Next-to-leading order prediction for the decay $\hat{I}¼\to e(e^{+}{e}^{-})\hat{I}½\bar{\hat{I}}½$

Abstract

We present the differential decay rates and the branching ratios of the muon decay with internal conversion, $\hat{I}¼\to e(e^{+}{e}^{-})\hat{I}½\bar{\hat{I}}½$, 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 $\hat{I}¼\to eee$ 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 $\hat{I}¼\to eee$ decay, the NLO corrections decrease the leading-order prediction by about $10-20\%$

18 pages, 4 figures. v2: version published in JHEP; discussion in section 4.2 extended