# NLO prediction for the decays $\tau \to \ell \ell'\ell' \nu \bar \nu$ and $\mu \to e e e \nu \bar\nu$

### Submission summary

 As Contributors: Matteo Fael Preprint link: scipost_201811_00002v1 Date accepted: 2019-01-10 Date submitted: 2018-11-03 Submitted by: Fael, Matteo Submitted to: SciPost Physics Proceedings Proceedings issue: The 15th International Workshop on Tau Lepton Physics (Amsterdam, 2018-09) Domain(s): Exp. & Theor. Subject area: High-Energy Physics - Phenomenology

### Abstract

These proceedings present the differential decay rates and the branching ratios of the tau and muon decays $\tau \to \ell \ell' \ell' \nu \bar\nu$ (with $\ell,\ell'=\mu,e$) and $\mu \to e e e \nu \bar \nu$ in the Standard Model at NLO. These five-body leptonic decays are a tool to study the Lorentz structure of weak interactions and to test lepton flavour universality. They are also a source of SM background to searches for the lepton-flavour-violating decays $\mu \to e e e$ and $\tau \to \ell \ell' \ell'$. Even if the shift in the branching ratios induced by radiative corrections turns out to be small and of order 1% - mainly due to a running effect of the fine structure constant - locally in the phase space these corrections can reach the 5 - 10% level, depending on the applied cuts. We found for instance that in the phase space region where the neutrino energies are small, and the momenta of the three charged leptons have a similar signature as in $\mu \to eee$ and $\tau \to \ell \ell'\ell'$, the NLO corrections decrease the leading-order prediction by about 10 - 20%.

### Submission & Refereeing History

Submission scipost_201811_00002v1 on 3 November 2018

## Reports on this Submission

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### Report

The conference contribution under consideration is entirely based on the reviewed journal publication JHEP 01 (2017) 84. It is well written and clear. Hence, in my opinion there is no need for a more detailed report.

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