Revisiting the flavor violating decays of the Tau and Mu leptons in the Standard Model with massive neutrinos

Abstract

The flavor violating leptonic decays of the \tauτ and \muμ leptons into three lighter charged leptons are revisited in the framework the Standard Model with massive neutrinos. In contrast to the previous prediction, we have found strongly suppressed rates for the \tau^-\to \mu^- \ell^+ \ell^-τ−→μ−ℓ+ℓ− (\ell=\mu, eℓ=μ,e) decays. Our results are in good agreement with the approximation of neglecting masses and momenta of the external particles in the loop integrals made in the first computation for the \mu^- \to e^-e^+ e^-μ−→e−e+e− decay.