Flavor violating leptonic decays of τ and μ leptons in the Standard Model with massive neutrinos

We have revisited the computations of the flavor violating leptonic decays of the τ and μ leptons into three lighter charged leptons in the Standard Model with massive neutrinos. We were driven by a claimed unnaturally large branching ratio predicted for the τ − → μ − l + l − (l = μ, e) decays (Pham, Eur Phys J C 8:513 1999), which was at odds with the corresponding predictions for the μ − → e−e−e+ processes (Petcov, Sov J Nucl Phys 25:340 1977). In contrast with the prediction in [17], our results are strongly suppressed and in good agreement with the approximationmade in Ref. [15], 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.Finally, we also acknowledge support from Conacyt through projects FOINS-296-2016 (Fronteras de la Ciencia), and 236394 and 250628 (Ciencia Básica)