A new family symmetry for SO(10) GUTs

Abstract

We argue that the projective special linear group PSL(2,7), also known as Sigma(168), has unique features which make it the most suitable discrete family symmetry for describing quark and lepton masses and mixing in the framework of SO(10) type unified models. In such models flavon fields in the sextet representation of PSL(2,7) play a crucial role both in obtaining tri-bimaximal neutrino mixing as well as in generating the third family charged fermion Yukawa couplings. In preparation for physical applications, we derive the triplet representation of PSL(2,7) in the basis S,T,U,V where S,T,U are the familiar triplet generators of S(4) in the diagonal charged lepton basis where T is diagonal. We also derive an analogous basis for the real sextet representation and identify the vacuum alignments which lead to tri-bimaximal neutrino mixing and large third family charged fermion Yukawa couplings.

23 pages, 2 figures

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Cited by in corpus (16)

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• A4xSU(5) SUSY GUT of Flavour with Trimaximal Neutrino Mixing
• On the finite subgroups of U(3) of order smaller than 512
• Measurable Neutrino Mass Scale in A4 x SU(5)
• Family symmetries and alignment in multi-Higgs doublet models
• Vacuum misalignment corrections to tri-bimaximal mixing and form dominance
• Order and Anarchy hand in hand in 5D SO(10)
• $\mathbf{SO}(10)\times {\mathbf{S}}_4$ Grand Unified Theory of Flavour and Leptogenesis
• From Flavour to SUSY Flavour Models
• A Built-in Horizontal Symmetry of $SO(10)$
• Modular Invariant Models of Leptons at Level 7
• Lepton-flavour violation in a Pati-Salam model with gauged flavour symmetry
• Combining Pati-Salam and Flavour Symmetries
• Flavor Symmetries in the Yukawa Sector of Non-Supersymmetric SO(10): Numerical Fits Using Renormalization Group Running
• Neutrino Mass Models: Impact of non-zero reactor angle
• A realistic pattern of fermion masses from a five-dimensional SO(10) model