner.

The LHC experiments presented a suite of impressive results based on increasingly creative and sophisticated analyses, including first observations of rare Standard Model (SM) processes and the most recent insights in the search for new physics. ATLAS reported the first observation of the production of a single top quark in association with a photon, a rare process that is sensitive to the existence of new particles. CMS observed for the first time the electroweak production of a pair of opposite-sign W bosons, which is crucial to investigate the mechanism of electroweak symmetry breaking. The millions of Higgs bosons produced so far at the LHC have enabled detailed measurements and open a new window on rare phenomena, such as the rate of Higgs-boson decays to a charm quark–antiquark pair. CMS presented the world’s most stringent constraint on the coupling between the Higgs boson and the charm quark, improving their previous measurement by more than a factor of five, while ATLAS measurements demonstrated that it is weaker than the coupling between the Higgs boson and the bottom quark. On the theory side, various new signatures for extended Higgs sectors were proposed.

The LHC experiments presented a suite of impressive results based on increasingly creative and sophisticated analyses

Of special interest is the search for heavy resonances decaying to high-mass dijets. CMS reported the observation of a spectacular event with four high transverse-momentum jets, forming an invariant mass of 8 TeV. CMS now has two such events, exceeding the SM prediction with a local significance of 3.9σ, or 1.6σ when taking into account the full range of parameter space searched. Moderate excesses with a global significance of 2–2.5σ were observed in other channels, for example in a search by ATLAS for long-lived, heavy charged particles and in a search by CMS for new resonances that decay into two tau pairs. Data from Run 3 and future High-Luminosity LHC runs will show whether these excesses are statistical fluctuations of the SM expectation or signals of new physics.

Flavour anomalies

The persistent set of tensions between predictions and measurements in semi-leptonic b → s ℓ⁺ℓ^– decays (ℓ = e, μ) were much discussed. LHCb has used various decay modes mediated by strongly suppressed flavour-changing neutral currents to search for deviations from lepton flavour universality (LFU). Other measurements of these transitions, including angular distributions and decay rates (for which the predictions are affected by troublesome hadronic corrections) as well as analyses of charged-current b→ cτ^– ν decays from BaBar, Belle and LHCb also show a consistent pattern of deviations from LFU. While none are individually significant enough to constitute clear evidence of new physics, they represent an intriguing pattern that can be explained by the same new-physics models. Theoretical talks on this subject proposed additional observables (based on baryon decays or leptons at high transverse momenta) to get more information on operators beyond the SM that would contribute to the anomalies. Updates from LHCb on several b → s ℓ⁺ℓ^–-related measurements with the full Run 1 and Run 2 datasets are eagerly awaited, while Belle II also has the potential to provide essential independent checks. The integrated SuperKEKB luminosity has now reached a third of the full Belle dataset, with Belle II presenting several impressive new results. These include measurements of the b → s ℓ⁺ℓ^– decay branching fractions with a precision limited by the sample size and precise measurements of charmed particle lifetimes, including the individual world-best D and Λ⁺_c  lifetimes, proving the excellent tracking and vertexing capabilities of the detector.

The other remarkable deviation from the SM prediction is the anomalous magnetic moment of the muon (g–2)_μ, for which the SM prediction and the recent Fermilab measurement stand 4.2σ apart – or less, depending on whether the hadronic vacuum polarisation contribution to (g–2)_μ is calculated using traditional “dispersive” methods or a recent lattice QCD calculation. The jury is still out on the theory side, but the ongoing analysis of Run 2 and Run 3 data at Fermilab will soon reduce the statistical uncertainty by more than a factor of two. The hottest issues in neutrinos – in particular their masses and mixing – were reviewed. The current leading long-baseline experiments – NOvA in the US and T2K in Japan – have helped to refine our understanding of oscillations, but the neutrino mass hierarchy and CP-violating phase remain to be determined. A great experimental effort is also being devoted to the search for neutrinoless double-beta decay (NDBD) which, if found, would prove that neutrinos are Majorana particles and have far-reaching implications in cosmology and particle physics. The GERDA experiment at Gran Sasso presented its final result, placing a lower limit on the NDBD half-life of 1.8 × 10²⁶ years.

While tensions between solar-neutrino bounds and the reactor antineutrino anomaly are mostly resolved, the gallium anomaly remains

Another very important question is the possible existence of “sterile” neutrinos that do not participate in weak interactions, for which theoretical motivations were presented together with the robust experimental programme. The search for sterile neutrinos is motivated by a series of tensions in short-baseline experiments using neutrinos from accelerators (LSND, Mini-BooNE), nuclear reactors (the “reactor antineutrino anomaly”) and radioactive sources (the “gallium anomaly”), which cannot be accounted for by the standard three-neutrino framework. In particular, MicroBooNE has neither confirmed nor excluded the electron-like low-energy excess observed by MiniBooNE. While tensions between solar-neutrino bounds and the reactor antineutrino anomaly are mostly resolved, the gallium anomaly remains.

Dark matter and cosmology

The status of dark-matter searches both at the LHC and via direct astrophysical searches was comprehensively reviewed. The ongoing run of the 5.9 tonne XENONnT experiment, for example, should elucidate the 3.3σ excess observed by XENON1T in low-energy electron recoil events. The search for axions, which provide a dark-matter candidate as well as a solution to the strong-CP problem, cover different mass ranges depending on the axion coupling strength. The parameter space is wide, and Moriond participants heard how a discovery could happen at any moment thanks to experiments such as ADMX. The status of the Hubble tension was also reviewed.

The many theory talks described various beyond-the-SM proposals – including extra scalars and/or fermions and/or gauge symmetries – aimed at explaining LFU violation, (g–2)_μ, the hierarchy among Yukawa couplings, neutrino masses and dark matter. Overall, the broad spectrum of informative presentations brilliantly covered the present status of open questions in phenomenological high-energy physics and shine a light on the many rich paths that demand further exploration.

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Ever since the W boson was discovered at CERN’s SppS four decades ago, successive collider experiments have pinned down its mass at increasing levels of precision. Unlike the fermion masses, the W mass is a clear prediction of the Standard Model (SM). At lowest order in electroweak theory, it depends solely on the mass of the Z boson and the value of the weak mixing angle. But higher-order corrections introduce an additional dependence on the gauge-boson couplings and the masses of other SM particles, in particular the heavy top quark and Higgs boson. With the precision of electroweak calculations now exceeding that of direct measurements, better knowledge of the measured W mass provides a vital test of the SM’s consistency.

The immediate reaction was silence

Chris Hays

A new measurement by the CDF collaboration based on data from the former Tevatron collider at Fermilab throws a curveball into this picture. Published today in Science, the CDF W-mass measurement – the most precise to date – stands 7σ from the SM prediction, upsetting decades of steady convergence between experiment and theory.

“I would say the immediate reaction was silence,” says Chris Hays, one of the CDF analysis leads, of the moment the measurement was unblinded on 19 November 2020. “Then there was some discussion to ensure the unblinding worked, i.e. that the value was correct, and to decide what would be the next steps.”

Long slog
CDF physicists have been measuring the mass of the W boson for more than 30 years via its decays to a lepton and a neutrino. In 2012, shortly after the Tevatron shut down, CDF published a W mass of 80,387 ± 12 (stat) ± 15 (syst) MeV based on 2.2 fb^-1 of data, which significantly exceeded the precision of all previous measurements at that time combined. After 10 years of careful analysis and scrutiny of the full Tevatron dataset (8.8 fb^-1, corresponding to about 4.2 million W-boson candidates), and taking into account an improved understanding of the detector and advances in the theoretical and experimental understanding of the W’s interactions with other particles, the new CDF result is twice as precise: 80,433.5 ± 6.4 (stat) ± 6.9 (syst) MeV.

In addition to the four-fold increase in statistics, the measurement benefits from a better understanding of systematic uncertainties. One significant change concerns the proton/antiproton parton distribution functions (PDFs), where the addition of LHC data to the PDF fits has reduced the uncertainty from 10 MeV to 3.9 MeV while also slightly raising the central value of the 2012 result.

“The 2012 and 2022 CDF values are in agreement at the level of two sigma accounting for the fact that approximately 25% of the events are in common, so the internal tension is not so significant,” explains CDF collaborator Mark Lancaster, who was an internal reviewer for the result. “But the tension with other results — particularly ATLAS at 80,370 ± 19 MeV and the SM at 80,357 ± 6 MeV — is significant. Many people from the LHC, Tevatron and theory community are presently working together to combine the results from the Tevatron, LHC and LEP and understand the correlations between them, e.g. in the PDFs and some of the higher order QCD and QED effects.”

It’s now up to theorists and other experiments to follow up on the CDF result, comments CDF co-spokesperson David Toback. “If the difference between the experimental and expected value is due to some kind of new particle or subatomic interaction, which is one of the possibilities, there’s a good chance it’s something that could be discovered in future experiments,” he says.

Cross checks
Results from the LHC experiments are crucial to enable a deeper understanding. One of the challenges  in measuring the W mass in high-rate proton-proton collisions at the LHC is event “pile-up”, which makes it hard to reconstruct the missing transverse energy from neutrinos. The higher collision energy at the LHC also means W bosons are produced with larger transverse momenta with respect to the beam axis, which needs to be properly modeled in order to measure the W boson mass precisely.

It takes years to build up the knowledge of the detector necessary to be able to address all the issues satisfactorily

Florencia Canelli

The ATLAS collaboration published the first high-precision measurement of the W mass at the LHC in 2018 based on data collected at a centre-of-mass energy of 7 TeV, and is currently working on new measurements. In September, based on 2016 data, LHCb published its first measurement of the W mass: 80,354 ± 32 MeV, and estimates that an uncertainty of 20 MeV or less is achievable with existing data. CMS is also proceeding with analyses that should soon see its first public result. “It’s an important measurement of our physics programme,” says CMS physics co-cordinator Florencia Canelli. “As the CDF result shows, precision physics can be a challenging and lengthy process: it takes a very long time to understand all aspects of the data to the level of precision required for a competitive W-mass measurement, and it takes years to build up the knowledge of the detector necessary to be able to address all the issues satisfactorily.”

The CDF result reiterates the central importance of precision measurements in the search for new physics, describe Claudio Campagnari (UC Santa Barbara) and Martijn Mulders (CERN) in a Perspective article accompanying the CDF paper. They point to the increased precision that will be available at the High-Luminosity LHC and the capabilities of future facilities such as the proposed Future Circular Collider, the e⁺e^– mode of which “would offer the best prospects for an improved W-boson mass measurement, with a projected sensitivity of 7 ppm”. Such a measurement would also demand the SM electroweak calculations be performed at higher orders, a challenge firmly in the sights of the theory community.

Following the 2012 discovery of the Higgs boson, it is not easy to tweak the SM parameters without ruining the excellent agreement with numerous measurements. Furthermore, unlike calculations such as that of the muon anomalous magnetic moment, which relies on significant input from QCD, the prediction of the W mass relies mostly on “cleaner” electroweak computations. Surveying possible new physics that could push the W mass to higher values than expected, the CDF paper points to hypotheses that offer a deeper understanding of the Higgs field, from which the SM particles get their masses. These include supersymmetry and Higgs-boson compositeness, both of which include a potential source of dark matter.

“Supersymmetry could make a significant change to the SM prediction of the W mass, although it seems difficult to explain as big an effect as seen experimentally,” says theorist John Ellis. “But one prediction I can make with confidence is a tsunami of arXiv papers in the weeks ahead.”

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Two fundamental characteristics of the Higgs boson (H) that have yet to be measured precisely are its self-coupling λ, which indicates how strongly it interacts with itself, and its quartic coupling to the vector bosons, which mediate the weak force. These couplings can be directly accessed at the LHC by studying the production of Higgs-boson pairs, which is an extremely rare process occurring about 1000 times less frequently than single-H production. However, several new-physics models predict a significant enhancement in the HH production rate compared to the Standard Model (SM) prediction, especially when the H pairs are very energetic, or boosted. Recently, the CMS collaboration developed a new strategy employing graph neural networks to search for boosted HH production in the four-bottom-quark final state, which is one of the most sensitive modes currently under examination.

H pairs are produced primarily via gluon and vector-boson fusion. The former production mode is sensitive to the self-coupling, while the latter probes the quartic coupling involving a pair of weak vector bosons and two Higgs bosons. The extracted modifiers of the coupling-strength parameters, κ_λ and κ_2V, quantify their strengths relative to the SM expectation.

This latest CMS search targets both production modes and selects two Higgs bosons with a high Lorentz boost. When each Higgs boson decays to a pair of bottom quarks, the two quarks are reconstructed as a single large-radius jet. The main challenge is thus to identify the specific H jet while rejecting the background from light-flavour quarks and gluons. Graph neural networks, such as the ParticleNet algorithm, have been shown to distinguish successfully between real H jets and background jets. Using measured properties of the particles and secondary vertices within the jet cone, this algorithm treats each jet as an unordered set of its constituents, considers potential correlations between them, and assigns each jet a probability to originate from a Higgs-boson decay. At an H-jet selection efficiency of 60%, ParticleNet rejects background jets twice as efficiently as the previous best algorithm (known as DeepAK8). A modified version of this algorithm is also used to improve the H-jet mass resolution by nearly 40%.

Using the full LHC Run-2 dataset, the new result excludes an HH production rate larger than 9 times the SM cross-section at 95% confidence level, versus an expected limit of 5. This represents an improvement by a factor of 30 compared to the previous best result for boosted HH production. The analysis yields a strong constraint on the HH production rate and κ_λ, and the most stringent constraint on κ_2V to date, assuming all other H couplings to be at their SM values (see figure 1). For the first time, and with the assumption that the other couplings are consistent with the SM, the result excludes the κ_2V = 0 scenario at over five standard deviations, confirming the existence of a quartic coupling between two vector bosons and two Higgs bosons. This search paves the way for a more extensive use of advanced machine-learning techniques, the exploration of the boosted HH production regime, and further investigation into the potentially anomalous character of the Higgs boson in Run 3 and beyond.

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The discovery of the Higgs boson and the comprehensive measurements of its properties provide a strong indication that the mechanism of electroweak symmetry breaking (EWSB) is compatible with the one predicted by Brout, Englert and Higgs (BEH) in 1964. But there remain unprobed features of EWSB, chiefly whether the form of the BEH potential follows the predicted “Mexican hat” shape. One of the parameters that determines the form of the BEH potential is the Higgs boson’s trilinear self-coupling, λ. Experimentally, this fundamental parameter can be measured via Higgs-boson pair (HH) production, where a single virtual Higgs boson splits into two Higgs bosons. However, such a measurement is very challenging as the Standard Model (SM) HH production cross-section is more than 1000 times lower than that of single Higgs-boson production.

Beyond the SM (BSM) physics with modified or new Higgs-boson couplings could lead to significantly enhanced HH production. Some BSM scenarios predict new heavy particles that may lead to resonant HH production, contrary to the non-resonant production featured by the triple-Higgs-boson coupling. New ATLAS results set tight constraints on both the non-resonant and resonant scenarios, showing that the boundaries of what can be achieved with the current and future LHC datasets can be significantly pushed.

The ATLAS collaboration recently released results of searches for HH production in three final states – bbγγ, bbττ and 4b (where one Higgs boson decays into two b-quarks and the other into two photons, two tau-leptons or two b-quarks) and their combination, exploiting the full LHC Run-2 dataset. The first two analyses target both resonant and non-resonant HH production, while the 4b analysis targets only resonant HH production. These three channels are the most sensitive final states in each scenario. The three decay modes of the second Higgs boson provide good sensitivity in different kinematic regions, so that the analyses are highly complementary. The HH → bbγγ process has the lowest branching ratio but high efficiency to trigger and reconstruct photons, as well as an excellent diphoton mass resolution, leading to the best sensitivity at low HH invariant masses. The HH → 4b final state has the highest branching ratio but suffers from the requirement to impose high transverse momentum b-jet trigger thresholds, the ambiguity in the Higgs boson reconstruction and the large multijet background. However, it provides the best sensitivity at high HH invariant masses. Finally, the HH → bbττ decay has a moderate branching ratio as well as a moderate background contamination, giving the best sensitivity in the intermediate HH mass range. 

BSM physics with new Higgs-boson couplings could lead to significantly enhanced HH production

With the latest analyses, a remarkably stringent observed (expected) upper limit of 3.1 (3.1) times the SM prediction on non-resonant HH production was obtained at 95% confidence level (CL). The coupling strength of the Higgs boson trilinear self-coupling in units of the SM value κ_λ is observed (expected) to be constrained between –1.0 and 6.6 (–1.2 and 7.2) at 95% CL (see figure 1). These are the world’s tightest constraints obtained on this process. The observed (expected) exclusion limits at 95% CL on the resonant HH production cross-section range between 1.1 and 595 fb (1.2 and 392 fb) for resonance masses between 250 and 5000 GeV. 

The sensitivity of the current analyses is still limited by statistical uncertainties and is expected to improve significantly with the future luminosity increase during LHC Run 3 and the HL-LHC programme. A comparison between the current results and previous partial Run-2 dataset results has shown that an improvement by more than a factor of three on the limits is achieved. A factor of two was expected from the larger dataset, and the remaining improvements arise from better object reconstruction and identification techniques, and new analy­sis methods. 

These latest results inspire confidence that the observation of the SM HH production and a precise measurement of the Higgs-boson trilinear self-coupling may be possible at the HL-LHC.

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The LHC was built in the 27 km tunnel originally excavated for LEP, the highest energy electron–positron collider ever built. Designed to study the carriers of the weak force, LEP’s greatest legacy is the accuracy with which it pinned down the properties of the Z boson. Among the highlights is the measurement of the Z boson’s invisible width and decay branching fraction, which was used to deduce that there are three, and only three, species of light neutrinos that couple to the Z boson. This measurement of the Z-boson invisible width from LEP has remained the most precise for two decades.

This precise measurement of the Z-boson invisible width is the first of its kind at a hadron collider

In a bid to provide an independent and complementary test of the Standard Model (SM) at a new energy regime, CMS has performed a precise measurement of the Z-boson invisible width – the first of its kind at a hadron collider. The analysis uses the experimental signature of a very energetic jet accompanied by large missing transverse momentum to select events where the Z boson decays predominantly to neutrinos. The invisible width is then extracted from the well-known relationship between the Z-boson coupling to neutrinos and its coupling to muons and electrons. 

While the production of a pair of neutrinos occurs through a pure Z interaction, the production of a pair of charged leptons can also occur through a virtual photon. The contribution of virtual photon exchange and the interference between photon and Z-boson exchange are determined to be less than 2% for a dilepton invariant mass range of 71–111 GeV, and was accounted for to allow the collaboration to compare the results directly to the Z’s decay to neutrinos. 

Figure 1 shows the missing transverse momentum distribution for the three key regions contributing to this measurement: the jets-plus-missing-transverse-momentum region; the dimuon-plus-jets region; and the dielectron-plus-jets region. For the dilepton regions, selected muons and electrons are not included in the calculation of the missing transverse momentum. The dominant background to the jets plus missing transverse momentum region is from a W boson decaying leptonically, and accounts for 35% of the events. Estimating this background with a high accuracy is one of the key aspects of the measurement, and was performed by studying several exclusive regions in data that are designed to be kinematically very similar to the signal region, but statistically independent. 

The invisible width of the Z boson was extracted from a simultaneous likelihood fit and measured to be 523 ±3 (stat) ±16 (syst) MeV. This 3.2% uncertainty in the final result is dominated by systematic uncertainties, with the largest contributions coming from the uncertainty in the efficiencies of selecting muons and electrons. In a fitting tribute to its predecessor and testament to the LHC entering a precision era of physics, this measurement from CMS is competitive with the LEP combined result of 503 ± 16 MeV and is currently the world’s most precise single direct measurement.

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Since the discovery of the Higgs boson at the LHC in 2012, physicists have a more complete understanding of the Standard Model (SM) and the origin of elementary particle mass. However, theoretical questions such as why the Higgs boson is so light remain. An attractive candidate explanation postulates that the Higgs boson is not a fundamental particle, but instead is a composite state of a new, strongly-interacting sector – similar to the pion in ordinary strong interactions. In such composite-Higgs scenarios, new partners of the top and bottom quarks of the SM could be produced and observed at the LHC. 

If they exist, VLQs could be very heavy, with masses at the TeV scale, and could be produced either singly or in pairs at the LHC.

Ordinary SM quarks come in left-handed and right-handed varieties, which behave differently in weak interactions. The hypothetical new quark partners, however, behave the same way in weak interactions, whether they are left- or right-handed. Composite-Higgs models, and several other theories beyond the SM, predict the existence of such “vector-like quarks” (VLQs). Searching for them is therefore an exciting opportunity for the LHC experiments. 

If they exist, VLQs could be very heavy, with masses at the TeV scale, and could be produced either singly or in pairs at the LHC. Furthermore, VLQs could decay into regular top or bottom quarks in combination with a W, Z or Higgs boson. This rich phenomenology warrants a varied range of complementary searches to provide optimal coverage. 

The ATLAS collaboration has recently carried out two VLQ searches based on the full Run–2 dataset (139 fb^–1) at 13 TeV. The first analysis targets pair-production of VLQs, focusing on the possibility that most VLQs decay to a Z boson and a top quark. To help identify likely signal events, leptonically decaying Z bosons were tagged in events with pairs of electrons or muons. To maximise the discriminating power between the VLQ signal and the SM background, machine-learning techniques using a deep neural network were employed to identify the hadronic decays of top quarks, Z, W or Higgs bosons, and categorise events into 19 distinct regions. 

The second analysis targets the single production of VLQs. While the rate of pair production of VLQs through regular strong interactions only depends on their mass, their single production also depends on their coupling to SM electroweak bosons. As a result, depending on the model under consideration, VLQs heavier than approximately 1 TeV might predominantly be produced singly, and a measurement would therefore uniquely allow insight into this coupling strength.

The analysis was optimised for VLQ decays to top quarks in combination with either a Higgs or a Z boson. Events with a single lepton and multiple jets were selected, and tagging algorithms were used to identify the boosted  leptonic and hadronic decays of top quarks, and the hadronic decays of Higgs and Z bosons. The presence of a forward jet, characteristic of the single VLQ production mode, was used (along with the multiplicity of jets, b-jets and reconstructed boosted objects) to categorise the analysed events into 24 regions.

The observations from both analyses are consistent with SM predictions, which allows ATLAS to set the strongest constraints to date on VLQ production. Together, the pair- and single-production analyses exclude VLQs with masses up to 1.6 TeV (see figure 1) and 2.0 TeV (see figure 2), respectively, depending on the assumed model. These two analyses are part of a broader suite of searches for VLQs underway in ATLAS. The combination of these searches will provide the greatest potential for the discovery of VLQs, and ATLAS therefore looks forward to the upcoming Run–3 data.

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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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The W boson was first directly observed in 1983 using the Super Proton Synchrotron proton–antiproton collider at CERN, resulting in a Nobel Prize the following year. Almost four decades later, the ATLAS collaboration has observed the simultaneous production of three W bosons for the first time.

The possible new interactions are represented by operator terms with anomalous triple and quartic gauge couplings

The study of multi-boson processes involving boson self-interactions provides unique insight into the nature of electroweak symmetry breaking and therefore enables rigorous tests of the Standard Model (SM). Likewise, deviations from SM predictions could indicate hints of beyond-Standard Model physics through, for example, interactions that exist at energies beyond the current reach of the LHC which avoid the requirement to create the particle directly. These effects could potentially result from interactions with virtual particles in loops or new amplitudes generated by a tree-level exchange. In an effective field theory (EFT) approach, the possible new interactions are represented by operator terms with anomalous triple and quartic gauge couplings, both of which are present in WWW production.

Signal events

At leading order, the WWW signal is produced through the different mechanisms presented in the Feynman diagrams shown in figure 1. While there are many decay modes, ATLAS used four final-state channels where the signal-to-background ratio is big enough to observe the signal. The first three channels result from the decay of two of the Ws into charged lepton–neutrino pairs, with the same electric- charge sign of the charged leptons, and the decay of the third W into a pair of quarks observed as hadronic jets: the two-lepton (2l) channel, with flavour combinations ee, eμ and μμ. Additionally, WWW production is measured in the three-lepton (3l) channel, where each W decays into a charged lepton–neutrino pair, requiring no same-flavour opposite-sign charged-lepton pairs, and thus reducing the Z-boson background.

A multivariate analysis using a boosted decision tree (BDT) was used to discriminate the signal from the background, with the BDT trained using 12 discriminating input variables in the 2l channel and 11 input variables in the 3l channel. A binned maximum likelihood fit was performed on the BDT distributions with four free-floating parameters: the signal strength and three normalisation factors for the dominant WZ background. The BDT distributions were fitted in the four signal regions simultaneously with the trilepton invariant mass distribution in three WZ control regions (WZ plus 0, 1, ≥ 2 jets). The resulting BDT distribution for the 3l channel is shown in figure 2.

The large event samples (139 fb^–1) provided by the full Run-2 data set, the implementation of multivariate techniques, and an improved ATLAS detector and reconstruction performance enabled the observation and the cross-section measurement of this rare process. The observed (expected) significance of the measurement is 8.2 (5.4) standard deviations compared to the hypothesis with no WWW signal. The cross section is measured to be 850 ± 100 (stat.) ± 80 (syst.) fb, as derived from the observed signal strength (the ratio of measured to predicted yields) of 1.66 ± 0.28. The observed signal significance is within 2.4σ of the SM prediction. The full Run-3 data set is anticipated to more than double the number of signal events and will enable a more precise measurement of WWW production. Higher precision cross-section measurements and detailed differential distributions will elucidate the compatibility with the SM, and an EFT approach can quantify the sensitivity to anomalous gauge couplings in a search for new physics.

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At the collision energies of the LHC, diboson processes have relatively high production cross sections and often produce relatively clean final states with two or more charged leptons. Consequently, multilepton final states resulting from diboson processes are powerful signatures to study the properties of the electroweak sector of the Standard Model. In particular, WZ production is sensitive to the strength of the triple gauge coupling that characterises the WWZ vertex, which derives from the non-Abelian nature of the electroweak sector. Additionally, as the Higgs mechanism is responsible for the appearance of longitudinally polarised gauge bosons, studying W and Z boson polarisation indirectly probes the validity of the Higgs mechanism.

The results include the first observation at any experiment of longitudinally polarised W bosons in diboson production

A recent result from the CMS collaboration uses the full power of the data taken during Run 2 of the LHC to learn as much as possible from WZ production in the decay channels involving three charged leptons (electrons or muons). The results include the first observation at any experiment of longitudinally polarised W bosons in diboson production.

Reconstruction and event selection were optimised to reduce contributions from processes with “non-isolated” electrons and muons produced in hadron decays – traditionally one of the primary sources of experimental uncertainty in such measurements. The total production cross section for WZ production was measured with a simultaneous fit to the signal-enriched region and three different control regions. This elaborate fitting scheme paid off, as the final result has a relative uncertainty of 4%, down from the 6% obtained in past iterations of the measurement. The results are all consistent with state-of-the-art theoretical predictions (figure 1, left).

A highlight of the analysis is the study of the polarisation of both the W and the Z bosons in the helicity frame, using missing transverse energy as a proxy for the transverse momentum of the neutrino in the W decay. This choice, coupled with the precisely measured four-momenta of the three leptons and the requirement that W boson be on-shell, allows both the W and Z momenta to be fully reconstructed. The angle between the W (Z) boson and the (negatively) charged lepton originating from its decay is then computed. The resulting distributions are fitted to extract the polarisation fractions f_R, f_L, and f_o, which correspond to the proportion of bosons in the left, right and longitudinally polarised states in WZ production.

The measured polarisation fractions are consistent within 1σ with the Standard Model predictions (figure 1, right), in accordance with our knowledge of the electroweak spontaneous symmetry breaking mechanism. The significance for the presence of longitudinally polarised vector bosons is measured to be 5.6σ for the W boson and well beyond 5σ for Z-boson production. These new studies pave the way for future measurements of doubly polarised diboson cross sections, including the challenging doubly longitudinal polarisation mode in WW, WZ or ZZ production.

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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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The production of four top quarks is an extremely rare event at the LHC, with an expected cross section five orders of magnitude below the production of a top-quark pair. With the heaviest elementary particle in the Standard Model produced four times in the final state, it is also one of the most spectacular processes accessible at the LHC. By combining two analyses, the ATLAS collaboration has uncovered the first strong evidence to support the existence of this unique event topology with sensitivity to theo­ries beyond the Standard Model (BSM).

This is the only process that could probe potentially anomalous effective four-heavy-fermion operators

As a result of its large mass, the top quark plays a special role in numerous BSM theories, and many of these theories predict an increase in the four-top-quark production cross section. In particular, four-top-quark production is the only process that could probe potentially anomalous effective four-heavy-fermion operators. The cross section is also sensitive to the value of the top-quark Yukawa coupling, as a result of contributions mediated by Higgs bosons. However, until now, four-top-quark production has not been observed, in part because of its tiny production rate, and in part because the experimental signature of this process is very complex, requiring up to 12 particles to be reconstructed from the top-quark decays. The search is also affected by background sources in kinematic regions that are at the limit of the domain of validity of the simulations. 

Despite these challenges, the ATLAS collaboration has recently released two studies of four-top-quark production using its full Run-2 data sample. The first study searches for events with two leptons (electrons or muons) with the same electric charge or with three leptons. This selection corresponds to only 13% of all possible four-top-quark final states, but is contaminated by only a small background, mainly from the production of a top-quark pair with a W, Z or Higgs boson and additional jets, or from events with one lepton with misidentified electric charge or a “fake” lepton that doesn’t correspond to a W or Z boson decay. Background processes were primarily simulated using the best available theoretical predictions; the rates of the most difficult ones were measured using control samples with similar properties to the signal events. The second study searches for events with one lepton or two oppositely-charged leptons. This selection retains 57% of the possible four-top-quark final states, but suffers from a large background from top-quark pairs produced in association with many jets, some of which are consistent with originating from b-quarks (b-jets). This background is difficult to model and was determined using data control samples. To better isolate the signal from the background, multivariate discriminants were trained in both analyses using distinct features of the signal, such as the number of b-jets and the kinematic properties of the reconstructed particles (see figure 1).

Results from the two studies were combined, leading to a four-top-quark cross-section measurement at 13 TeV of 25⁺⁷_–6 fb, which is consistent with the Standard Model prediction of 12.0 ± 2.4 fb within 2.0σ (see figure 2). The statistical significance of the signal corresponds to 4.7σ, providing strong evidence for this process, close to the observation threshold of 5σ. LHC Run-3 data, possibly at a higher centre-of-mass energy, will allow ATLAS to verify whether the larger measured cross section relative to the prediction is confirmed or not. 

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The electroweak session of the Rencontres de Moriond convened more than 200 participants virtually from 22 to 27 March in a new format, with pre-recorded plenary talks and group-chat channels that went online in advance of live discussion sessions. The following week, the QCD and high-energy interactions session took place with a more conventional virtual organisation.

The highlight of both conferences was the new LHCb result on R_K based on the full Run 1 and Run 2 data, and corresponding to an integrated luminosity of 9 fb^–1, which led to the claim of the first evidence for lepton-flavour-universality (LFU) violation from a single measurement. R_K is the ratio of the branching fractions for the decays B⁺ → K⁺ μ⁺ μ^– and B⁺ → K⁺ e⁺ e^–. LHCb measured this ratio to be 3.1σ below unity, despite the fact that the two branching fractions are expected to be equal by virtue of the well-established property of lepton universality (see New data strengthens R_K flavour anomaly). Coupled with previously reported anomalies of angular variables and the R_K*, R_D and R_D* branching-fraction ratios by several experiments, it further reinforces the indications that LFU may be violated in the B sector. Global fits and possible theoretical interpretations with new particles were also discussed. 

Important contributions

Results from Belle II and BES III were reported. Some of the highlights were a first measurement of the B⁺ → K⁺ νν decay and the most stringent limits to date for masses of axions between 0.2 and 1 GeV from Belle II, based on the first data they collected, and searches for LFU violation in the charm sector from BES III that for the moment give negative results. Belle II is expected to give important contributions to the LFU studies soon and to accumulate an integrated luminosity of 50 ab^–1 10 years from now.

ATLAS and CMS presented tens of new results each on Standard Model (SM) measurements and searches for new phenomena in the two conferences. Highlights included the CMS measurement of the W leptonic and hadronic branching fraction with an accuracy larger than that measured at LEP for the branching fractions to the electron and muon, and the updated ATLAS evidence of the four-top-production process at 4.7σ (with 2.6σ expected). ATLAS and CMS have not yet found any indications of new physics but continue to perform many searches, expanding the scope to as-yet unexplored areas, and many improved limits on new-physics scenarios were reported for the first time at both conference sessions.

Several results and prospects of electroweak precision measurements were presented and discussed, including a new measurement of the fine structure constant with a precision of 80 parts per trillion, and a measurement at PSI of the null electric dipole moment of the neutron with an uncertainty of 1.1 × 10^–26 e∙cm. Theoretical predictions of (g–2)_μ were discussed, including the recent lattice calculation from the Budapest–Marseille–Wuppertal group of the hadronic–vacuum–polarisation contribution, which, if used in comparison with the experimental measurement, would bring the tension with the (g–2)_μ prediction to within 2σ.

In the neutrino session, the most relevant recent new results of last year were discussed. KATRIN reported updated upper limits on the neutrino mass, obtained from the direct measurement of the endpoint of the electron spectrum of the tritium β decay, while T2K showed the most recent results concerning CP violation in the neutrino sector, obtained from the simultaneous measurement of the ν_μ and ν_μ disappearance, and ν_e and ν_e  appearance. The measurement disfavours at 90% CL the CP-conserving values 0 and π of the CP-violating parameter of the neutrino mixing matrix, δ_CP, and all values between 0 and π.

The quest for dark matter is in full swing and is expanding on all fronts. XENON1T updated delegates on an intriguing small excess in the low-energy part of the electron-recoil spectrum, from 1 to 7 keV, which could be interpreted as originating from new particles but that is also consistent with an increased background from tritium contamination. Upcoming new data from the upgraded XENONnT detector are expected to be able to disentangle the different possibilities, should the excess be confirmed. The Axion Dark Matter eXperiment (ADMX) is by far the most sensitive experiment to detect axions in the explored range around 2 μeV. ADMX showed near-future prospects and the plans for upgrading the detector to scan a much wider mass range, up to 20 μeV, in the next few years. The search for dark matter also continues at accelerators, where it could be directly produced or be detected in the decays of SM particles such as the Higgs boson.

The quest for dark matter is in full swing and is expanding on all fronts

ATLAS and CMS also presented new results at the Moriond QCD and high-energy-interactions conference. Highlights of the new results are: the ATLAS full Run-2 search for double-Higgs-boson production in the bbγγ channel, which yielded the tightest constraints to date on the Higgs-boson self-coupling, and the measurement of the top-quark mass by CMS in the single-top-production channel that for the first time reached an accuracy of less than 1 GeV, now becoming relevant to future top-mass combinations. Several recent heavy-ion results were also presented by the LHC experiments, and by STAR and PHENIX at RHIC, in the dedicated heavy-ion session. One highlight was a result from ALICE on the measurement of the Λ_c⁺ transverse-momentum spectrum and the Λ_c⁺ /D⁰ ratio in pp and p–Pb collisions, showing discrepancies with perturbative QCD predictions.

The above is only a snapshot of the many interesting results presented at this year’s Rencontres de Moriond, representing the hard work and dedication of countless physicists, many at the early-career stage. As ever, the SM stands strong, though intriguing results provoked lively debate during many virtual discussions.

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It came as quite a surprise because as far as I know, none of the people who have been honoured with the Breakthrough Prize had already received the Nobel Prize. Of course nothing compares with the Nobel Prize in prestige, if only because of the long history of great scientists to whom it has been awarded in the past. But the Breakthrough Prize has its own special value to me because of the calibre of the young – well, I think of them as young – theoretical physicists who are really dominating the field and who make up the selection committee.

The prize committee stated that you would be a recognised leader in the field even if you hadn’t made your seminal 1967 contribution to the genesis of the Standard Model. What do you view as Weinberg’s greatest hits?

There’s no way I can answer that and maintain modesty! That work on the electroweak theory leading to the mass of the W and Z, and the existence and properties of the Higgs, was certainly the biggest splash. But it was rather untypical of me. My style is usually not to propose specific models that will lead to specific experimental predictions, but rather to interpret in a broad way what is going on and make very general remarks, like with the development of the point of view associated with effective field theory. Doing this I hope to try and change the way my fellow physicists look at things, without usually proposing anything specific. I have occasionally made predictions, some which actually worked, like calculating the pion–nucleon and pion–pion scattering lengths in the mid-1960s using the broken symmetry that had been proposed by Nambu. There were other things, like raising the whole issue of the cosmological constant before the discovery of the accelerated expansion of the universe. I worried about that – I gave a series of lectures at Harvard in which I finally concluded that the only way I can understand why there isn’t an enormous vacuum energy is because of some kind of anthropic selection. Together with two guys here at Austin, Paul Shapiro and Hugo Martel, we worked out what was the most likely value that would be found in terms of order of magnitude, which was later found to be correct. So I was very pleased that the Breakthrough Prize acknowledged some of those things that didn’t lead to specific predictions but changed a general framework.

I wish I could claim that I had predicted the neutrino mass

You coined the term effective field theory (EFT) and recently inaugurated the online lecture series All Things EFT. What is the importance of EFT today?

My thinking about EFTs has always been in part conditioned by thinking about how we can deal with a quantum theory of gravitation. You can’t represent gravity by a simple renormalisable theory like the Standard Model, so what do you do? In fact, you treat general relativity the same way you treat low-energy pions, which are described by a low-energy non-renormalisable theory. (You could say it’s a low-energy limit of QCD but its ingredients are totally different – instead of quarks and gluons you have pions). I showed how you can generate a power series for any given scattering amplitude in powers of energy rather than some small coupling constant. The whole idea of EFT is that any possible interaction is there: if it’s not forbidden it’s compulsory. But the higher, more complicated terms are suppressed by negative powers of some very large mass because the dimensionality of the coupling constants is such that they have negative powers of mass, like the gravitational constant. That’s why they’re so weak.

If you recognise that the Standard Model is probably a low-energy limit of some more general theory, then you can consider terms that make the theory non-renormalisable and generate corrections to it. In particular, the Standard Model has this beautiful feature that in its simplest renormalisable version there are symmetries that are automatic: at least to all orders of perturbation theory, it can’t violate the conservation of baryon or lepton number. But if the Standard Model just generates the first term in a power series in energy and you allow for more complicated non-renormalisable terms in the Lagrangian, then you find it’s very natural that there would be baryon and lepton non-conservation. In fact, the leading term of this sort is a term that violates lepton number and gives neutrinos the masses we observe. I wish I could claim that I had predicted the neutrino mass, but there already was evidence from the solar neutrino deficit and also it’s not certain that this is the explanation of neutrino masses. We could have Dirac neutrinos in which you have left and right neutrinos and antineutrinos coupling to the Higgs, and in that way get masses without any violation of lepton-number conservation. But I find that thoroughly repulsive because there’s no reason in that case why the neutrino masses should be so small, whereas in the EFT case we have Majorana neutrinos whose small masses are much more natural.

On this point, doesn’t the small value of the cosmological constant and Higgs mass undermine the EFT view by pointing to extreme fine-tuning?

Yes, they are a warning about things we don’t understand. The Higgs mass less so, after all it’s only about a hundred times larger than the proton mass and we know why the proton mass is so small compared to the GUT or Planck scale; it is because the proton gets it mass not from the quark masses, which have to do with the Higgs, but from the QCD forces, and we know that those become strong very slowly as you come down from high energy. We don’t understand this for the Higgs mass, which, after all, is a term in the Lagrangian, not like the proton mass. But it may be similar – that’s the old technicolour idea, that there is another coupling alongside QCD that becomes strong at some energy where it leads to a potential for the Higgs field, which then breaks electroweak symmetry. Now, I don’t have such a theory, and if I did I wouldn’t know how to test it. But there’s at least a hope for that. Whereas regards to the cosmological constant, I can’t think of anything along that line that would explain it. I think it was Nima Arkani-Hamed who said to me, “If the anthropic effect works for the cosmological constant, maybe that’s the answer with the Higgs mass – maybe it’s got to be small for anthropic reasons.” That’s very disturbing if it’s true, as we’re going to be left waving our hands. But I don’t know.

Maybe we have 2500 years ahead of us before we get to the next big step

Early last year you posted a preprint “Models of lepton and quark masses” in which you returned to the problem of the fermion mass hierarchy. How was it received?

Even in the abstract I advertise how this isn’t a realistic theory. It’s a problem that I first worked on almost 50 years ago. Just looking at the table of elementary particle masses I thought that the electron and the muon were crying out for an explanation. The electron mass looks like a radiative correction to the muon mass, so I spent the summer of 1972 on the back deck of our house in Cambridge, where I said, “This summer I am going to solve the problem of calculating the electron mass as an order-alpha correction to the muon mass.” I was able to prove that if in a theory it was natural in the technical sense that the electron would be massless in the tree approximation as a result of an accidental symmetry, then at higher order the mass would be finite. I wrote a paper, but then I just gave it up after no progress, until now when I went back to it, no longer young, and again I found models in which you do have an accidental symmetry. Now the idea is not just the muon and the electron, but the third generation feeding down to give masses to the second, which would then feed down to give masses to the first. Others have proposed what might be a more promising idea, that the only mass that isn’t zero in the tree approximation is the top mass, which is so much bigger than the others, and everything else feeds down from that. I just wanted to show the kinds of cancellations in infinites that can occur, and I worked out the calculations. I was hoping that when this paper came out some bright young physicist would come up with more realistic models, and use these calculational techniques – that hasn’t happened so far but it’s still pretty early.

What other inroads are there to the mass/flavour hierarchy problem?

The hope would be that experimentalists discover some correction to the Standard Model. The problem is that we don’t have a theory that goes beyond the Standard Model, so what we’re doing is floundering around looking for corrections in the model. So far, the only one discovered was the neutrino mass and that’s a very valuable piece of data which we so far have not figured out how to interpret. It definitely goes beyond the Standard Model – as I mentioned, I think it is a dimension-five operator in the effective field theory of which the Standard Model is the renormalisable part.

The big question is whether we can cut off some sub-problem that we can actually solve with what we already know. That’s what I was trying to do in my recent paper and did not succeed in getting anywhere realistically. If that is not possible, it may be that we can’t make progress without a much deeper theory where the constituents are much more massive, something like string theory or an asymptotically safe theory. I still think string theory is our best hope for the future, but this future seems to be much further away than we had hoped it would be. Then I keep being reminded of Democritus, who proposed the existence of atoms in around 400 BCE. Even as late as 1900 physicists like Mach doubted the existence of atoms. They didn’t become really nailed down until the first years of the 20th century. So maybe we have 2500 years ahead of us before we get to the next big step.

Recently the LHC produced the first evidence that the Higgs boson couples to a second-generation fermion, the muon. Is there reason to think the Higgs might not couple to all three generations?

Before the Higgs was discovered it seemed quite possible that the explanation of the hierarchy problem was that there was some new technicolour force that gradually became strong as you came from very high energy to lower energy, and that somewhere in the multi-TeV range it became strong enough to produce a breakdown of the electroweak symmetry. This was pushed by Lenny Susskind and myself, independently. The problem with that theory was then: how did the quarks and leptons get their masses? Because while it gave a very natural and attractive picture of how the W and Z get their masses, it left it really mysterious for the quarks and leptons. It’s still possible that something like technicolour is true. Then the Higgs coupling to the quarks and leptons gives them masses just as expected. But in the old days, when we took technicolour seriously as the mechanism for breaking electroweak symmetry, which, since the discovery of the Higgs we don’t take seriously anymore, even then there was the question of how, without a scalar field, can you give masses to the quarks and leptons. So, I would say today, it would be amazing if the quarks and leptons were not getting their masses from the expectation value of the Higgs field. It’s important now to see a very high precision test of all this, however, because small effects coming from new physics might show up as corrections. But these days any suggestion for future physics facilities gets involved in international politics, which I don’t include in my area of expertise.

It’s still possible that something like technicolour is true

Any more papers or books in the pipeline?

I have a book that’s in press at Cambridge University Press called Foundations of Modern Physics. It’s intended to be an advanced undergraduate textbook that takes you from the earliest work on atoms, through thermodynamics, transport theory, Brownian motion, to early quantum theory; then relativity and quantum mechanics, and I even have two chapters that probably go beyond what any undergraduate would want, on nuclear physics and quantum field theory. It unfortunately doesn’t fit into what would normally be the plan for an undergraduate course, so I don’t know if it will be widely
adopted as a textbook. It was the result of a lecture course I was asked to give called “thermodynamics and quantum physics” that has been taught at Austin for years. So, I said “alright”, and it gave me a chance to learn some thermodynamics and transport theory.

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The Higgs boson discovered in 2012 by the ATLAS and CMS experiments is the pinnacle of the scientific results so far at the LHC. Measurements of its couplings to W and Z bosons and to heavy fermions have provided a strong indication that the mechanism of electroweak symmetry breaking is similar to that proposed by Brout, Englert and Higgs (BEH) more than 50 years ago. In this model, the BEH field exists throughout space with a non-zero field strength corresponding to the minimum of the BEH potential. The measurement of the shape of the BEH potential has become one of the main goals of experimental particle physics. It governs not only the nature of the electroweak phase transition in the early universe, when the BEH field gained its non-zero “vacuum expectation value” (VEV), but also the question of whether deeper minima than the present vacuum exist.

The measurement of the production of Higgs-boson pairs gives a direct way to measure λ

Interactions with the BEH VEV give mass not only to the W and Z bosons and the fermions, but also to the Higgs boson itself. If the mass of the Higgs boson is well known, the Standard Model (SM) can therefore predict the Higgs self-coupling, λ – the key unknown parameter in the shape of the BEH potential of the SM. The measurement of the production of Higgs-boson pairs (HH) gives a direct way to measure λ. Higgs-boson pair production is not yet established experimentally, as it is a thousand times less frequent than the production of a single Higgs boson. However, the presence of physics beyond the SM can substantially enhance the HH production rate. The search for HH production at the LHC is therefore an important test of the SM.

Best constraint

A recent result by the CMS collaboration describes a search for HH production in final states with two photons and two b-jets (figure 1). The large data sample collected during LHC Run 2 excludes a HH production rate larger than 7.7 times that predicted by the SM. CMS has set the best constraint to date on the ratio of the measured λ parameter to the SM prediction, κ_λ = 0.6^+6.3_–1.8.

The sensitivity of the analysis has been improved by about a factor four over the previous result that used the data collected in 2016, benefitting equally from the increase in luminosity and from a wealth of innovative analysis techniques. The electromagnetic calorimeter of the CMS experiment allows the measurement of H → γγ candidates with excellent resolution (about 1–2%). Advanced machine-learning techniques, including deep neural networks, were introduced to significantly improve the mass resolution of H → bb, from 15% down to 11%. The analysis combines information from the invariant mass of the HH system, reflecting the underlying physics processes, and a multivariate classifier exploring the kinematic properties as well as the identification of photons and b-jets.

Events were categorised to enhance the sensitivity to Higgs production via gluon fusion as well as, for the first time, vector-boson fusion. The latter constrains the quartic coupling between two vector bosons and two Higgs bosons, such as WWHH, which is an extremely rare interaction in the SM. In addition, dedicated categories from a previous analysis were added to account for the associated production of top quarks and a single Higgs boson, and to provide a simultaneous constraint on the top-quark Yukawa coupling and λ. Several hypotheses predicting new physics were also constrained. The results are an encouraging step forwards in the quest to measure the BEH potential and to further interrogate the SM.

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The growing LHC dataset eight years after the discovery of the Higgs boson allows the experiments to study its properties more and more precisely, searching for hints of physics beyond the Standard Model (SM). New phenomena might occur at energy scales beyond the reach of the LHC, pointing to the existence of so-far undiscovered particles with masses too heavy to be directly produced in 13 TeV proton–proton collisions. Without knowing the exact nature of the new physics, LHC data can be analysed to systematically constrain new types of interactions in the framework of an effective field theory (EFT). One historical EFT example is Fermi’s effective interaction model for nuclear beta decay, which is valid as long as the probed energy scale is well below the mass of the W boson. The move to constrain EFTs rather than signal strengths for couplings marks a new, more comprehensive phase in SM tests at the LHC.

The move to constrain EFTs marks a new, more comprehensive phase in SM tests at the LHC

Almost all types of new physics would give rise to new interactions with SM particles, with different models leaving different EFT footprints. As the underlying dynamics is not known and effects can be subtle, it is important to combine as many measurements as possible across the full spectrum of the LHC research programme.

A new ATLAS analysis presented at the Higgs 2020 conference, held online from 26 to 30 October, takes a first step in this direction. The analysis combines measurements of production cross-sections and kinematic variables of Higgs-boson events in several decay channels (diphoton, four-lepton and di-b-quark decays) to constrain new phenomena within the so-called SMEFT framework. The combination of measurements allows multiple new interactions involving the Higgs boson to be constrained simultaneously. This approach requires fewer hypotheses on the other unconstrained interactions than studying the EFT terms one measurement at a time. The results are therefore more generic and easier to interpret in a broader context.

Predicted to vanish

Figure 1 shows the allowed ranges for the coupling coefficients of new EFT interactions to which the ATLAS combined Higgs analysis is sensitive. The coefficient c⁽³⁾_Hq, for example, describes the strength of an effective four-particle interaction between two quarks, a gauge boson and the Higgs boson. The SM predicts all these coefficients to vanish, as their corresponding interactions are not present. Significant positive or negative deviations would indicate new physics. For instance, a non-vanishing value of c⁽³⁾_Hq  would cause deviations from the SM in the ZH and WH cross-sections at high transverse momentum of the Higgs boson, which are not observed in the measured channels.

All measurements are compatible with the SM, indicating that if new physics is present it either has a mass scale larger than 1 TeV (the reference scale for which these results are reported) – or it manifests itself in interactions to which the available measurements are not yet sensitive. In the meantime, thanks to the design of the analysis, the results can be added to wider EFT interpretations that combine measurements from different physics processes (e.g. electroweak- boson or top-quark production) studied by ATLAS and other experiments, providing a consistent and increasingly detailed mapping of the allowed new physics extensions of the SM.

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The H → ℓℓγ decay is particularly interesting as it is a loop process

The measurement of rare decays of the Higgs boson is a crucial component of the Higgs-boson physics programme at the LHC, since they probe potential new interactions with the Higgs boson introduced by possible extensions of the Standard Model. The H → ℓℓγ decay is particularly interesting in this respect as it is a loop process and the three-body final state allows the CP structure of the Higgs boson to be probed. However, the small expected signal-to-background ratio and the typically low dilepton invariant mass make the search for H → ℓℓγ highly challenging.

Bump hunt

The analysis performed by ATLAS searched for H → e⁺e^–γ and H → μ⁺μ^–γ decays. Special treatment was needed in particular for the electron channel: a dedicated electron trigger was developed as well as a specific identification algorithm. The predicted m_ℓℓ spectrum rises steeply towards lower values, with a kinematic cutoff at twice the final-state lepton mass. At such low electron–positron invariant masses, and given the large transverse momentum of their system, the electromagnetic showers induced by the electron and the positron in the ATLAS calorimeter can merge, requiring a specially developed reconstruction. Furthermore, a dedicated identification algorithm was developed for these topologies, and its efficiency was measured in data using photon detector-material conversions at low radius into an electron–positron pair from Z → ℓℓγ events.

The signal extraction is performed by searching in the ℓℓγ invariant mass (m_ℓℓγ) range between 110 and 160 GeV for a narrow signal peak over smooth background at the mass of the Higgs boson. The sensitivity to the H → ℓℓγ signal was increased by separating events in mutually exclusive categories based on lepton types and event topologies. ATLAS reports evidence in data for a H → ℓℓγ signal emerging over the background with a significance of 3.2σ (see figure). The Higgs boson production cross section times H → ℓℓγ branching fraction, measured for m_ℓℓ < 30 GeV, amounts to 8.7^+2.8_–2.7 fb. It corresponds to a signal strength – the ratio of the measured cross section times branching fraction to the Standard Model prediction – of 1.5 ± 0.5. With this, ATLAS has also extended the invariant-mass range of the lepton pair for the related Higgs-boson decay into a photon and a Z boson to lower masses, opening the door to future studies of three-body Higgs-boson decays and investigations of its underlying CP structure.

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The novelty of the Higgs boson derives largely from its apparently scalar nature. It is the only fundamental particle without spin. Additionally, it is the only fundamental particle with a self-coupling (gluons also couple to other gluons, but only to those with different colour combinations). Measurements of the couplings of the Higgs boson to the W and Z bosons at the LHC have confirmed its role in the generation of their masses, likewise for the charged third-generation fermions. Despite this great success, the Higgs boson is connected to many of the most troublesome aspects of the Standard Model (see “Connecting the Higgs to Standard Model enigmas” panel). It is for this reason that the recently concluded update of the European strategy for particle physics advocated an electron–positron Higgs factory as the highest priority collider after the LHC, to allow detailed study of this novel and unique particle.

Circular vs linear

The discovery of the Higgs boson at the relatively light mass of 125 GeV, announced by the ATLAS and CMS collaborations in 2012, had two important consequences for experiment. The first was the large number of potentially observable branching fractions available. The second was that circular, as well as linear, e⁺e^– machines could serve as Higgs factories. The two basic mechanisms for Higgs-boson production at such colliders are associated production, e⁺e^– → ZH, and vector-boson fusion. The former process is dominant at the low-energy first stage of the various Higgs factories under consideration, with vector-boson fusion becoming more important with increasing energy (see “Channeling the Higgs” figure). About a quarter of a million Higgs bosons would be produced per inverse attobarn of data, leading to substantial numbers of recorded events even after the branching ratios to observable modes are taken into account.

Four Higgs-factory designs are presently being considered. Two are linear accelerators, namely the International Linear Collider (ILC) under consideration in Japan and the Compact Linear Collider (CLIC) at CERN, while the other two are circular: the Future Circular Collider (FCC-ee) at CERN and the Circular Electron Positron Collider (CEPC) in China.

The beams in circular colliders continuously lose energy due to synchrotron radiation, causing the luminosity at circular colliders to decrease with beam energy roughly as E_b^–3.5. The advantage of circular colliders is their high instantaneous luminosity, in particular at the centre-of-mass energy relevant for the Higgs-physics programme (250 GeV), but even more so at lower energies such as those corresponding to the Z-boson mass (91 GeV). Electron and positron beams in a circular machine naturally achieve transverse polarisation, which can be exploited to make precise measurements of the beam energy via the electron and positron spin-precession frequencies.

In contrast, for linear colliders the luminosity increases roughly linearly with the beam energy. The advantages of linear accelerators are that they can be extended to higher energies, and the beams can be polarised longitudinally. The ZH associated cross section can be increased by 40% with longitudinal polarisations of –80% and 30% for electrons and positrons, respectively. This increase, coupled with the ability to isolate certain components of Higgs-boson production by tuning the polarisation, enables a linear machine to achieve similar precisions on Higgs-boson measurements with half the integrated luminosity of a circular machine.

FCC-ee, CEPC and ILC are foreseen to run for several years at a centre-of-mass energy of around 250 GeV, where the ZH production cross section is largest. Instead, CLIC plans to run its first stage at 380 GeV where both WW fusion and ZH production contribute, and tt production is possible. The circular colliders FCC-ee and CEPC envisage running at the Z-pole and the WW production threshold for long enough to collect of the order 10¹² Z bosons and 10⁸ WW pairs, enabling powerful electroweak and flavour-physics programmes (see “Compare and contrast” table). To achieve design luminosity, all proposed e⁺e^– colliders need beams focused to a very small size in one direction (30–70 nm for FCC-ee, 3–8 nm for ILC and 1–3 nm for CLIC), which are all below the values so far achieved at existing facilities.

Evolving designs

The proposed circular colliders are based on a combination of concepts that have been proven and used in previous and present colliders (LEP, SLC, PEP-II, KEKB, SuperKEKB, DAFNE). In Higgs-production mode the beam lifetime is limited by Bhabha scattering to about 30 minutes and therefore requires quasi-continuous injection or “top-up” as used by the B-factories. Each of the circular collider main concepts and parameters has been demonstrated in a previous machine, and thus the designs are considered mature. The total FCC-ee construction cost is estimated to be 10.5 billion CHF for energies up to 240 GeV, with an additional 1.1 billion CHF to go to the tt threshold. This includes 5.4 billion CHF for the tunnel, which could be reused later for a hadron collider. The CEPC cost has been estimated at $5 billion, including $1.3 billion for the tunnel. With the present design, the FCC-ee power consumption is 260–340 MW for the various energy stages (compared to 150 MW for the LHC).

The ILC was proposed in the late 1990s and a technical design report published in 2012. It uses superconducting RF cavities for the acceleration, as used in the currently operating European XFEL facility in Germany, to aim for gradients of 35 MV/m. The cost of the first energy stage (250 GeV) was estimated as $4.8–5.3 billion, with a power consumption of 130–200 MW, and an expression of interest to host the ILC as a global project is being considered in Japan. The CLIC accelerator uses a second beam, termed a drive-beam, to accelerate the primary beam, aiming for gradients in excess of 100 MV/m. This concept has been demonstrated with electron beams at the CLIC test facility, CTF3. The cost of the first energy stage of CLIC is estimated as 5.9 billion CHF with a power consumption of 170 MW, rising to 590 MW for final-stage operation at 3 TeV.

Another important difference between the proposed linear and circular colliders concerns the number of detectors they can host. Collisions at linear machines only occur at one interaction point, while in circular colliders at least two interaction points are proposed, doubling the luminosity available for analyses. Two detectors also offer the dual benefits of scientific competition and the cross-checking of results. At the ILC two detectors are proposed but they cannot run concurrently since they use the same interaction point.

FCC-ee and CLIC have both been proposed as CERN-hosted international projects, similar to the LHC or high-luminosity LHC (HL-LHC). At present, as recommended by the 2020 update of the European strategy for particle physics, a feasibility study for the FCC (including its post-FCC-ee hadron-collider stage, FCC-hh) is ongoing, with the goal of presenting an updated conceptual design report by the next strategy update in 2026. Among the e⁺e^– colliders, CLIC has the greatest capacity to be extended to the multi-TeV energy range. In its low-energy incarnation it could be realised either with the drive-beam or conventional technology. CEPC is conceptually and technologically similar to FCC-ee and has also presented a conceptual design report. Nearly all statements about FCC-ee also hold for CEPC except that CEPC’s design luminosity is about a factor of two lower, and thus it takes longer to acquire the same integrated luminosity. At circular colliders, the multi-TeV regime (at least 100 TeV in the case of FCC-hh) would be reached by using proton beams, similar to what was done with LHC following LEP.

Connecting the Higgs to Standard Model enigmas

In addition to the vacuum expectation value of the Higgs field and the mass of the Higgs boson, the discovery of the Higgs boson introduces a large number of parameters into the Standard Model. Among them are the Yukawa couplings of the nine charged fermions (in contrast, the gauge sector of the SM has only three free parameters). The Yukawa forces, of which only three have been discovered corresponding to the couplings to the charged third-generation fermions, are completely new. They are of disparate strengths and, unlike the other forces, are not subject to the constraint of local gauge invariance. They provide a parameterisation of the theory of flavour, rather than an explanation. It is of primary importance to discover, bound and characterise the Yukawa forces. In particular, the discovery of CP violation in the Yukawa couplings would go beyond the confines of the Standard Model.

Famously, because of its scalar nature, the quantum corrections to the Higgs boson mass are only bounded by the cut-off on the theory, demanding large renormalisations to maintain the mass at 125 GeV as measured. This issue is not so much a problem for the Standard Model per se. However, in the context of a more complete theory that aims to supersede and encompass the Standard Model, it becomes much more troubling. In effect, the degree of cancellation necessary to maintain the Higgs mass at 125 GeV effectively sabotages the predictive power of any more complete theory. This sabotage becomes deadly as the scale of the new physics is pushed to higher and higher energies.

The electroweak potential is another area of importance in which our current knowledge is fragmentary. Within the confines of the Standard Model the potential is completely specified by the position of its minimum – the vacuum expectation value and the second derivative of the potential at the minimum, the mass of the Higgs boson (or equivalently its self-coupling). We have no direct knowledge of the behaviour of the potential at larger field values further from the minimum. In addition, extrapolation of the currently understood Higgs potential to higher energy reveals a world teetering between stability and instability. Further information about the behaviour of the potential could help us to interpret the meaning of this result. A modified electroweak potential might also give rise to a first-order phase transition at high temperature, rather than the smooth crossover expected for the Standard Model Higgs potential. This would fulfil one of the three Sakharov conditions necessary to generate an asymmetry between matter and antimatter in our universe.

To quantify the scientific reach of the proposed colliders compared to current knowledge or the expectations for the HL-LHC, it is necessary to define figures-of-merit for the observables that will be measured. For the Higgs boson the focus is on the coupling strengths to the Standard Model bosons and fermions, as well as the couplings to any new particles. The strength with which the Higgs boson couples to the various particles, i, is denoted by κ_i, defined such that κ_i = 1 corresponds to the Standard Model. Non-standard phenomena are included in this “kappa” framework by introducing two new quantities: the branching ratio into invisible particles (determined by measuring the missing energy in identified Higgs events), and the branching ratio to untagged particles (determined by measuring the contributions to the total width accounted for by the observed modes, or by directly searching for anomalous decays).

Higgs-boson observables

At hadron colliders, only ratios of κ_i parameters can be measured, since a precise measurement of the total width of the Higgs boson is lacking (the expected total width of the Higgs boson in the Standard Model is 4.2 MeV, which is far too small to be resolved experimentally). To determine the absolute κ_i values at a hadron collider a further assumption needs to be made, either on decay rates of the Higgs boson to new particles or on one of the κ_i values. An assumption that is often made, and valid in many beyond-the-Standard-Model theories, is that κ_Z ≤ 1.

The kappa framework, however, by construction, does not parameterise possible effects coming from different Lorentz structures and/or the energy dependence of the Higgs couplings. Such effects could generically arise from the existence of new physics at higher scales and could lead not only to changes in the predicted rates, but also in distributions. Deviations of κ_i from 1 indicate a departure from the Standard Model, but do not provide a tool to diagnose its cause. This shortcoming is remedied in so-called effective-operator formalisms by including operators of mass dimension greater than four.

At e⁺e^– colliders a Higgs boson produced via e⁺e^– → ZH can be identified without observing its decay products. This measurement, of primary importance, is unique to e⁺e^– colliders. By measuring the Z decay products and with the precise knowledge of the momenta of the incoming e^– and e⁺ beams, the presence of the Higgs boson in ZH events can be inferred based on energy and momentum conservation alone, without actually tagging the Higgs boson. In this way one directly measures the coupling between the Higgs and Z bosons. In combination with the Higgs branching ratio to Z pairs it can be interpreted as a measurement of the Higgs-boson width. The first-stage e⁺e^– Higgs factories all constrain the total width at about the 2% level.

LHC and HL-LHC

To assess the potential impact of the e⁺e^– Higgs factories it is important to examine the point of departure provided by the LHC and HL-LHC. Since its startup in 2010 the LHC has made a monumental impact on our understanding of the Higgs sector. After the Higgs discovery in 2012, a measurement programme started and now, with nearly 150 fb^–1 of data analysed by ATLAS and CMS, much has been learned. The Higgs-boson mass has been measured with a precision of < 0.2%, its spin and parity confirmed as expected in the Standard Model, and its coupling to bosons and to third-generation charged fermions established with a precision of 5–10%.

With the HL-LHC and its experiments planned to operate from 2027, the precision on the coupling parameters and the branching ratios to new particles will be increased by a factor of 5–10 in all cases, typically resulting in a sensitivity of a few % (see “Kappa couplings” figure). The HL-LHC will also enable measurements of the very rare μ⁺μ^– decay, the first evidence for which was recently reported by CMS and ATLAS, and thus show whether the Higgs boson also generates the mass of a second-generation fermion. With the full HL-LHC dataset, corresponding to 3000 fb^–1 for each of ATLAS and CMS, it is expected that di-Higgs production will be established with a significance of four standard deviations. This will allow a determination of the Higgs-boson’s coupling to itself with a precision of 50%.

About a quarter of a million Higgs bosons could be produced per inverse attobarn of data

The LHC has also made enormous progress in the direct searches for new particles at high energies. With more than 1000 papers published on this topic, hunting down particles predicted by dozens of theoretical ideas, and no firm sign of a new particle anywhere, it is clear that the new physics is either heavier, or more weakly coupled or has other features that hides it in the LHC data. The LHC is also a precision machine for electroweak physics, having measured the W-boson mass and the top-quark mass with uncertainties of 0.02% and 0.3%, respectively. In addition, a large number of relevant cross-section measurements of multi-boson production have been made, probing the trilinear and quartic interactions of the gauge bosons with each other.

Higgs-factory impact

In terms of the measurement precision on the Higgs-boson couplings, the proposed Higgs factories are expected to bring a major improvement with respect to HL-LHC in most cases (see “Relative precision” figure). Only for the rare decays to muons, photons and Zγ, and for the very massive top quark, is this not the case. The highest precision (0.2% in the case of FCC-ee) is achieved on κ_Z since the main Higgs production mode, ZH, depends directly on it, regardless of the decay mode. For other Standard Model particles, improvement factors of two to four are typical. For the invisible and untagged decays, the constraints are improved to around 0.2% and 1%, respectively, for some of the Higgs factories. A new measurement, not possible at the LHC, is that of the charm–quark coupling, κ_c.

None of the initial stages of the proposed Higgs factories will be able to directly probe the self-coupling of the Higgs boson beyond the 50% expected from the HL-LHC, since the cross-sections for the relevant processes (e⁺e^– → ZHH and e⁺e^– → HHνν) are negligible at centre-of-mass energies below 400 GeV. The Higgs self-coupling, however, enters through loops also in single-Higgs production and indirect effects might therefore be observable, for instance as a small (< 1%) deviation in measurements of the inclusive ZH cross section. Measurements of the Higgs self-coupling exploiting the di-Higgs production process can only be performed at higher energy colliders. The ILC and CLIC project uncertainties of around 30% at their intermediate energies and around 10% at their ultimate energies, while FCC-hh projects a precision of around 5%. Similarly, for the Higgs coupling to the top quark, the HL-LHC precision of 3.2% will not be improved by the initial stages of any of the Higgs factories.

The proposed Higgs factories also have a rich physics programme at lower energies, particularly at the Z pole. FCC-ee, for instance, plans to run for four years at the Z pole to accumulate a total of more than 10¹² Z bosons – 100,000 times more than at LEP. This will enable a rich and unprecedented electroweak physics programme, constraining so-called oblique parameters (which are sensitive to violations of weak isospin) at the per-mille level, 100 times better than today. It will also enable a B-physics programme, complementary to that at Belle II and LHCb. At CEPC, a similar programme is possible, while at ILC and CLIC the luminosity when running at the Z pole is much lower: the typical number of Z-bosons that can be accumulated here is 10⁹, 100 times more than LEP but not at the same level as the circular colliders. FCC-ee’s electroweak programme also foresees a run at the WW threshold to enable a high-precision measurement of the W mass.

Concerning the large top-quark mass, measurements at the LHC suffer from uncertainties associated with renormalisation schemes and it is unlikely to improve the precision significantly at the HL-LHC beyond the currently achieved value of 400 MeV. At an e⁺e^– collider operating at the tt threshold (~350 GeV), a measurement of the top mass with total uncertainty of around 50 MeV and with full control of the issues associated with the renormalisation scheme is possible. In addition to its importance as a fundamental parameter of the Standard Model, the top mass is the dominant term in the evolution of the Higgs potential with energy to determine vacuum stability (see “Connecting the Higgs to Standard Model enigmas” panel).

To assess the potential impact of the e⁺e^– Higgs factories it is important to examine the point of departure provided by the LHC and HL-LHC

In short, a Higgs factory promises to expand our knowledge of nature at the smallest scales. The ZH cross-section measurement alone will probe fine tuning at a level of a few permille, about 30 times better than what we know today. This provides indirect sensitivity to new particles with masses up to 10–30 TeV, depending on their coupling strength, and could point to a new energy scale in nature.

But most of all the Higgs boson has not exhausted its ability to surprise. The rest of the Standard Model is a compact structure, exquisitely tested, and ruled by local gauge invariance and other symmetries. Compared to this, the Lagrangian of the Higgs sector is the wild west, where the final laws have yet to be written. Does the Higgs boson have a significant rate of invisible decays, which could be a key component in understanding the nature of dark matter in our universe? Does the Higgs boson act as a portal to other scalar degrees of freedom? Does the Higgs boson provide a source of CP violation? An electron–positron Higgs factory provides a tool to address these questions with unique clarity, when deviations between the measured and predicted values of observables are detected. Building on the data from the HL-LHC, it will be the perfect tool to elucidate the underlying laws of physics.

The post Targeting a Higgs factory appeared first on CERN Courier.

Finding Higgs bosons can seem esoteric to the uninitiated. The spouse of a colleague of mine has such trouble describing what their partner does that they read from a card in the event that they are questioned on the subject. Do you experience similar difficulties in describing what you do to loved ones? If so, then Ivo van Vulpen’s book How to find a Higgs boson may provide you with an ideal gift opportunity.

Readers will feel like they are talking physics over a drink with van Vulpen, who is a lecturer at the University of Amsterdam and a member of the ATLAS collaboration. Originally published as De melodie van de natuur, the book’s Dutch origins are unmistakable. We read about Hans Lippershey’s lenses, Antonie van Leeuwenhoeck’s microbiology, Antonius van den Broek’s association of charge with the number of electrons in an atom, and even Erik Verlinde’s theory of gravity as an emergent entropic force. Though the Higgs is dangled at the end of chapters as a carrot to get the reader to keep reading, van Vulpen’s text isn’t an airy pamphlet cashing in on the 2012 discovery, but a realistic representation of what it’s like to be a particle physicist. When he counsels budding scientists to equip themselves better than the North Pole explorer who sets out with a Hugo Boss suit, a cheese slicer and a bicycle, he tells us as much about himself as about what it’s like to be a physicist.

Van Vulpen is a truth teller who isn’t afraid to dent the romantic image of serene progress orchestrated by a parade of geniuses. 9999 out of every 10,000 predictions from “formula whisperers” (theorists) turn out to be complete hogwash, he writes, in the English translation by David McKay. Sociological realities such as “mixed CMS–ATLAS” couples temper the physics, which is unabashedly challenging and unvarnished. The book boasts a particularly lucid and intelligible description of particle detectors for the general reader, and has a nice focus on applications. Particle accelerators are discussed in relation to the “colour X-rays” of the Medipix project. Spin in the context of MRI. Radioactivity with reference to locating blocked arteries. Antimatter in the context of PET scans. Key ideas are brought to life in cartoons by Serena Oggero, formerly of the LHCb collaboration.

The weak interaction is like a dog on an attometre-long chain.

Attentive readers will occasionally be frustrated. For example, despite a stated aim of the book being to fight “formulaphobia”, Bohr’s famous recipe for energy levels lacks the crucial minus sign just a few lines before a listing of –3.6 eV (as opposed to –13.6 eV) for the energy of the ground state. Van Vulpen compares the beauty seen by physicists in equations to the beauty glimpsed by musicians as they read sheet music, but then prints Einstein’s field equations with half the tensor indices missing. But to quibble about typos in the English translation would be to miss the point of the book, which is to allow readers “to impress friends over a drink,” and talk physics “next time you’re in a bar”. Van Vulpen’s writing is always entertaining, but never condescending. Filled with amusing but perceptive one-liners, the book is perfectly calibrated for readers who don’t usually enjoy science. Life in a civilisation that evolved before supernovas would have no cutlery, he observes. Neutrinos are the David Bowie of particles. The weak interaction is like a dog on an attometre-long chain.

This book could be the perfect gift for a curious spouse. But beware: fielding questions on the excellent last chapter, which takes in supersymmetry, SO(10), and millimetre-scale extra dimensions, may require some revision.

The post How to find a Higgs boson appeared first on CERN Courier.

Until 2012, the list of elementary particles could be divided into just two broad classes: spin-1/2 matter particles (fermions) and spin-1 force carriers (vector bosons), with a spin-2 force carrier (the graviton) pencilled in by most theorists to mediate the gravitational force. The first jewel in the LHC’s crown is the discovery of an elementary spin-0 particle – the first and only particle of this type to have been discovered. The question of the spin of the Higgs boson is intrinsically linked to the dominant discovery mode in 2012: the decay into two photons. Conservation laws insist that only a spin-0 or spin-2 particle can decay into two photons.

To decide between the two spin options, a more complex study than just measuring decay rates was needed. The spin of the parent particle affects the angular distributions of the daughter particles of Higgs-boson decays. Studies began immediately within ATLAS and CMS, showing unambiguously that the newly discovered particle was spin-0. The ways in which this particle is produced and the ways in which it decays call for its identification with the only particle that was predicted by the Standard Model of particle physics that had not been observed by 2012 – the Higgs boson. The field related to this particle is the BEH field.

The next question was whether this new particle is elementary or composite. If the Higgs boson is actually a composite spin-0 particle, then there should be a whole series of new composite particles with different quantum numbers – in particular, spin-1 particles whose mass scale is roughly inversely proportional to the distance scale that characterises their internal structure.

One can test the question of whether the Higgs boson is elementary or composite in three ways. Firstly: indirectly. The virtual effects of these heavy spin-1 particles would modify the properties of the W and Z bosons. Part of the legacy of the LEP experiments, which operated at CERN between 1989 and 2000, and the SLD experiment, which operated in SLAC between 1992 and 1998, is a large class of precision measurements of these properties. The other two ways are pursued by the LHC experiments: the direct search for the new spin-1 particles, and precision measurements of properties of the Higgs boson itself, such as its couplings to electroweak vector-boson pairs, which would differ if it were composite. No such composite excitations have been discovered to date, and the Higgs boson shows no signs of internal structure down to a scale of 10^–19 m – some four orders of magnitude smaller than the proton.

A second jewel

The electromagnetic and strong interactions are mediated by massless mediators – the photon and the gluon. Consequently, they are long-range, though colour confinement – the phenomenon that quarks and gluons cannot be isolated – renders the long-range effects of the strong interaction unobservable. By contrast, weak interactions are mediated by massive mediators – the W and Z bosons – with masses of the order of 100 times larger than that of the proton. As a result, the weak force is exponentially suppressed at distances larger than 10^–18 m.

A common feature of the electromagnetic, strong and weak forces is that their mediators are all spin-1. This type of interaction is very special. By assuming that nature has certain gauge symmetries, our current quantum field theories can predict the existence of these types of interactions, and many of their features. There are numerous predictions stemming from these symmetries that have been successfully tested by experiments, such as the identical couplings between gluons and quarks of all flavours, the fact that photons don’t interact with each other, and the structure of higher-order corrections, for example the running of coupling constants and the anomalous magnetic moment of the electron and the muon. Yet, as the mass term in the Lagrangian isn’t invariant under gauge transformations, gauge symmetry predicts, at least naively, that the spin-1 force carriers should be massless. So, while the symmetries that predict the electromagnetic and strong interactions also explain why their force carriers are massless, the symmetry principle that predicts the weak interaction is challenged by the experimental fact that its force carriers are massive.

This conundrum has a possible solution if a symmetry is respected by the quantum field theory but not by the ground state of the universe (see “Broken symmetry” image). The theory’s predictions will then be different from those that would follow if the ground state were also symmetric. One way in which the symmetry can be broken is if there is a scalar field that does not vanish in the ground state. This is the case for the Higgs potential, which, unlike a purely parabolic potential, does not have rotational symmetry around its ground state. The weak-force carriers are affected by their interaction with the BEH field, and this interaction slows them down. Moving at speeds slower than the speed of light – the consequence of interacting with the BEH field in the ground state – is equivalent to having non-zero masses, making weak interactions short range. These insights also transformed our understanding of the early universe. Following the Glashow–Weinberg–Salam breakthrough shortly after the BEH proposal, the Standard Model presents a universe in which the ground state transitioned from zero to non-zero due to the spontaneous breaking of electroweak symmetry – a cosmological event that took place when the universe was about 10^-11 seconds old.

A BEH field different from zero in the ground state of the universe has important observational and experimental consequences. For example, if the symmetry were unbroken, a process where a single Higgs particle decays into a pair of Z bosons would be forbidden. But, once the ground state of the universe breaks the symmetry – the BEH field is non-zero – this process is allowed to occur. (Strictly speaking, the Higgs boson cannot decay into two Z bosons because the sum of their masses is larger than the mass of the Higgs boson, however, the Higgs boson can decay into a real Z boson and a virtual one that produces a pair of fermions.) Similarly, the symmetry would not allow a single Higgs-boson production from Z-boson fusion. But, once the ground state of the universe breaks the symmetry, the latter process is also allowed to occur.

An asymmetric ground state costs the theory none of its predictive power. The strength of the interaction of the Z boson with the BEH field, measured by the mass it gains from this interaction, is closely related to the strength of the interaction of the Z boson with the Higgs particle, measured by the rate at which the Higgs boson decays into two Z bosons, or by the rate at which it is produced by Z-boson fusion. This relation is commonly expressed as the ratio μ_ZZ* between the measured and the predicted rates: if the field related to the newly discovered spin-0 particle is indeed responsible for the mass of the Z boson, then μ_ZZ* = 1.

ATLAS and CMS have established a new law of nature

The rate of the Higgs decay into two Z bosons was first measured with 5σ significance by the ATLAS and CMS experiments in 2016. Its current value is μ_ZZ* ≈ 1.2 ± 0.1. The rate at which the Higgs boson decays into a pair of W bosons was measured in the same year. Its current value of μ_WW* ≈1.2 ± 0.1 also corresponds to the strength of interaction that would give the W boson its mass. Finally, the experiments measured the rate at which a single Higgs boson is produced in vector-boson fusion to be μ_VBF ≈ 1.2 ± 0.2. Thus, ATLAS and CMS have established a new law of nature: the force carriers of the weak interaction gain their masses via their interactions with the everywhere-present BEH field. The strength of this interaction is precisely the right size to limit the effects of the weak interaction to distances shorter than 10^–18 metres.

Third generation, third jewel

The third jewel in the crown of the LHC is the explanation for how the tau-lepton and the top and bottom quarks – members of the third, heaviest fermion family – gain their masses. The same electroweak symmetry that predicts that the weak-force carriers should be massless also predicts that all 12 spin-1/2 matter particles known to us should also be massless. Experiments have shown, however, that all the matter particles are massive, with the one possible exception of the lightest neutrino. The fact that this symmetry is broken in the ground state of the universe also opens the door to the possibility that matter particles gain masses. But via what mechanism? For the ground state of the BEH field to slow down the fermions as well as the W and Z bosons, a new type of interaction has to exist: an interaction with a spin-0 mediator – the Higgs boson itself. Discovering a Higgs-boson decay into a pair of fermions would mean the discovery of this new type of spin-0 mediated interaction, which was first proposed in a different context by Hideki Yukawa in the 1930s.

Yukawa interactions are fundamentally different from the interactions through which the W and Z bosons get their mass because they are not deduced from a symmetry principle. Another difference, in contrast not only to weak, but also to strong and electromagnetic interactions, is that the interaction strength is not quantised. However, the strength of the interaction of a matter particle with the BEH field, measured by the mass it gains from this interaction, is still closely related to the strength of the Yukawa interaction of that matter particle with the Higgs boson, measured by the rate at which the Higgs boson decays into two such fermions. Once again, if the field that gives the matter particles their masses is indeed the one related to the newly discovered spin-0 particle, then the measured decay rate of the Higgs particle to fermion pairs should give a value of unity to the corresponding μ-ratio.

The three heaviest spin-1/2 particles – the top quark, the bottom quark and the tau lepton – are expected to have the strongest couplings to the Higgs boson, and consequently the largest rates of Yukawa interactions with it. The first Yukawa interaction to be measured, with the significance in both the ATLAS and CMS analyses rising to 5σ in 2015, concerned the decay of a Higgs boson into a tau lepton–antilepton pair. The current decay rate is μ_τ+τ– ≈ 1.15 ± 0.15, which, within present experimental accuracy, corresponds to the strength of interaction that would give the tau lepton its mass. The rate of Higgs-boson decays into the bottom quark–antiquark pair was measured by ATLAS and CMS three years later. The current value is μ_bb– ≈ 1.04 ± 0.13. Within present experimental accuracy, this corresponds to the strength of interaction that would give the bottom quark its mass.

The potential of the LHC to discover new facts about nature and the universe is far from saturated

In the case of the top quark, the Higgs boson has a vanishingly tiny decay rate into a top–antitop pair, because the mass of each is individually larger than that of a Higgs boson, and both would have to be produced virtually. To extract the strength of the Higgs–top interaction, experiments instead measure the rate at which this trio of particles is produced. The rate of the production of a Higgs boson together with a top quark–antiquark pair was measured by the ATLAS and CMS experiments in 2018. The current value is μ_tt–h ≈ 1.3 ± 0.2. Within present experimental accuracy, this value corresponds to the strength of interaction that would give the top quark its mass. (The remaining third-generation particle, a neutrino, is at least 12 orders of magnitude lighter than the top quark, and is suspected to derive its mass via a different mechanism, which is unlikely to be tested experimentally in the near future.)

ATLAS and CMS have therefore discovered a new fact about nature: the third-generation charged particles – the tau lepton, the bottom quark and the top quark – also gain their masses via their interaction with the everywhere-present BEH field. This is also the discovery of the new and rather special Yukawa interactions among elementary particles, which are mediated by a spin-0 force carrier, the Higgs boson.

The path forward

Answering questions about nature’s fundamental workings almost always leads to new questions. The discovery of the Higgs boson has already been the source of at least two. Firstly, the value of the Higgs boson’s mass suggests the possibility that our universe is likely in an unstable state. In the extremely distant future, a transition to an entirely different universe with a different ground state could occur. Should this remain true as precision improves, not only is there nothing special about Earth, nor the solar system, nor even Milky Way galaxy, but the fundamental structure of the universe is itself only temporary. What’s more, the lightness of the mass of the Higgs boson compared to both the Planck scale (above which quantum-gravity effects become significant) and the “seesaw scale” (below which new particles, beyond those of the Standard Model, are predicted to exist), poses a challenge to the basic framework that we use to formulate the laws of nature. In quantum field theory, cancellations between tree-level and higher order loop-diagram contributions to the mass of the Standard Model Higgs boson are huge, and require extreme fine-tuning, perhaps by as many as 32 orders of magnitude, between seemingly unrelated constants of nature. Various ideas of how to restore “naturalness”, such as supersymmetry and Higgs compositeness, have been suggested, but the LHC experiments have not uncovered any of the TeV-scale particles predicted by these models and are ruling out ever-increasing swathes of parameter space for the models.

The potential of the LHC to discover new facts about nature and the universe is far from saturated. There are at least two additional, big open questions that are guaranteed to be answered, at least in part, by the LHC experiments. First is the understanding of the mechanism that gives second-generation particles – in particular the muon and the charm quark – their masses. That may be the same mechanism as the one that has been shown to give the third-generation fermions masses, or it may be different (for the latest progress, see Turning the screw on H → μμ). Second is the question of what happened at the electroweak phase transition in the early universe? It may have been a smooth crossover, where the value of the BEH field changed from zero to its present value continuously and uniformly in space, as predicted by the combination of the Standard Model of particle physics and the Big Bang model, or it may have been a first-order phase transition, where bubbles with a finite value of the BEH field nucleated within the surrounding plasma. A first-order phase transition could open the door to a new mechanism to explain the matter–antimatter imbalance in the universe. These deep questions depend on a new chapter of Higgs research concerning the self-interaction of the Higgs boson, which will be carried forward by a future collider.

Beyond constituting amazing intellectual and technological achievements, the LHC experiments have already made a series of profound discoveries about nature. The existence of a spin-0 particle whose non-zero force field is responsible for both the short range of weak interactions and, in a distinct way, the masses of spin-1/2 particles, represents three major discoveries. That theorists have long speculated on these new laws of nature ideas must not diminish the significance of establishing them experimentally. These three jewels in the crown of LHC research, the first steps in the exploration of Higgs physics, begin a trek to some of the most significant open questions in particle physics and cosmology.

The post One Higgs, three discoveries appeared first on CERN Courier.

The latest measurements of the Higgs boson by ATLAS and CMS follow 5σ observations of its coupling to the tau lepton in 2015 and to the top and bottom quarks in 2018, all of which are third-generation fermions. Its couplings to W and Z bosons have also been established at 5σ confidence. Within present experimental accuracy, all couplings between the Higgs boson and other Standard Model particles correspond to the strength of interaction that would give the particles their observed masses, according to the Brout–Englert–Higgs mechanism. In this model, the particles acquire mass through spontaneous symmetry breaking; the W and Z as a result of a local gauge symmetry and the fermions, such as the muon, as a result of Yukawa couplings to the Higgs field – a novel type of interaction among fundamental particles that is not derived from a symmetry principle. Any deviation from the expected couplings would imply that the Higgs sector is more complicated than this minimal scenario.

Couplings to lighter particles are expected to be proportionately smaller and more difficult to observe. The decay to two muons, H → μμ, is expected to occur with a branching fraction of just one in 5000 Higgs-boson decays, and is overwhelmed by backgrounds from the Drell–Yan process.

The new results sharpen the question of why there is a hierarchy of particle masses

John Ellis

The new ATLAS and CMS analyses, which deploy the entire 13 TeV Run-2 data set, include events where the Higgs boson was produced according to four topologies gluon fusion, which accounts for the creation of 87% of the Higgs bosons observed at the LHC; vector-boson fusion; the production of a Higgs boson in association with a weak vector boson; and its production in association with a top quark–antiquark pair. Uniquely, CMS simulated the background to the vector-boson-fusion signal rather than fitting it from data – a procedure that would have incurred additional statistical uncertainty – resulting in the topology contributing roughly equal statistical power compared to gluon fusion.

Machine learning
“The first evidence in CMS was reached thanks to the excellent performance of our muon and tracking systems, and an improved signal/background discrimination with machine-learning techniques,” says Andrea Rizzi, CMS physics co-coordinator.

The signature for the decay is a small excess of events near a muon-pair invariant mass of 125 GeV – the mass of a Higgs boson. CMS reports an overall signal strength of 1.2 ± 0.4, while ATLAS finds a signal strength of 1.2 ± 0.6, with the uncertainties dominated by their statistical component. “Both measurements are compatible with the Standard Model,” says ATLAS physics coordinator Klaus Mönig. “Assuming the H → μμ coupling predicted by the Standard Model, and extrapolating the current results, the combined sensitivity could get near the observation threshold of 5σ at the end of Run 3, from 2022 to 2024.”

If there is only a single Higgs field, it should provide the masses for all the Standard-Model particles, but there may be additional Higgs fields that could make contributions to their masses. The new results therefore reduce the scope available to such multi-Higgs models, and sharpen the question of why there is a hierarchy of particle masses, says John Ellis of King’s College London. “Why is the Higgs coupling to the muon so different from its coupling to the tau lepton, whereas the couplings of the W boson to tau leptons and muons are equal to within a couple of percent? The more we learn about the Higgs, the more mysterious it seems!”

The post Turning the screw on H → μμ appeared first on CERN Courier.

This was the first ICHEP meeting since the publication of the update of the European strategy for particle physics, which presented an ambitious vision for the future of CERN. Though VIP-guest Peter Gabriel – rock star and human rights advocate – may not have been aware of this when delivering his opening remarks, his urging that delegates speak up for science and engage with politicians resonated with the physicists virtually present.

Many scientific highlights were covered at ICHEP and it is only possible to scratch the surface here. The results from all four major LHC experiments were particularly impressive and the collective progress in understanding the properties of neutrinos shows no sign of slowing down.

Higgs physics
ATLAS and CMS presented the first evidence for the decay of the Higgs boson into a pair of muons. Combined, the results provide strong evidence for the coupling of the Higgs boson to the muon, with the strength of the coupling consistent with that predicted in the Standard Model. Prior to these new results, the Higgs had only been observed to couple to the much heavier third-generation fermions and the W and Z gauge bosons. The measurements also provide further evidence for the linearity of the Higgs coupling, now over four orders of magnitude (from the muon to top quark), indicating the universality of the Standard-Model Higgs boson as the mechanism through which all Standard Model particles acquire mass. These are highly non-trivial statements.

ATLAS also presented a combined measurement of the Higgs signal strength, which describes a common scaling of the expected Higgs-boson yields in all processes, of 1.06 ± 0.07. In this measurement, the experimental and theoretical uncertainties are now roughly equal, emphasising the ever-increasing importance of theoretical developments in keeping up with the experimental progress; a feature that will ultimately determine the precision that will be reached by the LHC and high-luminosity LHC (HL-LHC) Higgs physics programmes.

The range of Standard Model measurements presented at ICHEP 2020 by ATLAS and CMS was truly impressive

More generally, the precision we are seeing from the ATLAS and CMS Run 2 proton–proton data is truly impressive, and an exciting indication of what is to come as the integrated luminosity accumulated by the experiments ramps up, and then ramps up again in the HL-LHC era. One interesting new example was the first observation of WW production from photon–photon collisions, where the photons are radiated from the incoming proton beams. This is a neat measurement that demonstrates the breadth of physics accessible at the LHC.

Overall, the range of Standard Model measurements presented at ICHEP 2020 by ATLAS and CMS was truly impressive and we should not forget that it is still relatively early in the LHC programme. In parallel, direct searches for new phenomena, such as supersymmetry and the “unexpected”, continues apace. Results from direct searches at the energy frontier were covered in numerous parallel session presentations. The current status was summarised succinctly by Paris Sphicas (Athens) in his conference summary talk: “Looked for a lot of possible new things. Nothing has turned up yet. Still looking intensively.”

Flavour physics
Over the last few years, a number of deviations from theoretical predictions have been observed in B-meson decays to final states with leptons. Discrepancies have been observed in ratios of decays to different lepton species, and in the angular distribution of decay products. Taken alone, each of these discrepancies are not particularly significant, but collectively they may be telling us something new about nature. At ICHEP 2020, the LHCb experiment presented their recently published results on the angular analysis in B⁰ → K^*0 μ⁺μ^–. The overall picture remains unchanged. The full analysis of the LHCb Run-2 data set, including updated measurements of the relative rates of the muon and electron decay modes (R_K and R_K*), is eagerly awaited.

The search for rare kaon decays continues to attract interest

The search for rare kaon decays continues to attract interest. One of the most impressive results presented at ICHEP was the recent observation by NA62 of the extremely rare kaon decay, K⁺ → π⁺νν̄. Occurring only once in every 10 billion decays, this is an incredibly challenging measurement and the new NA62 result is the first statistically significant observation of this decay, based on just 17 events. Whilst the observed rate is consistent with the Standard Model expectation, its observation opens up a new future avenue for exploring the possible effects of new physics.

Neutrino physics
Neutrino physics continues to be one of the most active areas of research in particle physics, so it was not surprising that the neutrino parallel sessions were the best attended of the conference. This is a particularly interesting time, with long-baseline neutrino oscillation experiments becoming sensitive to the neutrino mass ordering, and beginning to provide constraints on CP violation. Updates were presented by the NOvA experiment in the USA and the T2K experiment in Japan. Both experiments favour the normal-ordering hypothesis, although not definitively, and there is currently a slight tension between the CP violation results from the two experiments. It is worth noting that the combined interpretation of the two experiments is quite complex. The NOvA and T2K collaborations are working on a combined analysis to clarify the situation.

There were also a number of presentations on the next generation of long-baseline neutrino oscillation experiments, DUNE in the US and Hyper-Kamiokande in Japan, which aim to make the definitive discovery of CP violation in the neutrino sector. In the context of DUNE, the progress with liquid-argon time-projection- chamber (LArTPC) detector technology is impressive. It was particularly pleasing to see a number of physics results from MicroBooNE at Fermilab, and the single-phase DUNE detector prototype at CERN (ProtoDUNE-SP), that are based on the automatic reconstruction of LArTPC images – a longstanding challenge.

Virtual success
A vast range of high-qualify scientific research was covered in the 800 parallel session presentations and summarised in the 44 plenary talks at ICHEP 2020. The quality of the presentations was high, and speakers coped well with the challenge of pre-recording talks. The “replay” sessions worked extremely well too – an innovation that is likely to persist in the post-COVID world. About 3000 people registered for the meeting, which is more than double the previous two events. It was particularly pleasing to learn that almost 2500 connected to the parallel sessions.

Despite the many successes, we all missed the opportunity to meet colleagues in person; it is often the informal discussions over coffee or in restaurants and bars that generate new ideas and, importantly, lead to new collaborations. Whilst virtual conferences are likely to remain a feature in the post- COVID world, they will not replace in-person events.

The post ICHEP’s online success appeared first on CERN Courier.

Protons accelerated by the LHC generate a large flux of quasi-real high-energy photons that can interact to produce particles at the electroweak scale. Using the LHC as a photon collider, the ATLAS collaboration announced a set of landmark results at the 40th International Conference on High Energy Physics last week, among which is the first observation of the photo-production of W-boson pairs.

As it proceeds via trilinear and quartic gauge-boson vertices involving two W bosons and either one or two photons, the production of a pair of W bosons from two photons (ɣɣ → WW) tests a longstanding prediction of the Standard Model (SM). This process is extremely rare but predicted precisely by electroweak theory, such that any observed deviation would suggest that new physics is at play. The measurement relies on the large 139 fb^–1 dataset of proton–proton collisions recorded by ATLAS in LHC Run 2.

Protons usually remain intact or are excited into a higher energy state in photon collisions, with the products of any subsequent decay not reaching the innermost components of the ATLAS detector. In these cases, the electron and muon decaying from the W bosons – an event topology chosen to avoid the high background for same-flavour lepton pairs – are the only particles detected in the vicinity. However, if charged particles arise from nearby proton–proton collisions, the clean ɣɣ → WW signal can be missed. The main background is W-boson pairs produced in head-on proton–proton collisions where particles from the break-up of the protons are not detected due to imperfect detector coverage or reconstruction (figure 1). A total of 127 background events were predicted compared with 307 events observed in the data, corresponding to a signal excess of 8.4 standard deviations. This establishes the existence of light transforming into particles with weak-scale masses – a remarkable and previously unobserved phenomenon.

Innovation

Precisely testing SM predictions of photon collisions requires accurate knowledge of the rate protons remain intact relative to those that break apart. This is challenging to predict theoretically and probing these rates unambiguously requires directly detecting the intact protons. The ATLAS forward-proton spectrometer (AFP) is becoming increasingly indispensable for this task. Among the newest additions to the ATLAS experiment, and located a few millimetres from the beam 210 m either side of the collision point, the AFP can detect protons that have been scattered in photon–photon collisions but which have nevertheless been focused by the LHC’s magnets. Its pioneering results so far analyse a standard-candle process where a proton is scattered in photon collisions that produce electron or muon pairs (ɣɣ → ℓℓ). For these signals, the measured proton energy loss is equal to that predicted from the lepton pairs measured in the main ATLAS detector (figure 2). ATLAS reported 180 events with a proton having matched kinematics to the lepton pair with an expected background of about 20 events. This corresponds to a significance exceeding nine standard deviations for both lepton flavours, establishing the presence of the signal and the successful operation of the AFP spectrometer in high-luminosity data. The detectors were sufficiently well understood to measure the cross sections of these processes.

Observing ɣɣ → WW and scattered protons in ɣɣ → ℓℓ interactions are long-awaited milestones in an emerging experimental programme studying photon collisions. These complement recent heavy-ion results where ATLAS measured muon pairs from photon collisions and the kinematic properties of light-by-light scattering – a very rare process predicted by quantum electrodynamics. Interestingly, the latter was also used to search for the axion-like particles predicted by certain extensions of the SM.

Observing ɣɣ → WW and scattered protons in ɣɣ → ℓℓ interactions are long-awaited milestones

The techniques developed to study ɣɣ → WW and ɣɣ → ℓℓ interactions lay the groundwork for future, more detailed tests of the SM. Further results using the AFP spectrometer can improve theoretical understanding of photon collisions that will also benefit future measurements of ɣɣ → WW production. These landmark experimental feats will only become more interesting with the increased dataset of Run 3 and the high-luminosity LHC.

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The electroweak (EW) sector of the Standard Model (SM) predicts self-interactions between W and Z gauge bosons through triple and quartic gauge couplings. Following first measurements at LEP and at the Tevatron during the 1990s, these interactions are now a core part of the LHC physics programme, as they offer key insights into EW symmetry breaking, which, in the case of the SM, causes the W and Z bosons to acquire mass as a result of the Brout–Englert–Higgs mechanism. The quartic coupling can be probed at colliders via rare processes such as tri-boson production, which the CMS collaboration observed for the first time earlier this year, and vector-boson scattering (VBS).

The scattering of longitudinally polarised W and Z bosons is a particularly interesting probe of the SM, as its tree-level amplitudes would violate unitarity at high energies without delicate cancellations from quartic gauge couplings and Higgs-boson contributions. Thus, the study of VBS processes provides key insight into the quartic gauge couplings as well as the Higgs sector. These processes offer sensitivity to enhancements caused by models of physics beyond the SM, which modify the Higgs sector with additional Higgs bosons contributing to VBS.

Vector-boson scattering is characterised by the presence of two forward jets, with a large di-jet invariant mass and a large rapidity separation. CMS previously reported the first observation of same-sign W^±W^± production using the data collected in 2016. The same-sign W^±W^± process is chosen because of the smaller background yield from other SM processes compared to the opposite-sign W^±W^∓ process. The collaboration has now updated this analysis and performed new studies of the EW production of two jets produced in association with WZ, and ZZ boson pairs using data collected between 2016 and 2018 at a centre-of-mass energy of 13 TeV, corresponding to 137 fb^–1. Vector-boson pairs were selected by their decays to electrons and muons. The W^±W^± and WZ production modes were studied by simultaneously measuring their production cross sections using several kinematical observables. The measured total cross section for W^±W^± production of 3.98 ± 0.45 (± 0.37 stat. only) fb is the most accurate to date, with a precision of roughly 10%. No deviation from SM predictions is evident.

Though the contribution from background processes induced by the strong interaction is considerably larger in the WZ and ZZ final states, the scattering centre-of-mass energy and the polarisation of the final-state bosons can be measured as these final states can be more fully reconstructed than in W^±W^± production. To optimally isolate signal from background, the kinematical information of the WZ and ZZ candidate events is exploited with a boosted decision tree and matrix element likelihood techniques, respectively (see figure). The observed statistical significances for the WZ and ZZ processes are 6.8 and 4.0 standard deviations, respectively, in line with the expected SM significances of 5.3 and 3.5 standard deviations. The possible presence of anomalous quartic gauge couplings could result in an excess of events with respect to the SM predictions. Strong new constraints on the structure of quartic gauge couplings have been set within the framework of dimension-eight effective-field-theory operators.

The observation of the EW production of W^±W^±, WZ and ZZ boson pairs is an essential milestone towards pre­cision tests of VBS at the LHC, and there is much more to be learned from the future LHC Run-3 data. The High-Lumin­osity LHC should allow for very precise investigations of VBS, including finding evidence for the scattering of longitudinally polarised W bosons.

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LHCP20 presentations covered a wide assortment of topics and several new results with significantly enhanced sensitivity than was previously possible. These included both precision measurements with excellent potential to uncover discrepancies that can be explained only by beyond the Standard Model (SM) physics and direct searches using innovative techniques and advanced analysis methods to look for new particles.

The first observation of the combined production of three massive vector bosons was reported by CMS

The first observation of the combined production of three massive vector bosons (VVV with V = W or Z) was reported by the CMS experiment. In the nearly 40 years that have followed the discovery of the W and Z boson, their properties have been measured very precisely, including via “diboson” measurements of the simultaneous production of two vector bosons. However, “triboson” simultaneous production of three massive vector bosons had eluded us so far, as the cross sections are small and the background contributions are rather large. Such measurements are crucial to undertake, both to test the underlying theory and to probe non-standard interactions. For example, if new physics beyond the SM is present at high mass scales not far above 1 TeV, then cross section measurements for triboson final states might deviate from SM predictions. The CMS experiment took advantage of the large Run 2 dataset and machine learning techniques to search for these rare processes. Leveraging the relatively background-free leptonic final states, CMS collaborators were able to combine searches for different decay modes and different types of triboson production (WWW, WWZ, WZZ and ZZZ) to achieve the first observation of combined heavy triboson production (with an observed significance of 5.7 standard deviations) and at the same time evidence for WWW and WWZ production with observed significances of 3.3 and 3.4 standard deviations, respectively. While the results obtained so far are in agreement with SM predictions, more data is needed for the individual measurements of the WZZ and ZZZ processes.

Four-top-quark production

The first evidence for four-top-quark production was announced by ATLAS. The top-quark discovery in 1995 launched a rich programme of top-quark studies that includes precision measurements of its properties as well as the observation of single-top-quark production. In particular, since the large mass of the top quark is a result of its interaction with the Higgs field, studies of rare processes such as the simultaneous production of four top quarks can provide insights into properties of the Higgs boson. Within the SM, this process is extremely rare, occurring just once for every 70 thousand pairs of top quarks created at the LHC; on the other hand, numerous extensions of the SM predict exotic particles that couple to top quarks and lead to significantly higher production rates. The ATLAS experiment performed this challenging measurement using the full Run-2 dataset using sophisticated techniques and machine-learning methods applied to the multilepton final state to obtain strong evidence for this process. The observed signal significance was found to be 4.3 standard deviations, in excess of the expected sensitivity of 2.4, assuming SM four-top-quark-production properties. While the measured value of the cross section was found to consistent with the SM prediction within 1.7 standard deviations, the data collected during Run 3 will shed further light on this rare process.

The LHCb collaboration presented, with unprecedented precision, measurements of two properties of the mysterious X(3872) particle. Originally discovered by the Belle experiment in 2003 as a narrow state in the J/ψπ⁺π⁻ mass spectrum of B⁺→J/ψπ⁺π⁻K⁺ decays, this particle has puzzled particle physicists ever since. The nature of the state is still unclear and several hypotheses have been proposed, such as its being an exotic tetraquark (a system of four quarks bound together), a two-quark hadron, or a molecular state consisting of two D mesons. LHCb collaborators reported the most precise mass measurement yet, and measured, for the first time, and with 5 standard-deviations significance, the width of the resonance (see LHCb interrogates X(3872) line-shape). Though the results favour its interpretation as a quasi-bound D⁰D^*0 molecule, more data and additional analyses are needed to rule out other hypotheses.

Antideuterons could be produced during the annihilation or decay of neutralinos or sneutrinos

The ALICE collaboration presented a first measurement of the inelastic low-energy antideuteron cross section using p-Pb collisions at a centre-of-mass energy per nucleon–nucleon pair of 5.02 TeV. Low-energy antideuterons (composed of an antiproton and an antineutron) are predicted by some models to be a promising probe for indirect dark-matter searches. In particular, antideuterons could be produced during the annihilation or decay of neutralinos or sneutrinos, which are hypothetical dark-matter particles. Contributions from cosmic-ray interactions in the low-energy range below 1-2 GeV per nucleon are expected to be small. ALICE collaborators used a novel technique that utilised the detector material as an absorber for antideuterons to measure the production and annihilation rates of low energy antideuterons. The results from this measurement can be used in propagation models of antideuterons within the interstellar medium for interpreting dark-matter searches, including intriguing results from the AMS experiment. Future analyses with higher statistics data will improve the modelling as well as extend these studies to heavier antinuclei.

The above are just a few of the many excellent results that were presented at LHCP2020. The extraordinary performance of the LHC coupled with progress reported by the theory community, and the excellent data collected by the experiments, has inspired LHC physicists to continue with their rich harvest of physics results despite the current world crisis. Results presented at the conference showed that huge progress has been made on several fronts, and that Run 3 and the High-Luminosity LHC upgrade programme will enable further exploration of particle physics at the energy frontier.

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Weighing in at 180 times the mass of the proton, the top quark is the heaviest elementary particle discovered so far. Because of its large mass, it is the only quark that does not form bound states with other quarks but decays immediately after it has been produced. Despite its short lifetime, its existence has far-reaching consequences. It governs the stability of the electroweak vacuum, gives large contributions to the mass of the W boson, and influences many other important observables through quantum-loop corrections. An accurate knowledge of its mass is important for our understanding of fundamental interactions.

The top quark governs the stability of the electroweak vacuum

The LHC’s high centre-of-mass energy makes it an ideal laboratory to study the properties of the top quark with unprecedented precision. Such studies demand that jets originating from light and bottom quarks are measured very accurately, however, subtleties remain even then, as exact calculations are not possible for low-energy quarks and gluons once they start to form bound states. In this regime, our approximations become inaccurate, because the mass of the bound states becomes as large as the energy of the underlying process. An exciting way to overcome these difficulties is to measure top quarks that have been produced with very high transverse momenta and thus large Lorentz boosts. In these topologies, the decay products are highly collimated, and can be clearly assigned to a decaying top quark. Effects from the formation of hadrons play a minor effect in boosted topologies as the top quarks, which were originally produced in quark–antiquark pairs, move apart from each other fast enough that their decays can be considered to happen independently.

Boosted precision

By reconstructing a boosted top quark in a single jet, a measurement of the jet mass can be translated into one of the top-quark mass. The CMS collaboration has carried out such a measurement using the √s = 13 TeV data collected in 2016, reconstructing the top-quark jets with the novel XCone algorithm to obtain a top quark mass of 172.6 ± 2.5 GeV (figure 1). Due to this new way of reconstructing jets, an improvement of more than a factor of three relative to an earlier measurement at √s = 8 TeV has been achieved. Although the uncertainty is larger than for direct measurements, where top quarks are reconstructed from multiple jets or leptons and missing transverse momentum (which currently yield a world average of 172.9 ± 0.4 GeV from a combination of CMS, ATLAS and Tevatron measurements), this new result shows for the first time the potential of using boosted top quarks for precision measurements.

The jet mass can be translated into the top-quark mass

Measuring the properties of the top quark at high momenta enables detailed studies of a theoretically compelling kinematic regime that has not been accessible before. Different effects, such as the collinear radiation of gluons and quarks, govern its dynamics compared to top-quark production at low energies. Exploiting the full Run-2 dataset should allow CMS to extend this measurement to higher boosts, and establish the boosted regime for a number of precision measurements in the top-quark sector in Run 3 and at the high-luminosity LHC.

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After the discovery of the long‑sought Higgs boson at a mass of 125 GeV, a major question in particle physics is whether the electroweak symmetry breaking sector is indeed as simple as the one implemented in the Standard Model (SM), or whether there are additional Higgs bosons. Additional Higgs bosons would occur, for example, in the presence of a second Higgs field, as realised in two‑Higgs doublet models, among which is the well‑known minimal supersymmetric extension of the SM (MSSM). The discovery of additional Higgs bosons could therefore be a gateway to new symmetries in nature.

ATLAS has recently released results of a search for heavy Higgs bosons decaying into a pair of tau leptons using the complete LHC Run 2 dataset (139 fb^–1 of 13 TeV proton–proton data). The new analysis provides a considerable increase in sensitivity to MSSM scenarios compared to previous results.

The MSSM features five Higgs bosons

The MSSM features five Higgs bosons, among which, the observed Higgs boson can be the lightest one. The couplings of the heavy Higgs bosons to down‑type leptons and quarks, such as the tau lepton and bottom quark, are enhanced for large values of tan β – the ratio of the vacuum expectation values of the two Higgs doublets, and one of the key parameters of the model. The heavy neutral Higgs bosons A (CP odd) and H (CP even) are produced mainly via gluon–gluon interactions or in association with bottom quarks. Their branching fractions to tau leptons can reach sizeable values across a large part of the model‑parameter space, making this channel particularly sensitive to a wide range of MSSM scenarios.

New search

The new ATLAS search requires the presence of two oppositely charged tau‑lepton candidates, one of which is identified as a hadronic tau decay, and the other as either a hadronic or a leptonic decay. To profit from the enhancement of the production of signal events in association with bottom quarks at large tan β values (for example when the heavy Higgs boson is radiated by a b‑quark produced in the collision of two gluons), the data are further categorised based on the presence or absence of additional b‑jets. One of the challenges of the analysis is the misidentification of backgrounds with hadronic jets as tau candidates. These backgrounds are estimated from data by measuring the misidentification probabilities and applying them to events in control regions representative of the event selection. The final discriminant is on the quantity m_T^tot, which is built from the combination of the transverse masses of the two tau‑lepton decay products (figure 1).

The data agree with the prediction assuming no additional Higgs bosons, despite a small, non‑significant excess around a putative signal mass value of 400 GeV. The measurement places limits on the production cross section that can be translated into constraints on MSSM parameters. One realisation of the MSSM is the hMSSM scenario, in which the knowledge of the observed Higgs‑boson mass is used to reduce the number of parameters. The A/H → ττ exclusion limit dominates over large parts of the parameter space (figure 2), but still leaves room for possible discoveries at masses above the top‑anti‑top quark production threshold. ATLAS continues to refine this and conduct further searches for heavy Higgs bosons in various final states.

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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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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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Though a free parameter in the Standard Model, the mass of the Higgs boson is important for both theoretical and experimental reasons. Most peculiarly from a theoretical standpoint, our current knowledge of the masses of the Higgs boson and the top quark imply that the quartic coupling of the Higgs vanishes and becomes negative tantalisingly close to, but just before, the Planck scale. There is no established reason for the Standard Model to perch near to this boundary. The implication is that the vacuum is almost but not quite stable, and that on a timescale substantially longer than the age of the universe, some point in space will tunnel to a lower energy state and a bubble of true vacuum will expand to fill the universe. Meanwhile, from an experi­mental perspective, it is important to continually improve measurements so that uncertainty on the mass of the Higgs boson eventually rivals the value of its width. At that point, measuring the Higgs-boson mass can provide an independent method to determine the Higgs-boson width. The Higgs-boson width is sensitive to the existence of possible undiscovered particles and is expected to be a few MeV according to the Standard Model.

The CMS collaboration recently announced the most precise measurement of the Higgs-boson mass achieved thus far, at 125.35 ± 0.15 GeV – a precision of roughly 0.1%. This very high precision was achieved thanks to an enormous amount of work over many years to carefully calibrate and model the CMS detector when it measures the energy and momenta of the electrons, muons and photons necessary for the measurement.

The most recent contribution to this work was a measurement of the mass in the di-photon channel using data collected at the LHC by the CMS collaboration in 2016 (figure 1). This measurement was made using the lead–tungstate crystal calorimeter, which uses approximately 76,000 crystals, each weighing about 1.1 kg, to measure the energy of the photons. A critical step of this analysis was a precise calibration of each crystal’s response using electrons from Z-boson decay, and accounting for the tiny difference between the electron and photon showers in the crystals.

This new result was combined with earlier results obtained with data collected between 2011 and 2016. One measurement was in the decay channel to two Z bosons, which subsequently decay into electron or muon pairs, and another was a measurement in the di-photon channel made with earlier data. The 2011 and 2012 data combined yield 125.06 ± 0.29 GeV. The 2016 data yield 125.46 ± 0.17 GeV. Combining these yields CMS’s current best precision of 125.35 ± 0.15 GeV (figure 2). This new precise measurement of the Higgs-boson mass will not, at least not on its own, lead us in a new direction of physics, but it is an indispensable piece of the puzzle of the Standard Model – and one fruit of the increasing technical mastery of the LHC detectors.

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As the heaviest known particle, the top quark plays a unique role in the Standard Model (SM), making its presence felt in corrections to the masses of the W and Higgs bosons, and also, perhaps, in as-yet unseen physics beyond the SM. During Run 2 of the Large Hadron Collider (LHC), high-luminosity proton beams were collided at a centre-of-mass energy of 13 TeV. This allowed ATLAS to record and study an unprecedented number of collisions producing top–antitop pairs, providing ATLAS physicists with a unique opportunity to gain insights into the top quark’s properties.

ATLAS has measured the top–antitop production cross-section using events where one top quark decays to an electron, a neutrino and a bottom quark, and the other to a muon, a neutrino and a bottom quark. The striking eμ signature gives a clean and almost background-free sample, leading to a result with an uncertainty of only 2.4%, which is the most precise top-quark pair-production measurement to date. The measurement provides information on the top quark’s mass, and can be used to improve our knowledge of the parton distribution functions describing the internal structure of the proton. The kinematic distributions of the leptons produced in top-quark decays have also been precisely measured, providing a benchmark to test programs that model top-quark production and decay at the LHC (figure 1).

The mass of the top quark is a fundamental parameter of the SM, which impacts precision calculations of certain quantum corrections. It can be measured kinematically through the reconstruction of the top quark’s decay products. The top quark decays via the weak interaction as a free particle, but the resulting bottom quark interacts with other particles produced in the collision and eventually emerges as a collimated “b-jet” of hadrons. Modelling this process and calibrating the jet measurement in the detector limits the precision in many top-quark mass measurements, however, 20% of the b-jets contain a muon that carries information relating to the parent bottom quark. By combining this muon with an isolated lepton from a W-boson originating from the same top-quark decay, ATLAS has made a new measurement of the top quark mass with a much-reduced dependence on jet modelling and calibration. The result is ATLAS’s most precise individual top-quark mass measurement to date: 174.48 ± 0.78 GeV.

Higher order QCD diagrams translate this imbalance into the charge asymmetry

At the LHC, top and antitop quarks are not produced fully symmetrically with respect to the proton-beam direction, with top antiquarks produced slightly more often at large angles to the beam, and top quarks, which receive more momentum from the colliding proton, emerging closer to the axis. Higher order QCD diagrams translate this imbalance into the so-called charge asymmetry, which the SM predicts to be small (~0.6%), but which could be enhanced, or even suppressed, by new physics processes interfering with the known production modes. Using its full Run-2 data sample, ATLAS finds evidence of charge asymmetry in top-quark pair events with a significance of four standard deviations, confidently showing that the asymmetry is indeed non-zero. The measured charge asymmetry of 0.0060 ± 0.0015 is compatible with the latest SM predictions. ATLAS also measured the charge asymmetry versus the mass of the top–antitop system, further probing the SM (figure 2).

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A team of researchers from the UK, Germany and the US has used data from the CLAS experiment at Jefferson Laboratory to confirm an anomalous measurement of ⍺_– — a key parameter in the theoretical description of the non-leptonic decays of Λ hyperons. ⍺_– describes the interference of parity-conserving and parity-violating amplitudes in the matrix element of the decay Λ → pπ^–, and its Particle Data Group listing had remained unchanged for over 40 years. The new value will have consequences for heavy-ion physics, measurements of the transverse polarisation of Λ hyperons, the decays of heavier strange baryons, and kaon production.

Prior to this year, the best measurement of ⍺_– was derived from π⁻p→ΛK⁰ interactions using liquid-hydrogen targets dating from the early 1970s. In May, however, the BESIII collaboration in Beijing published a new measurement ⍺_– = 0.750 ± 0.009 (stat) ± 0.004 (syst) based on observations of the decays of ΛΛ pairs from electron-positron collisions at the J/ψ resonance. The collaboration also reported a measurement of the corresponding parameter ⍺₊ = −0.758 ± 0.010 (stat) ± 0.007 (syst) for the charge-conjugate decay Λ → p̄π⁺, consistent with the conservation of CP symmetry — the most sensitive test with Λ baryons so far. The BESIII value is 17% (corresponding to more than five standard deviations) above the previously accepted value, ⍺_– = 0.642 ± 0.013. “We suspect previous experiments underestimated some systematic biases in their analyses,” says BESIII spokesperson Yuan Changzheng, of the Institute for High-Energy Physics in Beijing.

David Ireland of the University of Glasgow, and colleagues at George Washington University, the University of Bonn and Forschungszentrum Jülich, have now confirmed the BESIII measurement using kaon photo-production (γp→KΛ) data from the CLAS detector, which operated from 1998 to 2012. Their analysis exploited CLAS measurements of polarisation observables that describe the decay of the recoiling Λ→ pπ^– to infer the value of α_– using a theoretical tool known as Fierz identities. The value found, α_– = 0.721 ± 0.006 (stat) ± 0.005 (syst), is near to, but noticeably below, the BESIII value.

Any experiment that has used this value as part of their analysis should look again

David Ireland

“These data were not measured specifically to evaluate ⍺_–,” said Ireland, a former spokesperson of CLAS, “but when the BES result was reported, we realised that they represented a unique opportunity to make an independent estimate of the decay parameter.” Any experiment that has used this value as part of their analysis should look again, he continued. “It would be sensible for the time being to use both the BES and CLAS results to give a range of possible systematic uncertainty.”

The new analysis confirms the BESIII result “very nicely”, concurs Yuan, given that it is based on completely different data and a different technique. “BESIII has now accumulated another 8.7 billion J/ψ events, and the same process will be analysed to
further improve the precision, both statistical and systematic.”

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The first two days of the conference reviewed Higgs measurements, including a new ATLAS measurement of ttH production using Higgs boson decays to leptons, and a differential measurement of Higgs boson production in its decays to W-boson pairs using all of the CMS data from Run 2. These measurements showed continuing progress in coupling measurements, but the highlight of the precision presentations was a new determination of the Higgs boson mass from CMS using its decays to two photons. Combining this result with previous CMS measurements gives a Higgs boson mass of 125.35 ± 0.15 GeV/c², corresponding to an impressive relative precision of 0.12%. From the theory side, the challenges of keeping up with experimental precision were discussed. For example, the Higgs boson production cross section is calculated to the highest order of any observable in perturbative QCD, and yet it must be predicted even more precisely to match the expected experimental precision of the HL-LHC.

ATLAS presented an updated self-coupling constraint

One of the highest priority targets of the HL-LHC is the measurement of the self-coupling of the Higgs boson, which is expected to be determined to 50% precision. This determination is based on double-Higgs production, to which the self-coupling contributes when a virtual Higgs boson splits into two Higgs bosons. ATLAS and CMS have performed extensive searches for two-Higgs production using data from 2016, and at the conference ATLAS presented an updated self-coupling constraint using a combination of single- and double-Higgs measurements and searches.  Allowing only the self-coupling to be modified by a factor ?_λ in the loop corrections yields a constraint on the Higgs self-coupling of –2.3 < ?_λ < 10.3 times the Standard Model prediction at 95% confidence.

The theoretical programme of the conference included an overview of the broader context for Higgs physics, covering the possibility of generating the observed matter-antimatter asymmetry through a first- order electroweak phase transition, as well as possibilities for generating the Yukawa coupling matrices. In the so-called electroweak baryogenesis scenario, the cooling universe developed bubbles of broken electroweak symmetry with asymmetric matter-antimatter interactions at the boundaries, with sphalerons in the electroweak-symmetric space converting the resulting matter asymmetry into a baryon asymmetry. The matter-asymmetric interactions could have arisen through Higgs boson couplings to fermions or gauge bosons, or through its self-couplings. In the latter case the source could be an additional electroweak singlet or doublet modifying the Higgs potential.

The broader interpretation of Higgs boson measurements and searches was discussed both in the case of specific models and in the Standard Model effective field theory, where new particles appear at significantly higher masses (~1 TeV/c² or more). The calculations in the effective field theory continue to advance, adding higher orders in QCD to more electroweak processes, and an analytical determination of the dependence of the Higgs decay width on the theory parameters. Constraints on the number and values of these parameters also continue to improve through an expanded use of input measurements.

The conference wrapped up with a look into the crystal ball of future detectors and colliders, with a sobering yet inspirational account of detector requirements at the next generation of colliders. To solve the daunting challenges, the audience was encouraged to be creative and explore new technologies, which will likely be needed to succeed. Various collider scenarios were also presented in the context of the European Strategy update, which will wrap up early next year.

The newly minted Higgs conference will be held in late October or early November of 2020 in Stonybrook, New York.

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The LHC completed its Run 2 operations in December 2018, delivering a large dataset of proton–proton collisions at a centre-of-mass energy of 13 TeV. The ATLAS detector maintained a high level of readiness and performance throughout Run 2, resulting in 139 fb^–1 of data for physics analyses.

An increasingly consistent picture of the properties of the Higgs boson is being drawn in light of the Run 2 data. This is thanks to a wide range of measurements, and particularly through the establishment of its couplings with third-generation quarks following the observation of the H → bb decay and associated ttH production.

The H → γγ and H → ZZ* → 4ℓ final states, where 4ℓ denotes 4e, 2e2μ or 4μ, provide clean experimental signatures that played a leading role in the discovery of the Higgs boson, and are ideal for precision measurements that could reveal subtle effects from new physics. ATLAS presented updated results for these two channels using the full Run 2 dataset at the 2019 summer conferences.

Using improved identification and energy calibration of leptons, photons and jets, and new analysis techniques, a sample of about 210 H → ZZ* → 4ℓ signal events (figure 1) and 6550 H → γγ signal events were selected to perform a series of measurements. The properties of the Higgs boson are investigated by measuring inclusive, differential and per-production-mode cross sections that are sensitive to different modelling aspects.