Using the automation program GoSam, fully differential NLO corrections were obtained for the rare decay of the muon $muto e ubar u ee$. This process is an important Standard Model background to searches of the Mu3e collaboration for lepton-flavour violation, as it becomes indistinguishable from the signal $muto 3e$ if the neutrinos carry little energy. With our NLO program we are able to compute the branching ratio as well as custom-tailored observables for the experiment. With minor modifications, related decays of the tau can also be computed.
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