S_4 Flavor Symmetry Embedded into SU(3) and Lepton Masses and Mixing

TL;DR

This paper explores a lepton mass and mixing model based on embedding S_4 flavor symmetry into SU(3), using scalar VEVs and specific invariance conditions to explain observed mass relations and tribimaximal neutrino mixing.

Contribution

It introduces a novel S_4 flavor symmetry model embedded into SU(3) that explains lepton masses and mixing patterns through scalar VEVs and symmetry invariance conditions.

Findings

Derives a relation for charged lepton masses.

Explains tribimaximal neutrino mixing with right-handed neutrinos and scalar triplets.

Provides a symmetry-based framework for lepton flavor structure.

Abstract

Based on an assumption that an S_4 flavor symmetry is embedded into SU(3), a lepton mass matrix model is investigated. A Frogatt-Nielsen type model is assumed, and the flavor structures of the masses and mixing are caused by VEVs of SU(2)_L-singlet scalars \phi_u and \phi_d which are nonets (8+1) of the SU(3) flavor symmetry, and which are broken into 2+3+3' and 1 of S_4. If we require the invariance under the transformation (\phi^{(8)},\phi^{(1)}) \to (-\phi^{(8)},+\phi^{(1)}) for the superpotential of the nonet field \phi^{(8+1)}, the model leads to a beautiful relation for the charged lepton masses. The observed tribimaximal neutrino mixing is understood by assuming two SU(3) singlet right-handed neutrinos \nu_R^{(\pm)} and an SU(3) triplet scalar \chi.