Measurement of the positive muon anomalous magnetic moment to 127 ppb

From the source

1. The muon’s magnetic anomaly is now measured to 127 parts per billion. Combining the 2020-2023 data with the collaboration’s earlier runs gives a value of 1.165920705 for the anomaly, with an uncertainty of 148 in the last three digits. The new experimental world average, including the Brookhaven E821 result but dominated by Fermilab, is 1.165920715 with an uncertainty of 145 in the last three digits, or 124 parts per billion. The Fermilab measurements have improved the precision of the world average by more than a factor of four over the previous best.Abstract; Calculation of the muon anomaly, closing paragraphs; Figure 3

2. The quantity being measured is a direct reading of the vacuum. A lone Dirac particle would have a g factor of exactly 2; the anomaly is the fractional excess over that, and it arises entirely from radiative corrections from virtual particles — the flicker of the field around the muon. Schwinger’s 1948 calculation of the first term, the fine-structure constant divided by two pi, founded modern relativistic field theory. The electron’s anomaly is measured a thousand times more precisely, but the muon is roughly two hundred times heavier and that makes its anomaly about forty thousand times more sensitive to physics the Standard Model does not yet contain.Introduction, paragraphs 1 and 2

3. The measurement is a comparison of two frequencies and nothing else. Polarised muons are injected into a storage ring of 7.112 metre radius carrying a homogeneous 1.45 tesla vertical field, at a momentum chosen so that the electric focusing fields make no net contribution to the spin precession. The experiment then measures the difference between the muon’s spin-precession and cyclotron frequencies, and divides it by the nuclear magnetic resonance frequency of shielded protons in a spherical water sample sitting in the same field. Parity violation in muon decay, combined with the beam’s relativistic boost, makes the number of high-energy positrons hitting the twenty-four lead-fluoride calorimeters oscillate at exactly the frequency wanted. Everything else in the answer is a ratio of separately known fundamental constants.Experimental principle, paragraphs 1 to 3; equations 1 and 2

4. The analysis was blinded twice over, and cross-checked twenty times. Each analysis group worked with an unknown, fixed, pseudorandom offset in the precession frequency, on top of a hardware blind on the digitisation frequency that was set and monitored by Fermilab physicists outside the collaboration. Five groups using three different positron-reconstruction and pileup-correction algorithms produced seven asymmetry-weighted results plus thirteen further crosschecks; the twenty correlated values agreed within the statistical variation assessed from two hundred bootstrap samples. The hardware blind was removed only after every aspect of the determination was complete and frozen. The best-fit chi-squared for the largest dataset was 4007 for 4097 degrees of freedom.Anomalous precession frequency section, paragraphs 4 and 5 (omitted from the reproduced text for length)

5. Every correction is published with its own uncertainty, and they total 572 parts per billion. The measured frequency ratio is adjusted for the residual effect of the electric focusing fields, for vertical betatron motion, for three separate ways the observed muon ensemble’s average phase drifts with time, and for two magnetic-field transients — eddy currents from the fast injection kickers and vibration of the electrostatic quadrupole plates. The statistical uncertainty of 114 parts per billion still dominates: the total systematic uncertainty on the frequency ratio is 76 parts per billion, and the total on the anomaly for the new datasets is 139.Experimental principle, final paragraph; Table I; Beam-dynamics corrections and Muon-weighted magnetic field sections (omitted for length)

6. What to watch: the theory side of the comparison has moved, and it is not settled. The Muon g-2 Theory Initiative’s 2025 White Paper prediction agrees with this measurement — but it shifted considerably from the 2020 White Paper, almost entirely because it now uses lattice-QCD calculations alone for the leading-order hadronic vacuum polarisation, the contribution in which the muon’s field briefly becomes a cloud of quarks. The older route, a dispersion integral over measured electron-positron annihilation into hadrons, had shown a discrepancy with experiment, and a recent cross-section measurement increased the tension among the experimental inputs, so that route was left out of the 2025 prediction entirely. Work on both evaluations continues, and which one converges is the open question this measurement now waits on.Calculation of the muon anomaly, penultimate paragraph

The way in

How to cite it

Muon g-2 Collaboration (2025) Measurement of the positive muon anomalous magnetic moment to 127 ppb doi:10.1103/7clf-sm2v

Where it sits in the curriculum

• Sources, measurements, and the record
• What the vacuum is