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 Δ(75), a subgroup of SU(3), which can explain the observed quark and lepton masses and mixing angles. The model predicts tanβ≃1 and gives a τ neutrino mass ${\mathit{m}}_{\nu }$≃${\mathit{M}}_{\mathit{p}}$/${\mathit{G}}_{\mathit{F}}$ ${\mathit{M}}_{\mathrm{GUT}}^2$=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.