Charged Lepton Flavour Violating Radiative Decays ${\ell }_i\to {\ell }_j+\gamma$ in See-Saw Models with $A_4$ Symmetry

Abstract

The charged lepton flavour violating (LFV) radiative decays, $\mu \to e+\gamma$, $\tau \to \mu +\gamma$ and $\tau \to e+\gamma$ are investigated in a class of supersymmetric $A_4$ models with three heavy right-handed (RH) Majorana neutrinos, in which the lepton (neutrino) mixing is predicted to leading order (LO) to be tri-bimaximal. The light neutrino masses are generated via the type I see-saw mechanism. The analysis is done within the framework of the minimal supergravity (mSUGRA) scenario, which provides flavour universal boundary conditions at the scale of grand unification $M_X\approx 2\times 10^{16}$ GeV. Detailed predictions for the rates of the three LFV decays are obtained in two explicit realisations of the $A_4$ models due to Altarelli and Feruglio and Altarelli and Meloni, respectively.

Comments: Results unchanged, minor improvements made; version accepted for publication in JHEP