FLAVOR UNIFICATION AND DISCRETE NON-ABELIAN SYMMETRIES

Grand unified theories with fermions transforming as irreducible representations of a discrete non-Abelian flavor symmetry can lead to realistic fermion masses, without requiring small fundamental parameters. We construct a specific example of a supersymmetric GUT based on the flavor symmetry DELTA(75), a subgroup of SU(3), which can explain the observed quark and lepton masses and mixing angles. The model predicts tanbeta congruent-to 1 and gives a tau neutrino mass m(nu) congruent-to M(p)/G(F)M(GUT)2 = 10 eV, with other neutrino masses much lighter. Combined constraints of light quark masses and perturbative unification place flavor symmetry-breaking near the GUT scale; it may be possible to probe these extremely high energies by continuing the search for flavor-changing neutral currents.