Neutrino Oscillations from Discrete Non-Abelian Symmetries

Abstract

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 $SO(10) \times \Delta(75)$ 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 $\nu_\mu \rightarrow \nu_\tau$ 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 $\lambda_b^{GUT}=\lambda_\tau^{GUT}$, are found to be in conflict with the current experimental status. Attempts to correct these relations seem to lead to rather contrived models.