A See-Saw $S_4$ model for fermion masses and mixings

TL;DR

This paper proposes a supersymmetric $S_4$ flavor model that naturally explains neutrino mixing and mass hierarchies without soft breaking, and also accounts for quark mixing with controlled corrections.

Contribution

The paper introduces a natural vacuum alignment solution in an $S_4 imes Z_5$ model that reproduces Tri-Bimaximal neutrino mixing and realistic quark mixing without additional soft breaking terms.

Findings

Achieves Tri-Bimaximal neutrino mixing with natural vacuum alignment.

Generates realistic charged lepton and quark mass hierarchies.

Predicts corrections to mixing angles at the order of ${ m O}(\lambda_C^2)$.

Abstract

We present a supersymmetric see-saw $S_4$ model giving rise to the most general neutrino mass matrix compatible with Tri-Bimaximal mixing. We adopt the $S_4\times Z_5$ 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 ${\cal O}(\lambda_C^2)$. Applied to the quark sector, the symmetry group $S_4\times Z_5$ can give a leading order $V_{CKM}$ proportional to the identity as well as a matrix with ${\cal O}(1)$ coefficients in the Cabibbo $2\times 2$ submatrix. Higher order corrections produce non vanishing entries in the other $V_{CKM}$ entries which are generically of ${\cal O}(\lambda_C^2)$.