Radiative corrections to elastic muon-proton scattering at low momentum transfers

TL;DR

This paper calculates radiative corrections for elastic muon-proton scattering at low momentum transfers, focusing on their impact on upcoming experiments and highlighting the importance of soft photon radiation beyond the soft photon approximation.

Contribution

It provides a systematic calculation of order α/π radiative corrections, including vacuum polarization, form factors, two-photon exchange, and soft photon radiation, tailored to the AMBER experiment.

Findings

Minor proton structure-dependent corrections from form factors and two-photon exchange.

Soft photon radiation dominates the radiative corrections.

The bremsstrahlung process requires extension beyond the soft photon approximation.

Abstract

We systematically calculate the radiative corrections of order $\alpha/\pi$ to elastic muon-proton scattering at low momentum transfers. These include vacuum polarization, photon-loop form factors of the muon and the proton, two-photon exchange corrections and soft photon radiation. In particular, we discuss these corrections for the kinematics of the upcomimg AMBER experiment with a $100\,$GeV muon beam energy. It is found that for the ratio to the Born cross section, only the minor terms from the photon-loop form factors of the proton and two-photon exchange depend on the proton structure predetermined by the strong interactions. Since a prominent role among the radiative corrections is played by soft photon radiation, the calculation of the bremsstrahlung process $\mu p \to\mu p \gamma$ should be extended beyond the soft photon approximation and tailored to the specific experimental conditions.