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

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