S4 Flavor Model of Quarks and Leptons

TL;DR

This paper develops an $S_4$ flavor model within SU(5) GUT to unify quark and lepton flavors, predicting mixing angles including the Cabibbo angle, and offers a framework for understanding fermion mass hierarchies.

Contribution

It introduces a novel $S_4$ flavor symmetry assignment in an SU(5) GUT framework, predicting fermion mixing angles and providing a basis for further refinement.

Findings

Predicts the Cabibbo angle as 15 degrees

Achieves tri-bimaximal neutrino mixing

Provides a foundation for improved CKM angle predictions

Abstract

We present an $S_4$ flavor model to unify quarks and leptons in the framework of the SU(5) GUT. Three generations of $\bar 5$-plets in SU(5) are assigned $3_1$ of $S_4$ while the first and the second generations of 10-plets in SU(5) are assigned to be 2 of $S_4$, and the third generation of 10-plet is to be $1_1$ of $S_4$. Right-handed neutrinos are also assigned 2 for the first and second generations and $1_1$ for the third generation, respectively. Taking vacuum alignments of relevant gauge singlet scalars, we predict the quark mixing as well as the tri-bimaximal mixing of neutrino flavors. Especially, the Cabbibo angle is predicted to be $15^{\circ}$ in the limit of the vacuum alignment. We can improve the model to predict observed CKM mixing angles.