Lepton-number-violating four-body tau lepton decays

Abstract

We study the four-body ${\ensuremath{\tau}}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{\ensuremath{\tau}}{l}^{\ifmmode\pm\else\textpm\fi{}}{l}^{\ifmmode\pm\else\textpm\fi{}}{X}^{\ensuremath{\mp}}$ decays where $l=e$ or $\ensuremath{\mu}$ and $X=\ensuremath{\pi}$, $K$, $\ensuremath{\rho}$, and ${K}^{*}$ mesons. These decay processes violate the total lepton number ($|\ensuremath{\Delta}L|=2$) and can be induced by the exchange of Majorana neutrinos. We consider a scenario where these decays are dominated by the exchange of only one heavy neutrino, which produces an enhancement of the decay amplitude via the resonant mechanism. Searches for these novel decay channels with branching fractions sensitivities of $O({10}^{\ensuremath{-}7})$ can provide constraints on the parameter space of the Majorana neutrinos, which are stronger than the ones obtained from $\ensuremath{\Delta}L=2$ decays of charged pseudoscalar mesons.