SUSY adjoint SU(5)SU(5) grand unified model with S4S4 flavor symmetry

We construct a supersymmetric (SUSY) SU(5)SU(5) model with the flavor symmetry S4×Z3×Z4S4×Z3×Z4. Three generations of adjoint matter fields are introduced to generate the neutrino masses via the combined type I and type III see-saw mechanism. The first two generations of the 10-dimensional representation in SU(5)SU(5) are assigned to be a doublet of S4S4, the second family 10 is chose as the first component of the doublet, and the first family as the second component. Tri-bimaximal mixing in the neutrino sector is predicted exactly at leading order, charged lepton mixing leads to small deviation from the tri-bimaximal mixing pattern. Subleading contributions introduce corrections of order λc2 to all three lepton mixing angles. The model also reproduces a realistic pattern of quark and charged lepton masses and quark mixings. The phenomenological implications of the model are analyzed in detail.