Fermilab’s final word on muon g-2

Fermilab’s Muon g-2 collaboration has given its final word on the magnetic moment of the muon. The new measurement agrees closely with a significantly revised Standard Model (SM) prediction. Though the experimental measurement will likely now remain stable for several years, theorists expect to make rapid progress to reduce uncertainties and resolve tensions underlying the SM value. One of the most intriguing anomalies in particle physics is therefore severely undermined, but not yet definitively resolved.

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

Move on up

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

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

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

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

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

Significant shift

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

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

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

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

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

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