[5][6] The radius of the proton is defined by a formula which can be calculated by quantum electrodynamics and be derived from either atomic spectroscopy or by electron–proton scattering.
[9] Measurements of hydrogen's energy levels are now so precise that the accuracy of the proton radius is the limiting factor when comparing experimental results to theoretical calculations.
However, the much higher mass of a muon causes it to orbit 207 times closer than an electron to the hydrogen nucleus, where it is consequently much more sensitive to the size of the proton.
This experiment allowed the measurements to be 2.7 times more accurate, but also found a discrepancy of 7.5 standard deviations smaller than the expected value.
His personal assumption is that past measurements have misgauged the Rydberg constant and that the current official proton size is inaccurate.
[21] In a paper by Belushkin et al. (2007),[22] including different constraints and perturbative quantum chromodynamics, a smaller proton radius than the then-accepted 0.877 femtometres was predicted.
In one of the attempts to resolve the puzzle without new physics, Alarcón et al. (2018)[26] of Jefferson Lab have proposed that a different technique to fit the experimental scattering data, in a theoretically as well as analytically justified manner, produces a proton charge radius from the existing electron scattering data that is consistent with the muonic hydrogen measurement.
These authors suggest that the older spectroscopic analysis did not include quantum interference effects that alter the shape of the hydrogen lines.
[31] A re-analysis of experimental data, published in February 2022, found a result consistent with the smaller value of approximately 0.84 fm.