Rare muon and tau decays in A4 models

We analyze the most general dimension-six effective Lagrangian, invariant under the flavour symmetry A4×Z3×U(1)FN proposed to reproduce the near tri-bimaximal lepton mixing observed in neutrino oscillations. The effective Lagrangian includes four-lepton operators that violate the individual lepton numbers in the limit of exact flavour symmetry and allow unsuppressed processes satisfying the rule ΔLeΔLμΔLτ=±2. The most stringent bounds on the strength of the new interactions come from the observed universality of leptonic muon and tau decays, from the agreement between the Fermi constant measured in the muon decay and that extracted from the mW/mZ ratio, and from the limits on the rare decays τ−→μ+e−e− and τ−→e+μ−μ−. We also investigate these effects in a specific supersymmetric (SUSY) realization of the flavour symmetry and we find large suppression factors for all the processes allowed by the selection rule. We explain why this rule is violated in the SUSY context and we provide a complete picture of lepton flavour violation in the SUSY version of A4×Z3×U(1)FN.