Lepton flavour violation in models with A4 flavour symmetry

We analyze lepton flavour violating transitions, leptonic magnetic dipole moments (MDMs) and electric dipole moments (EDMs) in a class of models characterized by the flavour symmetry A4×Z3×U(1)FN, whose choice is motivated by the approximate tri-bimaximal mixing observed in neutrino oscillations. We construct the relevant low-energy effective Lagrangian where these effects are dominated by dimension six operators, suppressed by the scale M of new physics. All the flavour breaking effects are universally described by the vacuum expectation values 〈Φ〉 of a set of spurions. We separately analyze both a supersymmetric and a general case. While the observed discrepancy δaμ in the anomalous MDM of the muon suggests M of order of a few TeV, several data require M above 10 TeV, in particular the limit on EDM of the electron. In the general case also the present limit on BR(μ→eγ) requires M>10TeV, at least. The branching ratios for μ→eγ, τ→μγ and τ→eγ are all expected to be of the same order. In the supersymmetric case the constraint from μ→eγ is softened and it can be satisfied by a smaller scale M. In this case both the observed δaμ and the current bound on BR(μ→eγ) can be satisfied, at the price of a rather small value for |〈Φ〉|, of the order of a few percents, that reflects on a similar value for θ13.