Constraints on the rare tau decays from mu --> e gamma in the supersymmetric see-saw model

TL;DR

This paper explores the relationship between mu --> e gamma and tau decays in the supersymmetric see-saw model, establishing a lower bound on mu decay rates based on tau decay measurements, with implications for future experiments.

Contribution

It derives a lower bound on mu --> e gamma decay rate in terms of tau decay rates within the supersymmetric see-saw framework, assuming no cancellations among high-energy parameters.

Findings

A lower bound on BR(mu --> e gamma) in terms of tau decay branching ratios.

Present B-factories can potentially discover tau decays but not both simultaneously.

The bound depends on supersymmetric parameters and the absence of cancellations.

Abstract

It is now a firmly established fact that all family lepton numbers are violated in Nature. In this paper we discuss the implications of this observation for future searches for rare tau decays in the supersymmetric see-saw model. Using the two loop renormalization group evolution of the soft terms and the Yukawa couplings we show that there exists a lower bound on the rate of the rare process mu --> e gamma of the form BR(mu --> e gamma) > C BR(tau --> mu gamma) BR(tau --> e gamma), where C is a constant that depends on supersymmetric parameters. Our only assumption is the absence of cancellations among the high-energy see-saw parameters. We also discuss the implications of this bound for future searches for rare tau decays. In particular, for large regions of the mSUGRA parameter space, we show that present B-factories could discover either tau --> mu gamma or tau --> e gamma, but not both.