A measurement that’s off by 7 standard deviations may hint at new physics.
In The Puzzle of the Proton and the Muon, Matt Strassler is skeptical:
Well, 7 standard deviations (or “sigmas”) is far more than the 3 to 5 standard deviations that are typically considered impressive. However, one should remember that statistically significant results simply imply discovery of either (a) something about nature or (b) a human error… with the latter always more likely. The famous faster-than-light neutrinos disagreed with Einstein’s prediction by 6 standard deviations, and all that meant was that someone made a mistake.
I.e, the number of standard deviations means nothing if there is some unknown factor
pushing the results consistently in one direction or another.
But a number of my colleagues have shown, in various ways, that to introduce a new force that would affect muonic hydrogen by this amount, and not muck up previous measurements of the properties of muons or electrons or protons or neutrons, and not show up in the decays of other well-studied particles, is extremely difficult; it requires arranging multiple cancellations between multiple effects, at a level that is highly unpalatable.
On top of this difficulty, the discrepancy is not (in my personal view) as crisp as it looks at first glance. The calculations required to extract the proton’s size are very complicated indeed, and have many ingredients and steps; the measurements are not very sensitive to the proton’s size, so highly precise measurements and a heck of a lot of theoretical processing are both needed before one can extract the desired information.