Collisional energy loss of a fast muon in a hot QED 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 $\mathcal{O}(1)$ in $\ensuremath{-}dE/dx\ensuremath{\propto}\mathrm{ln}E+\mathcal{O}(1)$. Considering first the $t$-channel contribution to $\ensuremath{-}dE/dx$, we show that the terms $\ensuremath{\sim}\mathcal{O}(1)$ are sensitive to the full kinematic region for the momentum exchange $q$ in elastic scattering, including large values $q\ensuremath{\sim}\mathcal{O}(E)$. We thus redress a previous calculation by Braaten and Thoma, which assumed $q\ensuremath{\ll}E$ 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 $\ensuremath{-}dE/dx$. Our results might have implications in the QCD case of parton collisional energy loss in a quark gluon plasma.