I think this is a helpful extract from Quanta magazine:
"However, even as many particle physicists are likely to be celebrating — and racing to propose new ideas that could explain the discrepancy — a paper published today in the journal Nature casts the new muon measurement in a dramatically duller light. The paper, which appeared just as the Fermilab team unveiled its new measurement, suggests that the muon’s measured wobbliness is exactly what the Standard Model predicts.
In the paper, a team of theorists known as BMW present a state-of-the-art supercomputer calculation of the most uncertain term that goes into the Standard Model prediction of the muon’s magnetic moment. BMW calculates this term to be considerably larger than the value adopted last year by the consortium, a group known as the Theory Initiative. BMW’s larger term leads to a larger overall predicted value of the muon’s magnetic moment, bringing the prediction in line with the measurements.
If the new calculation is correct, then physicists may have spent 20 years chasing a ghost. But the Theory Initiative’s prediction relied on a different calculational approach that has been honed over decades, and it could well be right. In that case, Fermilab’s new measurement constitutes the most exciting result in particle physics in years.
“This is a very sensitive and interesting situation,” said Zoltan Fodor, a theoretical particle physicist at Pennsylvania State University who is part of the BMW team.
BMW’s calculation itself is not breaking news; the paper first appeared as a preprint last year. Aida El-Khadra, a particle theorist at the University of Illinois who co-organized the Theory Initiative, explained that the BMW calculation should be taken seriously, but that it wasn’t factored into the Theory Initiative’s overall prediction because it still needed vetting. If other groups independently verify BMW’s calculation, the Theory Initiative will integrate it into its next assessment.
Dominik Stöckinger, a theorist at the Technical University of Dresden who participated in the Theory Initiative and is a member of the Fermilab Muon g-2 team, said the BMW result creates “an unclear status.” Physicists can’t say whether exotic new particles are pushing on muons until they agree about the effects of the 17 Standard Model particles they already know about.
Regardless, there’s plenty of reason for optimism: Researchers emphasize that even if BMW is right, the puzzling gulf between the two calculations could itself point to new physics. But for the moment, the past 20 years of conflict between theory and experiment appear to have been replaced by something even more unexpected: a battle of theory versus theory."
