The muon anomaly that dissolved

A muon is a heavier cousin of the electron. Like the electron, it behaves like a tiny magnet, and when it moves through a magnetic field its magnetic axis wobbles, or precesses, at a rate set by a quantity physicists call g. A simple quantum theory predicts that g is exactly 2. It is not quite, because the muon is constantly interacting with short-lived virtual particles that flicker in and out of the vacuum around it. The small difference from 2, called the anomalous magnetic moment, is one of the most precisely calculable quantities in physics.

The first correction was worked out by Julian Schwinger in 1948, and it is simple enough to fit on a gravestone, which is where it ended up: the fine-structure constant divided by two pi, about 0.00116. The full modern value for the muon is 0.00116592. Almost all of it comes from that one early term. The drama of the past twenty years has played out in the digits after that.

Why the muon

If an unknown particle existed, it would add its own contribution to the vacuum and push the measured value away from the prediction. The size of such an effect typically grows with the square of the mass of the particle being measured, and a muon is about 207 times as heavy as an electron. It is therefore roughly 43,000 times more sensitive to heavy new physics than the electron is, while still living long enough, about 2.2 millionths of a second at rest, to be stored in a ring and studied. That is why experiments at Brookhaven National Laboratory and then Fermilab spent more than two decades measuring it.

A discrepancy that grew

Brookhaven’s experiment, which ended in 2001, found a value slightly higher than the Standard Model prediction. The storage ring was then shipped 5,000 kilometers by sea and road to Fermilab, near Chicago, where a new experiment began. Its first results, in 2021, confirmed Brookhaven’s. By 2023 the combined disagreement with the consensus prediction had passed five standard deviations.

In June 2025, Fermilab released its final result, with a precision of 127 parts per billion, equivalent to measuring the circumference of Earth to about five meters. The measurement itself held steady. What changed was the prediction.

The measurement held steady. What changed was the prediction.

The hardest part of the calculation

Most of the Standard Model prediction can be calculated to extraordinary precision. The difficult part is the contribution of particles made of quarks and gluons, called hadronic vacuum polarization, because the strong force cannot be handled with the usual approximations.

For years, the consensus value relied on experimental data: measurements of how often electron-positron collisions produce hadrons, fed through a mathematical relation. In 2020, a group using lattice quantum chromodynamics, a brute-force supercomputer simulation of quarks and gluons on a grid of spacetime, obtained a result that sat much closer to the experimental value. Other lattice groups followed with similar answers. Then a new electron-positron experiment, CMD-3 in Novosibirsk, produced data that disagreed with the older measurements.

In 2025 the international Muon g-2 Theory Initiative updated its consensus prediction to rely on the lattice calculations.

What the numbers actually say

Stated in units of 10^-11, the anomaly shrinks to a few digits that are easy to compare. The world-average measurement ends in 2,071.5, with an uncertainty of 14.5. The 2020 prediction ended in 1,810, with an uncertainty of 43, leaving a gap of about 260 units, more than five standard deviations. The 2025 prediction ends in 2,033, with an uncertainty of 62, leaving a gap of about 38, well inside its error bar.

Two details in that comparison often go unmentioned. The prediction moved by more than five of its old error bars, which says something about how far those error bars could be trusted. And the theoretical uncertainty got larger: at 62 units it is now more than four times the experimental one. The experiment has outrun the theory. “Agreement” here does not mean that the Standard Model has been confirmed to 127 parts per billion. It means that within a rather wider band, no disagreement can be claimed.

What is left

The muon no longer points clearly to new physics. But the episode left a genuine puzzle: why do the data-driven calculations disagree with the lattice simulations, and with each other? The answer may lie in subtle experimental issues in older electron-positron measurements, or in something not yet understood. Either way, the anomaly has migrated from the muon to the hadrons, and a planned experiment at CERN called MUonE aims to measure the same contribution by an independent route.

There is also more measuring to do. An experiment in Japan, at J-PARC, plans to measure the same quantity with a completely different technique, using slow muons and no large storage ring. Independent confirmation matters, especially for a number that spent twenty years as the most famous discrepancy in particle physics.

The lesson runs beyond this one number. Anomalies in fundamental physics are usually framed as a contest between nature and the Standard Model. Here, the decisive contest was between two ways of calculating the Standard Model. Cosmologists now living through the Hubble tension may find the story familiar.

Sources

• Muon g-2 Collaboration, “Measurement of the Positive Muon Anomalous Magnetic Moment to 127 ppb”, 2025
• Muon g-2 Theory Initiative, “The anomalous magnetic moment of the muon in the Standard Model: an update”, 2025
• CMD-3 Collaboration, measurement of the e⁺e^- → π⁺π^- cross section, 2023