Neutrino Oscillations from Discrete Non-Abelian Symmetries

I discuss a SUSY-GUT model with a non-Abelian discrete family symmetry that explains the observed hierarchical pattern of quark and lepton masses. This $SO(10) \times Δ(75)$ model predicts modified quadratic seesaw neutrino masses and mixing angles which are interesting for three reasons: i.) they offer a solution to the solar neutrino problem, ii.) the tau neutrino has the right mass for a cosmologically interesting hot dark matter candidate, and iii.) they suggest a positive result for the $ν_μ\rightarrow ν_τ$ oscillation searches by the CHORUS and NOMAD collaborations. However, the model shares some problems with many other predictive GUT models of quark and lepton masses. Well-known and once successful mass and angle relations, such as the $SU(5)$ relation $λ_b^{GUT}=λ_τ^{GUT}$, are found to be in conflict with the current experimental status. Attempts to correct these relations seem to lead to rather contrived models.

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