Next-to-leading order prediction for the decay mu -> e (e(+)e(-))nu(nu)over-bar

We present the di ff erential decay rates and the branching ratios of the muon decay with internal conversion, mu -> e (e(+)e(-)) nu(nu) over bar, in the Standard Model at next-to-leading order (NLO) in the on-shell scheme. This rare decay mode of the muon is among the main sources of background to the search for mu -> eee decay. We found that in the phase space region where the neutrino energies are small, and the three-electron momenta have a similar signature as in the mu -> eee decay, the NLO corrections decrease the leading-order prediction by about 10 - 20% depending on the applied cut.