Extraction of the proton radius from electron-proton scattering data

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

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