Hossenfelder is always good on these topics:
One thing that pops into your eye right away is that the mean value of the new measurement isn’t so different from earlier data analyses. The striking thing about this new analysis is the small error bar. That the error bar is so small is the reason why this result has such a high statistical significance. They quote a disagreement with the standard model at 6.9 sigma. That’s well above the discovery threshold in particle physics which is often somewhat arbitrarily put at 5 sigma.
What did they do to get the error bar so small? Well for one thing they have a lot of data. But they also did a lot of calibration cross-checks with other measurements, which basically means they know very precisely how to extract the physical parameters from the raw data, or at least they think they do. Is this reasonable? Yes. Is it correct? I don’t know. It could be. But in all honesty, I am very skeptical that this result will hold up. More likely, they have underestimated the error and their result is actually compatible with the other measurements.
But if it does hold up, what does it mean? It would mean that the standard model is wrong because there’d be a measurement that don’t fit together with the predictions of the theory. Then what? Well then we’d have to improve the standard model. Theoretical particle physicists have made many suggestions for how to do that, the most popular one has for a long time been supersymmetry. It’s also one of the possible explanations for the new anomaly that the authors of the paper discuss.Sabine Hossenfelder, “Did the W-boson just “break the standard model”?” at BackRe(Action) (April 30, 2022)
The paper is open access.
Anyway, Rob Sheldon has the story here. Sheldon: What this paper and journo piece reveals is the desperation felt in the particle physics community. They so desperately need the Standard Model to fail.