Flavor violating leptonic decays of $\tau$ and $\mu$ leptons in the Standard Model with massive neutrinos

Abstract

We have revisited the computations of the flavor violating leptonic decays of the $\tau$ and $\mu$ leptons into three lighter charged leptons in the Standard Model with non-vanishing neutrino masses. We were driven by a claimed unnaturally large branching ratio predicted for the ${\tau }^{-}\to {\mu }^{-}{\ell }^{+}{\ell }^{-}$ ($\ell =\mu ,e$) decays \cite{Pham:1998fq}, which was at odds with the corresponding predictions for the ${\mu }^{-}\to e^{-}{e}^{-}{e}^{+}$ processes \cite{Petcov:1976ff}. In contrast with the prediction in \cite{Pham:1998fq}, our results are strongly suppressed and in good agreement with the approximation done in ref.~\cite{Petcov:1976ff}, where masses and momenta of the external particles were neglected in order to deal with the loop integrals. However, as a result of keeping external momenta and masses in the computation of the dominant penguin and box diagrams- we even find slightly smaller branching fractions. Therefore, we confirm that any future observation of such processes would be an unambiguous manifestation of new physics beyond the Standard Model

arXiv comment24 pages, 3 Figures, a new evaluation of the Branching fractions and new appendix added, main conclusion remains unchanged, some typos corrected

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