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 ${\nu }_{\mu }\to {\nu }_{\tau }$ 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.

16 pages, uses harvmac, epsf, tables, 4 figures

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Cited by in corpus (18)

• Flavour physics of leptons and dipole moments
• Models of Neutrino Masses and Mixings
• Tri-Bimaximal Neutrino Mixing and the Family Symmetry Z_7 x Z_3
• The Flavor Group Delta(3n^2)
• The Flavor Group Delta(6n^2)
• Simple Finite Non-Abelian Flavor Groups
• Discrete Flavor Symmetry, Dynamical Mass Textures, and Grand Unification
• Nonabelian Discrete Symmetries, Fermion Mass Textures and Large Neutrino Mixing
• T(13) Flavor Symmetry and Decaying Dark Matter
• Horizontal Symmetry for Quark and Squark Masses in Supersymmetric SU(5)
• Neutrino physics from a U(2) flavor symmetry
• Dicyclic Horizontal Symmetry and Supersymmetric Grand Unification
• Non-Abelian Discrete Flavor Symmetries
• LHC Higgs Production and Decay in the T' Model
• A Note on Embedding Nonabelian Finite Flavor Groups in Continuous Groups
• Electron and Muon $g-2$ Contributions from the $T^{\prime }$ Higgs Sector
• Are supersymmetric models with large tan(beta) natural ?
• Higgs-Flavor Groups, Naturalness, and Dark Matter