Resonant CP violation in rare tau decay

TL;DR

This paper investigates CP violation in rare tau decays mediated by Majorana neutrinos, calculating branching ratios and asymmetries, and identifying conditions where CP asymmetry could be experimentally observed.

Contribution

It introduces a detailed analysis of CP asymmetry in tau decays involving multiple heavy Majorana neutrinos, highlighting scenarios with observable CP violation.

Findings

CP asymmetry is small but significant when neutrino mass difference is comparable to decay width.

Branching ratios are calculated for tau decays with Majorana neutrinos.

Regions of neutrino mixing parameters are identified for potential future experimental detection.

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 ${\rm Br}(\tau^{\pm})$ 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.