Adjoint SUSY $SU(5)$ Grand Unified Model with $S_4$ Flavor Symmetry

TL;DR

This paper develops a supersymmetric $SU(5)$ grand unified model with $S_4$ flavor symmetry, predicting neutrino mixing patterns and realistic quark and lepton masses, with detailed phenomenological analysis.

Contribution

It introduces a novel SUSY $SU(5)$ model incorporating $S_4$ flavor symmetry and adjoint matter fields to explain neutrino and quark/lepton masses and mixings.

Findings

Predicts exact tri-bimaximal neutrino mixing at leading order.

Reproduces realistic quark and charged lepton mass patterns.

Provides detailed phenomenological implications of the model.

Abstract

We construct a supersymmetric (SUSY) $SU(5)$ model with the flavor symmetry $S_4\times Z_3\times Z_4$. Three generations of adjoint matter fields are introduced to generate the neutrino masses via the combined type I and type III see-saw mechanism. The first two generations of the the $\mathbf{10}$ dimensional representation in $SU(5)$ are assigned to be a doublet of $S_4$, the second family $\mathbf{10}$ is chose as the first component of the doublet, and the first family as the second component. Tri-bimaximal mixing in the neutrino sector is predicted exactly at leading order, charged lepton mixing leads to small deviation from the tri-bimaximal mixing pattern. Subleading contributions introduce corrections of order $\lambda^2_c$ to all three lepton mixing angles. The model also reproduces a realistic pattern of quark and charged lepton masses and quark mixings. The phenomenological implications of the model are analyzed in datail.