Five-body leptonic decays of muon and tau leptons

Abstract

We study the five-body decays ${\mu }^{-}\to e^{-}{e}^{+}{e}^{-}{\nu }_{\mu }{\bar{\nu }}_e$ and ${\tau }^{-}\to {\ell }^{-}{\ell }^{\prime +}{\ell }^{\prime -}{\nu }_{\tau }{\bar{\nu }}_{\ell }$ for $\ell ,{\ell }^{\prime }=e,\mu$ within the Standard Model (SM) and in a general effective field theory description of the weak interactions at low energies. We compute the branching ratios and compare our results with two previous, mutually discrepant, SM calculations. By assuming a general structure for the weak currents we derive the expressions for the energy and angular distributions of the three charged leptons when the decaying lepton is polarized, which will be useful in precise tests of the weak charged current at Belle II. In these decays, leptonic $\mathbf{T}$-odd correlations in triple products of spin and momenta --which may signal time reversal violation in the leptonic sector-- are suppressed by the tiny neutrino masses. Therefore, a measurement of such $\mathbf{T}$-violating observables would be associated to neutrinoless lepton flavor violating (LFV) decays, where this effect is not extremely suppressed. We also study the backgrounds that the SM five-lepton lepton decays constitute to searches of LFV $L^{-}\to {\ell }^{-}{\ell }^{\prime +}{\ell }^{\prime -}$ decays. Searches at high values of the invariant mass of the ${\ell }^{\prime +}{\ell }^{\prime -}$ pair look the most convenient way to overcome the background.

40 pages, 6 figures, extended discussion of results in the case of the effective lagrangian approach; other minor corrections/modifications are added

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Cited by in corpus (14)

• $\tau$ dipole moments via radiative leptonic $\tau$ decays
• Fully differential NLO predictions for the rare muon decay
• Numerical calculation of the decay widths, the decay constants, and the decay energy spectra of the resonances of the delta-shell potential
• Next-to-leading order prediction for the decay $\mu \to e(e^{+}{e}^{-})\nu \bar{\nu }$
• Michel parameters in radiative muon decay
• Lepton flavor violation by two units
• A new method for measurement of the Michel parameters that describe the daughter muon polarization in the ${\tau }^{-}\to {\mu }^{-}{\bar{\nu }}_{\mu }{\nu }_{\tau }$ decay
• Lepton-pair production in di-pion $\tau$ lepton decays
• Improved description of di-lepton production in ${\tau }^{-}\to {\nu }_{\tau }{P}^{-}$ decays
• TAUOLA update for decay channels with $e^{+}{e}^{-}$ pairs in the final state
• Lepton flavor violation by three units
• Five-body $D\to V$ Semileptonic Decays
• Fully differential NLO predictions for rare and radiative lepton decays
• Can a Nonstandard Invisible Pair Mimic the Michel Distribution?