Lepton mixing predictions including Majorana phases from [formula omitted] flavour symmetry and generalised CP

Stephen F King,Thomas Neder

doi:10.1016/j.physletb.2014.07.043

Abstract

Generalised CP transformations are the only known framework which allows to predict Majorana phases in a flavour model purely from symmetry. For the first time generalised CP transformations are investigated for an infinite series of finite groups, Δ(6n2)=(Zn×Zn)⋊S3. In direct models the mixing angles and Dirac CP phase are solely predicted from symmetry. The Δ(6n2) flavour symmetry provides many examples of viable predictions for mixing angles. For all groups the mixing matrix has a trimaximal middle column and the Dirac CP phase is 0 or π. The Majorana phases are predicted from residual flavour and CP symmetries where α21 can take several discrete values for each n and the Majorana phase α31 is a multiple of π. We discuss constraints on the groups and CP transformations from measurements of the neutrino mixing angles and from neutrinoless double-beta decay and find that predictions for mixing angles and all phases are accessible to experiments in the near future.

Highlights

The question of the origin of neutrino masses and mixing parameters is of fundamental importance
One approach are so-called direct models of neutrino masses [1] where a discrete non-Abelian family symmetry group is broken to a Z2 × Z2 group in the Neutrino sector, and a Z3 subgroup in the charged lepton sector
The consequences for neutrino mixing from a ∆(6n2) flavour symmetry in direct models have been studied in detail in [5] for arbitrary even n

Summary

Introduction

The question of the origin of neutrino masses and mixing parameters is of fundamental importance. One approach are so-called direct models of neutrino masses [1] where a discrete non-Abelian family symmetry group is broken to a Z2 × Z2 group in the Neutrino sector, and a Z3 subgroup in the charged lepton sector In such a model the lepton mixing angles and the lepton Dirac CP phase are completely fixed by symmetry. Promoting CP to a symmetry at high energies which is broken allows to impose further constraints on mass matrices of charged leptons and Majorana neutrinos In this case the interplay between CP and flavour symmetries has to be carefully discussed [15,16,17,18,19,20,21,22,23,24,25,26,27,28,29].

Generalised CP transformations and flavour symmetries

The consistency equation

Inner and outer automorphisms

Conclusions