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

Comments: 24 pages, 3 Figures, a new evaluation of the Branching fractions and new appendix added, main conclusion remains unchanged, some typos corrected