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$L\,\to\, l\, l'\, l'\, ν_l\, ν_L$ in the SM and beyond

We study the $L\to l l' l' ν_l ν_L$ decays ($L=τ,μ$; $l,l'=μ,e$) 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 $3.5\,σ$ anomaly found in $τ\to e γ\barν_eν_τ$ could be checked using our precise prediction for the $τ\to e e e \barν_eν_τ$ 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.