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 $r_E=0.895(20)\mathrm{fm}$ and magnetic radius $r_M=0.776(38)\mathrm{fm}$. A similar analysis applied to world data (excluding Mainz data) implies $r_E=0.916(24)\mathrm{fm}$ and $r_M=0.914(35)\mathrm{fm}$. The Mainz and world values of the charge radius are consistent, and a simple combination yields a value $r_E=0.904(15)\mathrm{fm}$ that is $4\sigma$ larger than the CREMA Collaboration muonic hydrogen determination. The Mainz and world values of the magnetic radius differ by $2.7\sigma$, and a simple average yields $r_M=0.851(26)\mathrm{fm}$. 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.

• Received 26 May 2015

DOI:https://doi.org/10.1103/PhysRevD.92.013013