Fermion Masses and Mixings in a S4 Based Model

TL;DR

This paper constructs a supersymmetric S4-based model that naturally produces Tri-bimaximal neutrino mixing and realistic quark masses, with stable vacuum alignment from spontaneous symmetry breaking.

Contribution

It develops a novel S4 symmetry model that achieves realistic lepton and quark mass hierarchies with stable vacuum alignment, extending previous flavor symmetry approaches.

Findings

Achieves correct charged lepton mass hierarchy.

Produces Tri-bimaximal neutrino mixing pattern.

Obtains realistic quark mass and mixing angles.

Abstract

It has been recently claimed that the symmetry group S4 yields to the Tri-bimaximal neutrino mixing in a "natural" way from the group theory point of view. Approving of this feature as an indication, we build a supersymmetric model of lepton and quark masses based on this family symmetry group. In the lepton sector, a correct mass hierarchy among the charged leptons is achieved together to a neutrino mass matrix which can be diagonalized by the Tri-bimaximal pattern. Our model results to be phenomenologically unequivalent with respect to other proposals based on different flavour groups but still predicting the Tri-bimaximal mixing. In the quark sector a realistic pattern for masses and mixing angles is obtained. The flavour structures of the mass matrices in both the sectors come from the spontaneously symmetry breaking of S4, due to several scalar fields, which get non-zero vacuum expectation values. A specific vacuum alignment is required and it is shown to be a natural results of the minimization of the scalar potential and, moreover, to be stable under the corrections from the higher order terms.