Theoretical constraints on the rare tau decays in the MSSM

TL;DR

This paper explores the theoretical limits of rare tau decays in the MSSM, establishing a lower bound on muon decay rates based on tau decay observations, with implications for future experiments.

Contribution

It derives a model-independent lower bound on muon decay BR from tau decay BRs and discusses experimental prospects within the MSSM framework.

Findings

Observation of both tau decays implies a lower bound on muon decay BR.

Current B-factories could detect one of the tau decays but not both.

Derived the constant C in a general effective theory setup.

Abstract

The Minimal Supersymmetric Standard Model contains in general sources of tau lepton flavour violation which induce the rare decays tau --> mu gamma and tau --> e gamma. We argue in this paper that the observation of both rare processes would imply a lower bound on the radiative muon decay of the form BR(mu --> e gamma) > C BR(tau --> mu gamma) BR(tau --> e gamma). We estimate the size of the constant C without specifying the origin of the tau flavour violation in the supersymmetric model and we discuss the implications of our bound for future searches of rare lepton decays. In particular, we show that, for a wide class of models, present B-factories could discover either tau --> mu gamma or tau --> e gamma, but not both. We also derive for completeness the constant C in the most general setup, pursuing an effective theory approach.