A realistic pattern of lepton mixing and masses from $$S_4$$ S 4 and CP

Ferruccio Feruglio,Claudia Hagedorn,Robert Ziegler

doi:10.1140/epjc/s10052-014-2753-2

Abstract

We present a supersymmetric model with the flavour symmetry S4 x Z3 and a CP symmetry which are broken to a Z3 subgroup of the flavour symmetry in the charged lepton sector and to Z2 x CP (x Z3) in the neutrino one at leading order. This model implements an approach, capable of predicting lepton mixing angles and Dirac as well as Majorana phases in terms of one free parameter. This parameter, directly related to the size of the reactor mixing angle theta_{13}, can be naturally of the correct order in our model. Atmospheric mixing is maximal, while sin^2 theta_{12} is larger than 1/3. All three phases are predicted: the Dirac phase is maximal, whereas the two Majorana phases are trivial. The neutrino mass matrix contains only three real parameters at leading order and neutrino masses effectively only depend on two of them. As a consequence, they have to be normally ordered and the absolute neutrino mass scale and the sum of the neutrino masses are predicted. The vacuum of the flavons can be correctly aligned. We study subleading corrections to the leading order results and show that they are small.

Highlights

The discovery of neutrino oscillations and the first information on lepton mixing angles has led to an intense research in this field
We present a supersymmetric model with the flavour symmetry S4 × Z3 and a CP symmetry which are broken to a Z3 subgroup of the flavour symmetry in the charged lepton sector and to Z2×CP (×Z3) in the neutrino one at leading order
The spontaneous breaking of these symmetries to a Z3 subgroup in the charged lepton and to Z2×CP (×Z3) in the neutrino sector leads to a mixing matrix with one free parameter

Summary

Introduction

The discovery of neutrino oscillations and the first information on lepton mixing angles has led to an intense research in this field. A well-known example is given by the μτ reflection symmetry [29–32], which exchanges a muon (tau) neutrino with a tau (muon) antineutrino in the charged lepton mass basis If this symmetry is imposed, the atmospheric mixing angle is predicted to be maximal, while θ13 is in general non-vanishing for a maximal Dirac phase δ. This separation is achieved by the Z3 symmetry as well as with the help of an additional Z16 group that is, in general, responsible for forbidding unwanted operators. The maximality of the atmospheric mixing angle and of the Dirac phase are consequences of the invariance of the neutrino mass matrix under the μτ reflection symmetry in the charged lepton mass basis. Some details of the group theory of S4 are found in Appendix A

Approach

Model with S4 and CP

Leading order results

Next-to-leading order results

Flavon superpotential

Summary