Physicists Solve a Muon Mystery. Now, Old Results Don’t Add Up.

At first, their predictions were 10 times fuzzier than data-driven inferences. Low-energy particles tend to spread out, so capturing their possible positions requires using a huge lattice. High-energy particles need a comparatively smaller grid, but one with an extremely fine mesh. “Back then, it was unimaginable that one day lattice would reach the same precision” as the data-driven method, said Kalman Szabo, a professor at Wuppertal who was involved in the effort.

It took a decade of developing clever computational techniques — and waiting for increased computing power — for the BMW group to wrangle grids that were both sufficiently big and sufficiently detailed. But wrangle them they did. In 2021, on the same day that Fermilab released its updated muon g–2 measurement, the BMW group’s result appeared in the journal Nature.

According to the BMW group’s lattice calculation, Fermilab’s muons were wobbling exactly as they should. Since then, independent lattice groups have published matching calculations.

Today, many physicists believe the muon mystery is no more: According to the lattice simulations, the muon’s extra wobble can be explained entirely by the emission and reabsorption of known particles obeying the known laws of the known forces.

So why does the data-driven method indicate otherwise?

Inconsistent Experiments

To figure out what’s going on, physicists are drilling into the electron-positron collisions driving the data-driven method. These collisions are supposed to be a direct window into quark behavior, but calculations based on this data disagree with both the latest experimental results and BMW’s prediction. So what’s really going on in the aftermath of those collisions?

In the city of Novosibirsk in southern Siberia, the VEPP-2000 collider has been crashing electrons into positrons on and off since the turn of the millennium. It’s a relatively gentle collider, operating at 6,000 times lower energy than CERN’s Large Hadron Collider, near Geneva.

The VEPP-2000 features two detectors that precisely count how often certain bundles of quarks, known as pions, pop out of the electron-positron crashes — data that physicists have been using to infer how much the strong force was messing with muons.

In 2010, physicists installed a completely new detector. They then used it to more precisely measure this pion production rate, which they published in 2023. After the refresh, they found that the rate changed significantly.

“It was a surprise. No one expected it to be like that,” said Fedor Ignatov, a physicist at the University of Liverpool in the UK and member of the team.

Physicists had seen faint hints that something strange was going on with the pion rate. They noticed that measurements of it from experiments in Italy and the United States were starting to drift apart. But the dramatic divergence of the new measurement from the detector’s own past results, along with the collaboration’s claim of high precision, made the situation hard to ignore.

Physicists have pored over the result. “No measurement has been scrutinized more,” Keshavarzi said. So far, no problems have been found.

Members of the BMW group then used a lattice simulation to predict the pion rate in 2024. Their calculation largely agrees with the most recent results. And preliminary data from the other detector at the VEPP-2000 collider also seem to match the new rate. Meanwhile, a 2023 analysis of data collected earlier at yet another experiment at a collider, BABAR in California, sits in striking agreement with the older rate.

All of this leaves physicists wondering what’s really going on in all these collider experiments. The discrepancies point either to signs of unknown particles meddling with the quarks, or to overlooked details generating the mistaken impression that quarks are misbehaving. Either way, particle physicists can’t rest until they have solved the new electron-positron mystery, and figured out whether the old pion rate, or the new pion rate, is the right one.

“There are four decades of measurements that preceded that, that were all done in different ways, that were all done by different people, that were all done by different experiments, that all paint a completely different picture,” Keshavarzi said. “There is so much still left to do.”