A Grid Simulation Matches the Muon Wobble, Doubting Older Estimates

The most complete calculation of how muons wobble now matches the experiment, and that success has put an older kind of prediction in doubt. The particle at issue is the muon, a much heavier relative of the electron. It behaves like a tiny bar magnet, so when it circles in a magnetic field, it traces smaller wobble circles. The size is set by a number called the g-factor, which would be exactly 2 for an isolated muon, and the tiny excess beyond 2 reflects nudges from every other particle that briefly appears and vanishes around it.

The hard part is accounting for quarks, which are tightly bound by the strong force into larger particles. Gravity is so feeble researchers can set it aside, and the other two relevant forces can be handled with a conventional calculation. The strong force defies that approach, so physicists found two workarounds that now disagree.

One workaround counts particles from collisions. An electron and its antimatter counterpart, a positron, meet and annihilate, and the energy reappears as fresh particles including clusters built from quarks. The more often those clusters appear, the larger their expected tug on the muon should be. This measurement-based prediction was refined in part by Alex Keshavarzi, a senior research fellow at University College London, in his doctoral research in 2018.

The other workaround simulates space on a grid. The method resembles weather forecasting, where forecasters split the sky into large cubes and figure the average shift over time instead of following each gust. Here researchers split space into cubes and model the collective behavior of quarks. A team working in Budapest, Marseille, and Wuppertal, known as the BMW group, began that effort in 2014. At first its outcome was 10 times less precise than the measurement-based estimate. "Back then, it was unimaginable that one day lattice would reach the same precision" as the measurement-based approach, said Kalman Szabo, a professor at Wuppertal. A decade of improved methods and faster computers closed the gap.

In 2021, the same day Fermilab in Illinois released a precise new wobble measurement, the BMW result was published in the journal Nature. It matched the measurement. Other teams using grids have since reached the same outcome, and many researchers now consider the original mismatch resolved. The discrepancy between the measurement-based forecast from June 2020 and Fermilab's April 2021 result had nearly reached the strict threshold physicists require to claim new particles.

Attention has therefore turned to the old collision data behind the measurement-based forecast. In Novosibirsk in Siberia, the VEPP-2000 collider smashes electrons and positrons at about one six thousandth the energy of CERN's Large Hadron Collider. After installing a completely new detector in 2010, the team published a more precise count in 2023 of how often the crashes produce particles called pions, the key quark clusters for the forecast. The rate had shifted significantly from earlier results. "It was a surprise. No one expected it to be like that," said Fedor Ignatov, a physicist at the University of Liverpool and member of the team. That new rate lines up with grid simulations, which suggests the older collision numbers, not the muon theory, may be at fault.