Next-to-leading order prediction for the decay μ → e e + e − ν ν ¯ $$ \mu \to e\kern0.22em \left({e}^{+}{e}^{-}\right)\;\nu \kern0.2em \overline{\nu} $$

Abstract

We present the differential decay rates and the branching ratios of the muon decay with internal conversion, µ → e (e + e − ) νν, 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 µ → 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 µ → eee decay, the NLO corrections decrease the leading-order prediction by about 10 − 20% depending on the applied cut.

Radiative corrections to double-Dalitz decays revisited

“…[5] results, which we give for convenience in the fifth column from Table II. 18 As a result, we find discrepancies at the 1% level, which is nevertheless often of similar size as TFF effects This is due to charge conjugation-see for instance the comments on p. 8 from Ref. [39]. 15 As a cross-check, we computed independently the scalar five-point function, D 0 , in terms of four-point functions using the method in Ref.…”

Fully differential NLO predictions for the rare muon decay

“…Correction [17] no cuts 3.605(1) · 10 −5 −6.74(4) · 10 −8 −0.19% −6.69(5) · 10 −8 E / < 100 · m e 2.121(1) · 10 −6 −9.46(2) · 10 −8 −4.5% −9.47(6) · 10 −9 E / < 50 · m e 7.153(2) · 10 −9 −4.57(1) · 10 −10 −6.4% −4.55(3) · 10 −10 E / < 20 · m e 2.119(1) · 10 −11 −2.14(4) · 10 −12 −10.1% −2.17(1) · 10 −12 E / < 10 · m e 3.071(1) · 10 −13 −4.05(1) · 10 −14 −13.2% −4.04(2) · 10 −14 Table 1. The branching ratio of the rare decay in the on-shell scheme for various cuts on the invisible energy E /.…”

Fully differential NLO predictions for the radiative decay of muons and taus

“…After some partial results [17,22] a full next-to-leading (NLO) calculation for the BR was presented in [23,24]. As for a related calculation of the rare decays of leptons [25], the results presented in [23,24] allow to obtain the differential decay width at NLO with cuts on the photon and electron energy and angles between them. In this article, we generalize these results and present a fully differential Monte Carlo program.…”