Collisional energy loss of a fast muon in a hot QED plasma

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 proportional to lnE+O(1). Considering first the t-channel contribution to -dE/dx, we show that the terms similar to O(1) are sensitive to the full kinematic region for the momentum exchange q in elastic scattering, including large values q similar to 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.