On the accuracy of the optical determination of the proton charge radius

Abstract

Determination of the proton charge radius by different methods has produced an inconsistency. The most precise value (from spectroscopy of muonic hydrogen) strongly disagrees with three less accurate values (from spectroscopy of ordinary hydrogen and deuterium, from relative measurements of the cross section of the elastic electron-proton scattering at MAMI and from evaluation of the world data on absolute measurements of e-p cross sections). Here, we question the accuracy of the determination of the proton charge radius by means of spectroscopy of ordinary hydrogen and deuterium and demonstrate that its accuracy was probably overestimated. In particular, we revisit determination from each relevant transition and find that the results of two optical experiments, which are the most statistically important, are not perfectly consistent. The inconsistency is rather a `tension' between the results than their discrepancy, however, it implies that a more conservative estimation of the uncertainty is needed. With the more realistic estimation of the uncertainty, the results for the proton charge radius from spectroscopy of ordinary and muonic atoms are rather in fair agreement.