SUSY SU(5)× S 4 GUT flavor model for fermion masses and mixings with adjoint, large θ 13 PMNS

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 〈φ ν 〉 ∼ λ c 〈φ e 〉. 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 12  ∼ 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 13 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 12 small. we also present some phenomenological numerical results predicted by the model.