The electromagnetic effects of axions (1-spheres with virtual cross sections) and leptons (2-spheres with virtual cross sections) might suggest that some form of electromagnetic uncertainty might be approximated by (axion mass)/(electron mass).
Can the proton charge radius puzzle be resolved in terms of electromagnetic effects from axions?
Proton radius puzzle, Wikipedia
According to Graf and Steffen, "If the Peccei-Quinn (PQ) mechanism is the explanation of the strong CP problem, axions will pervade the Universe as an extremely weakly interacting light particle species."
According to Derbin et al., "If the axions or other axion-like pseudo scalar particles couple with electrons then they are emitted from Sun by the Compton process and by bremstrahlung ...:
What is the magnitude of the uncertainty in determining the fine structure constant?
Fine structure constant, Wikipedia
Hanneke, Fogwell, and Gabrielse (2008) estimated 1/(fine structure constant) as: 137.035999084(51)
.000000051/137.035999084 = 3.72... * 10^-10
(electron mass) * 3.72 * 10^-10 = 1.901 * 10^-4 eV/c^2
P. J. Mohr, B. N. Taylor, and D. B. Newell (2015) estimated 1/(fine structure constant) as: 137.035999139(31)
.000000031/137.035999139 = 2.262... * 10^-10
(electron mass) * 2.262 * 10^-10 = 1.156 * 10^-4 eV/c^2
How might the proton radius puzzle be related to uncertainties in determining the fine structure constant?
In the article "The Rydberg constant and proton size from atomic hydrogen" Beyer et al. (2017) stated (p. 80), "Line shape distortions caused by quantum interference from distant neighboring atomic resonances have recently come into the focus of the precision spectroscopy community ... To the best of our knowledge, this effect has been considered in the analysis of only one of the previous H experiments and was found to be unimportant for that particular experimental scheme ... The effect was found to be responsible for discrepancies in the value of the fine structure constant α extracted from various precision spectroscopy experiments in helium ... The root of the matter is that natural line shapes of atomic resonances may experience deviations from a perfect Lorentzian when off-resonant transitions are present."
Are axions a likely source of off-resonant transitions? Could the older experiments for determining the proton charge radius have failed to eliminate axion interactions as a source of inflating the value of the proton radius? Could the 2017 experiment by Beyer et al. be failing to take into account axion interactions? What might happen if experiments for measuring the proton charge radius were performed at 4 different levels of shielding -- on the surface, in a slightly deep mine, in a moderately deep mine, and in a very deep mine -- to check for possible axion production of off-resonant transitions? By assuming a precise value for the axion mass could the 2017 experiment by Beyer et al. be modified for axion detection?
If most of the proton charge radius puzzle can be explained by uncertainty in estimating the finite structure constant due to unexpected axion detection, then (1.2 ± 1.0) * 10^-4 eV/c^2 might be a plausible estimate for the axion mass.