Radiative corrections to the average bremsstrahlung energy loss of high-energy muons

High-energy muons can travel large thicknesses of matter. For underground neutrino and cosmic ray detectors the energy loss of muons has to be known accurately for simulations. In this article the next-to-leading order correction to the average energy loss of muons through bremsstrahlung is calculated using a modified Weizs\"acker-Williams method. An analytical parametrisation of the numerical results is given.