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A new family symmetry for SO(10) GUTs

A new family symmetry for SO(10) GUTs
A new family symmetry for SO(10) GUTs
We argue that the projective special linear group PSL2(7), also known as ?(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 PSL2(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 PSL2(7) in the basis S,T,U,V where S,T,U are the familiar triplet generators of S4 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.
0550-3213
269-289
King, Stephen F.
f8c616b7-0336-4046-a943-700af83a1538
Luhn, Christoph
59a723a0-9d34-48e8-9b97-9d608ad196c8
King, Stephen F.
f8c616b7-0336-4046-a943-700af83a1538
Luhn, Christoph
59a723a0-9d34-48e8-9b97-9d608ad196c8

King, Stephen F. and Luhn, Christoph (2009) A new family symmetry for SO(10) GUTs. Nuclear Physics B, 820 (1-2), 269-289. (doi:10.1016/j.nuclphysb.2009.05.020).

Record type: Article

Abstract

We argue that the projective special linear group PSL2(7), also known as ?(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 PSL2(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 PSL2(7) in the basis S,T,U,V where S,T,U are the familiar triplet generators of S4 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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Published date: 11 October 2009

Identifiers

Local EPrints ID: 154395
URI: http://eprints.soton.ac.uk/id/eprint/154395
ISSN: 0550-3213
PURE UUID: 59c90482-84ec-422e-bb8b-3bc389c5ee2f

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Date deposited: 25 May 2010 10:25
Last modified: 02 Dec 2019 21:20

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