Tri-bimaximal neutrino mixing and the family symmetry Z7⋊Z3

2007/06/30 by Christoph Luhn, Salah Nasri, Pierre Ramond · 6 citations
Mathematics · Physics and Astronomy · #Abelian group #Astrophysics and Cosmic Phenomena #Combinatorics #Electron #Geometry #Group (periodic table) #Lepton #Mathematics #Mixing (physics) #Neutrino #Neutrino Physics Research #Particle physics #Particle physics theoretical and experimental studies #Physics #Quantum mechanics #Symmetry (geometry) #hep-ph #hep-th

paper · pdf · doi:10.1016/j.physletb.2007.06.059

published as Phys.Lett.B652:27-33,2007 · 15 pages, matches published version, updated references

openalex publication_date 2007/07/02 · arxiv created 2007/09/11 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

The Non-Abelian finite group PSL₂(7) is the only simple subgroup of SU(3) with a complex three-dimensional irreducible representation. It has two maximal subgroups, S₄ which, along with its own A₄ subgroup, has been successfully applied in numerous models of flavor, as well as the 21 element Frobenius group Z₇ x Z₃, which has gained much less attention. We show that it can also be used to generate tri-bimaximal mixing in the neutrino sector, while allowing for quark and charged lepton hierarchies.

Citations

• Non-Abelian Discrete Flavor Symmetries
• Obtaining the neutrino mixing matrix with the tetrahedral group
• S3 symmetry and tri-bimaximal mixing
• Symmetries and generalisations of tri-bimaximal neutrino mixing
• A4 family symmetry and quark–lepton unification
• A model realizing the Harrison-Perkins-Scott lepton mixing matrix
• Tri-bimaximal neutrino mixing from discrete subgroups of SU(3) and SO(3) family symmetry
• Model for fermion masses and lepton mixing inSO(10)×A4
• AN APPROACH TO PERMUTATION SYMMETRY FOR THE ELECTROWEAK THEORY

Cited by

• Heterotic non-abelian orbifolds
• Proton hexality from an anomalous flavor U(1) and neutrino masses: Linking to the string scale
• Neutrino Mass and Flavour Models
• Tri-bimaximal neutrino mixing and θ13
• A4 Family Symmetry from SU(5) SUSY GUTs in 6d
• Dirac CP phases in a 3 + 1 neutrino scenario with μ -τ symmetry