We determine the O(α) correction to the energy spectrum of electrons produced in the decay of muons bound in atoms. We focus on the high-energy end of the spectrum that constitutes a background for the muon-electron conversion and will be precisely measured by the upcoming experiments Mu2e and COMET. The correction suppresses the background by about 15%.
Szafron, R., & Czarnecki, A. (2016). High-energy electrons from the muon decay in orbit: Radiative corrections. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 753, 61–64. https://doi.org/10.1016/j.physletb.2015.12.008