Lepton flavour violating semileptonic tau decays in constrained MSSM-seesaw scenarios

TL;DR

This paper investigates lepton flavor violating semileptonic tau decays within constrained MSSM scenarios, providing detailed loop calculations and identifying key channels for experimental testing of LFV and Higgs sector effects.

Contribution

It offers a comprehensive one-loop analysis of tau decays in CMSSM and NUHM, highlighting the significance of various mediators and proposing approximate formulas for experimental comparison.

Findings

Discrepancies found in predicted BRs for certain channels.

Identifies $ au o \mu \, ext{eta}$, $ au o \\mu \, ext{eta'}$, and $ au o \\mu K^+K^-$ as promising channels.

Provides useful approximate formulas for semileptonic decay rates.

Abstract

In this work we study the Lepton Flavour Violating semileptonic $\tau$ decays: 1) $\tau \to \mu PP$ with $PP= \pi^+\pi^-, \pi^0\pi^0, K^+K^-, K^0 {\bar K}^0$; 2) $\tau \to \mu P$ with $P=\pi^0, \eta, \eta'$ and 3) $\tau \to \mu V$ with $V = \rho^0, \phi$. We work within the context of two constrained MSSM scenarios: the CMSSM and NUHM. A full one-(SUSY)loop computation is presented and the importance of the various contributions, the $\gamma$-, $Z$-, and Higgs bosons mediated ones are analysed. The hadronization of quark bilinears is performed within the chiral framework. Some discrepancies in the predicted rates for BR($\tau \to \mu \eta$), BR($\tau \to \mu \eta'$) and BR($\tau \to \mu K^+K^-$) are found with respect to previous estimates, which will be commented here. These three channels will be shown to be the most competitive ones to test simultaneously the Lepton Flavour Violation and the Higgs sector. We further present here a set of approximate formulas for all the semileptonic channels which we believe can be useful for further comparison with present and future data.