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A new family symmetry for [formula omitted]GUTs

Authors
Journal
Nuclear Physics B
0550-3213
Publisher
Elsevier
Publication Date
Volume
820
Identifiers
DOI: 10.1016/j.nuclphysb.2009.05.020
Keywords
  • Particle Physics
Disciplines
  • Physics

Abstract

Abstract We argue that the projective special linear group PSL 2 ( 7 ) , also known as Σ ( 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.

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