Extraction of the proton radius from electron-proton scattering data

Abstract

We perform a new analysis of electron-proton scattering data to determine the proton electric and magnetic radii, enforcing model-independent constraints from form factor analyticity. A wide-ranging study of possible systematic effects is performed. An improved analysis is developed that rebins data taken at identical kinematic settings and avoids a scaling assumption of systematic errors with statistical errors. Employing standard models for radiative corrections, our improved analysis of the 2010 Mainz A1 Collaboration data yields a proton electric radius ${r}_{E}=0.895(20)\text{ }\text{ }\mathrm{fm}$ and magnetic radius ${r}_{M}=\phantom{\rule{0ex}{0ex}}0.776(38)\text{ }\text{ }\mathrm{fm}$. A similar analysis applied to world data (excluding Mainz data) implies ${r}_{E}=0.916(24)\text{ }\text{ }\mathrm{fm}$ and ${r}_{M}=0.914(35)\text{ }\text{ }\mathrm{fm}$. The Mainz and world values of the charge radius are consistent, and a simple combination yields a value ${r}_{E}=0.904(15)\text{ }\text{ }\mathrm{fm}$ that is $4\ensuremath{\sigma}$ larger than the CREMA Collaboration muonic hydrogen determination. The Mainz and world values of the magnetic radius differ by $2.7\ensuremath{\sigma}$, and a simple average yields ${r}_{M}=0.851(26)\text{ }\text{ }\mathrm{fm}$. The circumstances under which published muonic hydrogen and electron scattering data could be reconciled are discussed, including a possible deficiency in the standard radiative correction model which requires further analysis.