Evaluation of the strength of electron-proton scattering data for determining the proton charge radius

TL;DR

This paper reanalyzes electron-proton scattering data to assess its effectiveness in determining the proton charge radius, finding results consistent with a range that does not resolve existing measurement discrepancies.

Contribution

It demonstrates that current scattering data cannot definitively resolve the proton charge radius discrepancy between muonic and electronic measurements.

Findings

Proton charge radius estimates range from 0.84 to 0.89 fm.

Low-$Q^2$ fits yield consistent $R_E$ values.

Data cannot resolve the proton radius discrepancy.

Abstract

Precisely measured electron-proton elastic scattering cross sections [Phys. Rev. Lett. {\bf 105}, 242002 (2010)] are reanalyzed to evaluate their strength for determining the rms charge radius ($R_{\rm E}$) of the proton. More than half of the cross sections at lowest $Q^2$ are fit using two single-parameter form-factor models, with the first based on a dipole parametrization, and the second on a linear fit to a conformal-mapping variable. These low-$Q^2$ fits extrapolate the slope of the form factor to $Q^2$=0 and determine $R_{\rm E}$ values of approximately 0.84 and 0.89~fm, respectively. Fits spanning all $Q^2$, in which the single constants are replaced with cubic splines at larger $Q^2$, lead to similar results for $R_{\rm E}$. We conclude that the scattering data is consistent with $R_{\rm E}$ ranging from at least 0.84 to 0.89~fm, and therefore cannot resolve the discrepancy between determinations of $R_{\rm E}$ made using muonic and electronic hydrogen-atom spectroscopy.