Flavor unification and discrete non-Abelian symmetries.

Grand unified theories with fermions transforming as irreducible representations of a discrete nonabelian 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 ∆(75) — a subgroup of SU(3) — which can explain the observed quark and lepton masses and mixing angles. The model predicts tanβ ≃ 2 − 5 and gives a τ neutrino mass mν ≃ Mp/GFM GUT = 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. UCSD/PTH 93-30, hep-ph/9311281 October 1993 † Alfred P. Sloan Fellow and NSF Presidential Young Investigator.