Low-Energy Lepton-Proton Bremsstrahlung via Effective Field Theory

TL;DR

This paper calculates the lepton-proton bremsstrahlung cross section at low energies using chiral perturbation theory, revealing limitations of common approximations and issues with standard power counting in electron scattering, relevant for the MUSE experiment.

Contribution

It provides a systematic NLO calculation of lepton-proton bremsstrahlung in chiral perturbation theory and identifies the inapplicability of the peaking approximation at MUSE kinematics.

Findings

Peaking approximation is invalid for muon-proton scattering at MUSE energies.

Next-to-next-to-leading order pion loop contributions are unexpectedly enhanced.

Corrects a misprint in a widely cited review article.

Abstract

We present a systematic calculation of the cross section for the lepton-proton bremsstrahlung process l + p --> l' + p + gamma in chiral perturbation theory at next-to-leading order. This process corresponds to an undetected background signal for the proposed MUSE experiment at PSI. MUSE is designed to measure elastic scattering of low-energy electrons and muons off a proton target in order to extract a precise value of the proton's r.m.s. radius. We show that the commonly used peaking approximation, which is used to evaluate the radiative tail for the elastic cross section, is not applicable for muon-proton scattering at the low-energy MUSE kinematics. Furthermore, we point out a certain pathology with the standard chiral power counting scheme associated with electron scattering, whereby the next-to-next-to-leading order contribution from the pion loop diagrams is kinematically enhanced and numerically of the same magnitude as the next-to-leading order corrections. We correct a misprint in a commonly cited review article.