Lepton Flavour Violation in Models with A4 Flavour Symmetry

TL;DR

This paper investigates lepton flavor violation, magnetic and electric dipole moments within A4 flavor symmetry models, analyzing how new physics at multi-TeV scales can explain observed anomalies and experimental bounds.

Contribution

It introduces a detailed effective Lagrangian framework for lepton flavor violation in A4-based models, comparing supersymmetric and general cases, and discusses implications for new physics scales.

Findings

Muon anomalous magnetic moment discrepancy suggests new physics around a few TeV.

Electron EDM and mu -> e gamma limits imply new physics scale above 10 TeV.

Supersymmetric case allows smaller scale M while satisfying experimental constraints.

Abstract

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 x Z3 x 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 <Phi> of a set of spurions. We separately analyze both a supersymmetric and a general case. While the observed discrepancy delta a_mu 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(mu -> e gamma) requires M >10 TeV, at least. The branching ratios for mu -> e gamma, tau -> mu gamma and tau -> e gamma are all expected to be of the same order. In the supersymmetric case the constraint from mu -> e gamma is softened and it can be satisfied by a smaller scale M. In this case both the observed delta a_mu and the current bound on BR(mu -> e gamma) can be satisfied, at the price of a rather small value for |<Phi>|, of the order of a few percents, that reflects on a similar value for theta_{13}.