Construction of an SO(10)xU(1)(F) model of the Yukawa interactions

We construct a supersymmetric SO(10)XU(1)(F) model of the Yukawa interactions at the grand unification scale from knowledge of a phenomenological set of mass matrices obtained by a previous bottom-up approach. The U(1)(F) family symmetry determines the textures for the Majorana and generic Dirac mass matrices, while the SO(10) symmetry relates each particular element of the up, down, neutrino, and charged lepton Dirac matrices. The dominant second and third family contributions in the Dirac sector are renormalizable, while the remaining contributions to the Dirac mass matrices are of higher order, restricted by the U(1)F family symmetry to a small set of tree diagrams, and mainly complex symmetric. The tree diagrams for the Majorana mass matrix are all nonrenormalizable and of progressively higher order, leading to a nearly geometrical structure. Pairs of 1, 45, 10, and 126 Higgs representations enter with those having large vacuum expectation values breaking the symmetry down to SU(3)(c)XSU(2)(L)XU(l)(Y) near the grand unification scale. In terms of 12 parameters expressed as the Yukawa couplings times vacuum expectation values for the Higgs representations employed, a realistic set of 15 quark and lepton masses (including those for the three heavy right-handed Majorana neutrinos) and eight mixing parameters emerges for the neutrino scenario involving the nonadiabatic conversion of solar neutrinos and the depletion of atmospheric muon neutrinos through oscillations into tau neutrinos.