Fermion masses in E_6 grand unification with family permutation symmetries

Abstract

Neutrino masses have been extensively studied in the context of discrete symmetries. A family permutation symmetry easily explains all neutrino oscillations and their mixing angles. However it is not obvious the embedding of such symmetry in a grand unified theory where all fermions live in the same representation. We show that it is possible to embed such a horizontal discrete symmetry in a grand unified theory. We discuss an E_6 GUT model as in [1], but differently from [1], we take the SM Higgs doublet in the 351' to have (+3,+5) charges with respect the additional U(1)_r X U(1)_t. This choice makes possible two different horizontal symmetry breaking patterns and a distinction between neutrinos and the rest of matter fermions.

12 pages

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• Revisiting Bimaximal Neutrino Mixing in a Model with S4 Discrete Symmetry
• S4 Flavor Symmetry and Fermion Masses: Towards a Grand Unified theory of Flavor
• A Simplest A4 Model for Tri-Bimaximal Neutrino Mixing
• Tri-Bimaximal Lepton Mixing and Leptogenesis
• An A4 model for lepton masses and mixings
• The Cabibbo Angle in a Supersymmetric D14 Model
• Gauge boson families in grand unified theories of fermion masses: E_6^4 x S_4
• Non-Abelian discrete R symmetries
• Exceptional Lie Algebras, SU(3) and Jordan Pairs Part 2: Zorn-type Representations
• Towards the minimal renormalizable supersymmetric $E_6$ model
• Theoretical Models of Neutrino Mixing: Recent Developments