A see-saw S4 model for fermion masses and mixings

Abstract

We present a supersymmetric see-saw S4 model giving rise to the most general neutrino mass matrix compatible with tri-bimaximal mixing. We adopt the S4 × Z5 flavour symmetry, broken by suitable vacuum expectation values of a small number of flavon fields. We show that the vacuum alignment is a natural solution of the most general superpotential allowed by the flavour symmetry, without introducing any soft breaking terms. In the charged lepton sector, mass hierarchies are controlled by the spontaneous breaking of the flavour symmetry caused by the vevs of one doublet and one triplet flavon fields instead of using the Froggatt–Nielsen U(1) mechanism. The next to leading order corrections to both charged lepton mass matrix and flavon vevs generate corrections to the mixing angles as large as . Applied to the quark sector, the symmetry group S4 × Z5 can give a leading order VCKM proportional to the identity as well as a matrix with coefficients in the Cabibbo 2 × 2 submatrix. Higher order corrections produce nonvanishing entries in the other VCKM entries which are generically of .