S4 Flavor Symmetry of Quarks and Leptons in SU(5) GUT

Abstract

We have presented a $S_4$ flavor model to unify quarks and leptons in the framework of the SU(5) GUT. Three generations of $\bar5$-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 $S_4$. The 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 as well as the non-vanishing $U_{e3}$ of the neutrino flavor mixing.