Spontaneous CP violation from vacuum alignment in $S_4$ models of leptons

TL;DR

This paper develops $S_4$-based lepton models with generalized CP symmetry, demonstrating spontaneous symmetry breaking in the flavon potential that leads to specific CP violation patterns and predicting trimaximal lepton mixing.

Contribution

It introduces two realistic models of leptons with spontaneous CP violation from vacuum alignment in $S_4$ models, controlling CP breaking through flavon potential parameters.

Findings

Models predict trimaximal lepton mixing patterns.

CP is either fully preserved or maximally broken in the models.

Spontaneous symmetry breaking is achieved via flavon potential in $S_4$ frameworks.

Abstract

We construct models of leptons based on $S_4$ family symmetry combined with a generalised CP symmetry $H_{CP}$. We show how the flavon potential can spontaneously break the symmetry $S_4 \rtimes H_{CP}$ down to $Z_2 \times H^{\nu}_{CP}$ in the neutrino sector, where the choice of preserved CP symmetry $H^{\nu}_{CP}$ is controlled by free (real) parameters in the flavon potential. We propose two realistic models of this kind, one at the effective level and one at the renormalisable level. Both models predict trimaximal lepton mixing with CP being either fully preserved or maximally broken, with the intermediate possibility forbidden by the structure of the models.