Resonant CP violation in rare tau decay

Abstract

In this work, we study the lepton number violating tau decays via intermediate on-shell Majorana neutrinos $N_j$ into two scalar mesons and a lepton ${\tau }^{\pm }\to M_1{}^{\pm }{N}_j\to M_1^{\pm }{M}_2^{\pm }{\ell }^{\mp }$. We calculate the Branching ratios $Br({\tau }^{\pm })$ and the CP asymmetry $(\Gamma ({\tau }^{+})-\Gamma ({\tau }^{-}))/(\Gamma ({\tau }^{+})+\Gamma ({\tau }^{-}))$ for such decays, in a scenario that contain at least two heavy Majorana neutrinos. The results show that the CP asymmetry is small, but becomes comparable with the branching ratio $\mathrm{Br}({\tau }^{\pm })$ when their mass difference is comparable with their decay width, $\Delta M_N\sim {\Gamma }_N$. On the other hand, we present regions of the heavy-light neutrino mixing elements, in which the $CP$ asymmetry could be explore in future tau factories.

Comments: 18 pages, New references