Parton distributions in radiative corrections to the cross section of electron-proton scattering

TL;DR

This paper applies the parton model and structure function approach to calculate radiative corrections in electron-proton scattering, providing explicit formulas for one- and two-loop corrections relevant for proton radius measurements.

Contribution

It introduces a method to compute radiative corrections using parton distributions in the context of electron-proton scattering experiments.

Findings

Explicit one-loop correction formulas for arbitrary momentum transfers.

Cancellation of correction contributions at small momentum transfers.

Leading logarithmic two-loop corrections derived.

Abstract

The structure function approach and the parton picture, developed for the theoretical description of the deep inelastic electron-proton scattering, also proved to be very effective for calculation of radiative corrections in Quantum Electrodynamics. We use them to calculate radiative corrections to the cross section of electron-proton scattering due to electron-photon interaction, in the experimental setup with the recoil proton detection, proposed by A.A. Vorobev to measure the proton radius. In the one-loop approximation, explicit expressions for these corrections are obtained for arbitrary momentum transfers. It is shown that, at momentum transfers small compared with the proton mass, various contributions to the corrections mutually cancel each other with power accuracy. In two loops, the corrections are obtained in the leading logarithmic approximation.