A Model for Tri-bimaximal Mixing from a Completely Broken $A_4$

Abstract

We propose a new $A_4$ model in which both the right-handed neutrinos and right-handed charged leptons transform as $A_4$ singlets. We reproduce tri-bimaximal mixing pattern exactly although the $A_4$ symmetry is broken completely at leading order in both the neutrino and charged lepton sectors. The charged lepton mass hierarchies are controlled by the spontaneous breaking of the flavor symmetry. The light neutrino spectrum is predicted to be of normal type and the lightest neutrino is massless at leading order. Although the reactor angle ${\theta }_{13}$ is expected to be of order ${\lambda }_c^2$ from the next to leading order corrections, this model cannot be ruled out by current experimental data including the latest T2K results. Leptogenesis is realized via the resonant leptogenesis of the second and the third heavy right-handed neutrinos which are degenerate at leading order. The phenomenological consequences for lepton flavor violation are discussed in detail.

28 pages, 3 figures

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