Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2009-05-12
Nucl.Phys.B820:269-289,2009
Physics
High Energy Physics
High Energy Physics - Phenomenology
23 pages, 2 figures
Scientific paper
10.1016/j.nuclphysb.2009.05.020
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.
King Stephen F.
Luhn Christoph
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