Collisional Energy Loss of a Fast Muon in a Hot QED Plasma

TL;DR

This paper refines the calculation of the collisional energy loss of a high-energy muon in a hot QED plasma by including full kinematic effects and additional scattering channels, revealing new constant and logarithmic contributions.

Contribution

It provides a more accurate calculation of muon energy loss by considering large momentum transfers and including Compton scattering, correcting previous approximations.

Findings

Corrects previous calculations by including large momentum transfer effects.

Identifies additional large logarithm from Compton scattering.

Highlights implications for QCD parton energy loss in quark-gluon plasma.

Abstract

We calculate the collisional energy loss of a muon of high energy $E$ in a hot QED plasma beyond logarithmic accuracy, i.e., we determine the constant terms of order O(1) in $-dE/dx \propto \ln{E}+ O(1)$. Considering first the $t$-channel contribution to $-dE/dx$, we show that the terms $\sim O(1)$ are sensitive to the full kinematic region for the momentum exchange $q$ in elastic scattering, including large values $q \sim O(E)$. We thus redress a previous calculation by Braaten and Thoma, which assumed $q << E$ and could not find the correct constant (in the large $E$ limit). The relevance of 'very hard' momentum transfers then requires, for consistency, that $s$ and $u$-channel contributions from Compton scattering must be included, bringing a second modification to the Braaten-Thoma result. Most importantly, Compton scattering yields an additional large logarithm in $-dE/dx$. Our results might have implications in the QCD case of parton collisional energy loss in a quark gluon plasma.