Radiative corrections to real and virtual muon Compton scattering revisited

TL;DR

This paper provides a detailed analytical calculation of one-loop radiative corrections to muon Compton scattering and muon-nucleus bremsstrahlung, crucial for experimental analyses like those at CERN's COMPASS.

Contribution

It offers a new closed-form analytical computation of radiative corrections for muon Compton scattering and extends this to muon-nucleus bremsstrahlung, including treatment of divergencies and comparison with prior methods.

Findings

Radiative corrections are small, with the anomalous magnetic moment contributing minimally.

Results are consistent with previous calculations using different methods.

The calculations are relevant for calibrating experiments measuring pion polarizabilities.

Abstract

We calculate in closed analytical form the one-photon loop radiative corrections to muon Compton scattering $\mu^- \gamma \to \mu^- \gamma $. Ultraviolet and infrared divergencies are both treated in dimensional regularization. Infrared finiteness of the (virtual) radiative corrections is achieved (in the standard way) by including soft photon radiation below an energy cut-off $\lambda$. We find that the anomalous magnetic moment $\alpha/2\pi$ provides only a very small portion of the full radiative corrections. Furthermore, we extend our calculation of radiative corrections to the muon-nucleus bremsstrahlung process (or virtual muon Compton scattering $\mu^-\gamma_0^* \to \mu^- \gamma $). These results are particularly relevant for analyzing the COMPASS experiment at CERN in which muon-nucleus bremsstrahlung serves to calibrate the Primakoff scattering of high-energy pions off a heavy nucleus with the aim of measuring the pion electric and magnetic polarizabilities. We find agreement with an earlier calculation of these radiative corrections based on a different method.