$L\,\to\, l\, l'\, l'\, \nu_l\, \nu_L$ in the SM and beyond

TL;DR

This paper provides precise calculations of specific lepton decay processes within the Standard Model and effective field theory, clarifies previous discrepancies, and suggests experimental strategies to detect lepton flavor violation without neutrinos.

Contribution

It offers improved theoretical predictions for $L o l l' l' u_l u_L$ decays and proposes methods to identify lepton flavor violation through di-$l'$ mass distributions and asymmetries.

Findings

Resolved discrepancies in SM decay rate calculations.

Predicted decay distributions to identify LFV processes.

Suggested experimental analyses using existing data.

Abstract

We study the $L\to l l' l' \nu_l \nu_L$ decays ($L=\tau,\mu$; $l,l'=\mu,e$) in the Standard Model (SM) and in the effective field theory (EFT) description of the weak charged current at low energy, both for polarized and unpolarized $L$, keeping the $l,l'$ mass dependence. We clarify the discrepancy between two previous SM calculations of the decay rate improving their precision. The recent $3.5\,\sigma$ anomaly found in $\tau\to e \gamma\bar{\nu}_e\nu_\tau$ could be checked using our precise prediction for the $\tau\to e e e \bar{\nu}_e\nu_\tau$ decays, which shall be measured analyzing already existing data from the first generation B-factories. It is shown how measurements of the di-$l'$ mass distribution (with appropriate cuts) and $T$-asymmetries are able to reveal the corresponding lepton flavor violating (LFV) processes without neutrinos in the final state.