# Neutrino Mixing and Leptonic CP Violation from $S_4$ Flavour and Generalised CP Symmetries

## TL;DR

This paper explores models of neutrino mixing based on $S_4$ flavor symmetry combined with generalized CP symmetry, predicting mixing angles, CP violation phases, and neutrinoless double beta decay outcomes.

## Contribution

It classifies viable mixing patterns within $S_4$ and generalized CP frameworks, providing new predictions for CP phases and neutrinoless double beta decay.

## Key findings

- Classified all phenomenologically viable mixing patterns.
- Derived predictions for Dirac and Majorana CPV phases.
- Estimated effective Majorana mass for neutrinoless double beta decay.

## Abstract

We consider a class of models of neutrino mixing with $S_4$ lepton flavour symmetry combined with a generalised CP symmetry, which are broken to residual $Z_2$ and $Z_2 \times H^\nu_{\rm CP}$ symmetries in the charged lepton and neutrino sectors, respectively, $H^\nu_{\rm CP}$ being a remnant CP symmetry of the neutrino Majorana mass term. In this set-up the neutrino mixing angles and CP violation (CPV) phases of the neutrino mixing matrix depend on three real parameters - two angles and a phase. We classify all phenomenologically viable mixing patterns and derive predictions for the Dirac and Majorana CPV phases. Further, we use the results obtained on the neutrino mixing angles and leptonic CPV phases to derive predictions for the effective Majorana mass in neutrinoless double beta decay.