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

Understand

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.