Abstract
We propose an S 4 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 S 4. The second generation of 10 is to be 12 of S 4. Right-handed neutrinos of singlet 1 and three generations of \( \overline{\mathbf{5}} \) are all assigned to be 31 of S 4. The VEVs of two sets of flavon fields are allowed a moderate hierarchy, that is 〈Φν〉 ∼ λ c 〈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 m τ = m b and the popular Georgi-Jarlskog relation m μ = 3m s as well as a new mass relation \( {m}_e=\frac{8}{27}{m}_d \) in which the novel Clebsch-Gordan (CG) factor arises from the adjoint field H 24. The GUT relation leads to a sizable mixing angle θ e12 ∼ θ c and the correct quark mixing matrix V CKM can also be realised in the model. The resulting CKM-like mixing matrix of charged leptons modifies the vanishing θ ν13 in TBM mixing to a large \( {\theta}_{13}^{\mathrm{PMNS}}\simeq {\theta}_c/\sqrt{2} \), in excellent agreement with experimental results. A Dirac CP violation phase ϕ 12 ≃ ±π/2 is required to make the deviation from θ ν12 small. We also present some phenomenological numerical results predicted by the model.
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Zhao, Y., Zhang, PF. SUSY SU(5)×S 4 GUT flavor model for fermion masses and mixings with adjoint, large θ PMNS13 . J. High Energ. Phys. 2016, 32 (2016). https://doi.org/10.1007/JHEP06(2016)032
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DOI: https://doi.org/10.1007/JHEP06(2016)032