Radiative corrections beyond the ultra relativistic limit in unpolarized ep elastic and Møller scatterings for the PRad Experiment at Jefferson Laboratory

Abstract

The clear 7σ discrepancy between measurements of the proton charge radius from muonic hydrogen Lamb shifts and those from hydrogen Lamb shift and electron scattering lead to both intense theoretical and experimental efforts to understand and explain this difference. In this regard, a new experiment (PRad) based on unpolarized ep elastic scattering cross section measurements normalized to Møller scattering is underway at Jefferson Laboratory to extract the proton charge radius based on new proton electric form factor down to values of momentum transfer squared Q 2, as low as 10−4 GeV/c)2. To reach the precision of the experiment in such a small Q 2 region requires reliable knowledge of radiative corrections. In this paper, we present a complete calculation of radiative corrections for unpolarized elastic ep and Møller scatterings performed within a covariant formalism resulting in the set of explicit formulas beyond the ultra relativistic approximation (m 2 ≪ Q 2), and numerical results for the kinematics of the PRad experiment.