Lepton flavour violation in a supersymmetric model with [formula omitted] flavour symmetry

Abstract

We compute the branching ratios for μ → e γ , τ → μ γ and τ → e γ in a supersymmetric model invariant under the flavour symmetry group A 4 × Z 3 × U ( 1 ) FN , in which near tri-bimaximal lepton mixing is naturally predicted. At leading order in the small symmetry breaking parameter u, which is of the same order as the reactor mixing angle θ 13 , we find that the branching ratios generically scale as u 2 . Applying the current bound on the branching ratio of μ → e γ shows that small values of u or tan β are preferred in the model for mass parameters m SUSY and m 1 / 2 smaller than 1000 GeV. The bound expected from the on-going MEG experiment will provide a severe constraint on the parameter space of the model either enforcing u ≈ 0.01 and small tan β or m SUSY and m 1 / 2 above 1000 GeV. In the special case of universal soft supersymmetry breaking terms in the flavon sector a cancellation takes place in the amplitudes and the branching ratios scale as u 4 , allowing for smaller slepton masses. The branching ratios for τ → μ γ and τ → e γ are predicted to be of the same order as the one for μ → e γ , which precludes the possibility of observing these τ decays in the near future.