SUSY SU(5)×S4 GUT flavor model for fermion masses and mixings with adjoint, large θ13PMNS

We propose an S4 flavor model based on supersymmetric (SUSY) SU(5) GUT. The first and third generations of 10 dimensional representations in SU(5) are all assigned to be 11 of S4. The second generation of 10 is to be 12 of S4. Right-handed neutrinos of singlet 1 and three generations of 5¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \overline{\mathbf{5}} $$\end{document} are all assigned to be 31 of S4. The VEVs of two sets of flavon fields are allowed a moderate hierarchy, that is 〈Φν〉 ∼ λc〈Φe〉. Tri-Bimaximal (TBM) mixing can be produced at both leading order (LO) and next to next to leading order (NNLO) in neutrino sector. All the masses of up-type quarks are obtained at LO. We also get the bottom-tau unification mτ = mb and the popular Georgi-Jarlskog relation mμ = 3ms as well as a new mass relation me=827md\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {m}_e=\frac{8}{27}{m}_d $$\end{document} in which the novel Clebsch-Gordan (CG) factor arises from the adjoint field H24. The GUT relation leads to a sizable mixing angle θ12e ∼ θc and the correct quark mixing matrix VCKM can also be realised in the model. The resulting CKM-like mixing matrix of charged leptons modifies the vanishing θ13ν in TBM mixing to a large θ13PMNS≃θc/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\theta}_{13}^{\mathrm{PMNS}}\simeq {\theta}_c/\sqrt{2} $$\end{document}, in excellent agreement with experimental results. A Dirac CP violation phase ϕ12 ≃ ±π/2 is required to make the deviation from θ12ν small. We also present some phenomenological numerical results predicted by the model.