Charge-asymmetric correlations in elastic lepton- and antilepton-proton scattering from real photon emission

TL;DR

This paper develops a comprehensive theoretical framework for analyzing charge asymmetries in lepton-proton scattering, accounting for real photon emission effects beyond the ultrarelativistic limit, applicable to various experimental conditions.

Contribution

It introduces explicit formulas and a numerical approach for charge asymmetry analysis including real photon emission, extending beyond ultrarelativistic approximations.

Findings

Derived expressions for charge asymmetry including real photon emission.

Numerical analysis applicable to both ultrarelativistic and moderately relativistic kinematics.

Infrared divergence cancellation using Bardin-Shumeiko and Tsai techniques.

Abstract

Observation of charge asymmetry by comparing electron and positron, or muon and anti-muon, scattering on a hadronic target presently serves as an experimental tool to study two-photon exchange effects. In addition to two-photon exchange, real photon emission also contributes to the charge asymmetry. We present a theoretical formalism, explicit expressions, and a numerical analysis of hard photon emission for the charge asymmetry in lepton- and antilepton-proton scattering. Different kinematic conditions are considered, namely, either fixed transferred momentum squared or a fixed lepton scattering angle. The infrared divergence from real photon emission is treated by the Bardin-Shumeiko technique and canceled with the soft part of the two-photon exchange contribution extracted and calculated using Tsai approach. All final expressions are obtained beyond the ultrarelativistic approximation with respect to the lepton mass that allows to evaluate numerically of the considered effects not only for ultrarelativistic leptons (JLab) and but for moderately relativistic (MUSE) kinematics, too.