Proton charge radius from electron scattering

TL;DR

This paper reviews and refines methods for determining the proton charge radius from electron scattering data, addressing model dependence issues and achieving a consistent radius estimate that differs from muonic hydrogen results.

Contribution

It introduces an approach incorporating large-radius charge density knowledge to reduce model dependence in proton radius extraction from electron scattering data.

Findings

Proton radius from electron scattering is estimated as 0.887 ± 0.012 fm.

The analysis reduces model dependence and yields consistent results across different parameterizations.

The electron scattering derived radius disagrees with the muonic hydrogen measurement.

Abstract

The rms-radius $R$ of the proton charge distribution is a fundamental quantity needed for precision physics. This radius, traditionally determined from elastic electron-proton scattering via the slope of the Sachs form factor $G_e(q^2)$ extrapolated to momentum transfer $q^2$=0, shows a large scatter. We discuss the approaches used to analyze the e-p data, partly redo these analyses in order to identify the sources of the discrepancies, and explore alternative parameterizations. The problem lies in the model dependence of the parameterized $G(q)$ needed for the extrapolation. This shape of $G(q<q_{min})$ is closely related to the shape of the charge density $\rho (r)$ at large radii $r$, a quantity which is ignored in most analyses. When using our {\em physics} knowledge about this large-$r$ density together with the information contained in the high-$q$ data, the model dependence of the extrapolation is reduced and different parameterizations of the pre-2010 data yield a consistent value for $R = 0.887 \pm 0.012fm$. This value disagrees with the more precise value $0.8409 \pm 0.0004 fm$ determined from the Lamb shift in muonic hydrogen.