Theoretical constraints on the rare tau decays in the MSSM

The Minimal Supersymmetric Standard Model contains in general sources of tau lepton flavour violation which induce the rare decays τ → μγ and τ → eγ. 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(μ → eγ) ≳ C × BR(τμ → γ)BR(τ → eγ). 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 τ → μγ or τ → eγ, but not both. We also derive for completeness the constant C in the most general setup, pursuing an effective theory approach.