Neutrino tri-bi-maximal mixing from a non-Abelian discrete family symmetry

I. de Medeiros Varzielas,S.F. King,G.G. Ross

doi:10.1016/j.physletb.2007.03.009

Abstract

The observed neutrino mixing, having a near maximal atmospheric neutrino mixing angle and a large solar mixing angle, is close to tri-bi-maximal. We argue that this structure suggests a family symmetric origin in which the magnitude of the mixing angles are related to the existence of a discrete non-Abelian family symmetry. We construct a model in which the family symmetry is the non-Abelian discrete group �(27), a subgroup of SU(3) in which the tri-bi-maximal mixing directly follows from the vacuum structure enforced by the discrete symmetry. In addition to the lepton mixing angles, the model accounts for the observed quark and lepton masses and the CKM matrix. The structure is also consistent with an underlying stage of Grand Unification.

Highlights

IntroductionThe observed neutrino oscillation parameters are consistent with a tri-bi-maximal structure [1]:
The observed neutrino oscillation parameters are consistent with a tri-bi-maximal structure [1]: − UP MNS ∝ (1)It has been observed that this simple form might be a hint of an underlying family symmetry, and several models have been constructed that account for this structure of leptonic mixing (e.g. [2])
We have constructed a complete theory of fermion masses and mixings based on the spontaneous breaking of the discrete non-Abelian symmetry group Z3 ⋉ Z3′

Summary

Introduction

The observed neutrino oscillation parameters are consistent with a tri-bi-maximal structure [1]:. It has been observed that this simple form might be a hint of an underlying family symmetry, and several models have been constructed that account for this structure of leptonic mixing A desirable feature of a complete model of quark and lepton masses and mixing angles is that it should be consistent with an underlying Grand Unified structure, either at the field theory level or at the level of the superstring. Using this we show how the desired vacuum structure arises through the appearance of the additional invariants allowed by Z3 ⋉ Z3′ but not by SU (3)f.

Field content and symmetries

Symmetry breaking

M φi23 ψi φj23 ψcj H

Majorana terms

Summary and conclusions