Lepton Mixing Predictions from (Generalised) CP and Discrete Flavour Symmetry

TL;DR

This paper explores how discrete flavor symmetries, specifically the $ ext{Delta}(6n^2)$ series, combined with generalized CP symmetry, can predict lepton mixing angles and phases, including Majorana phases, in neutrino models.

Contribution

It provides a comprehensive analysis of lepton mixing predictions from $ ext{Delta}(6n^2)$ flavor groups with generalized CP symmetry, including the effects of residual symmetries.

Findings

Predictions for mixing angles and Dirac CP phase.

Inclusion of Majorana phases with generalized CP symmetry.

The interplay of flavor group and CP symmetry is crucial.

Abstract

An important class of flavour groups, that are subgroups of $U(3)$ and that predict experimentally viable lepton mixing parameters including Majorana phases, is the $\Delta(6n^2)$ series. The most well-known member is $\Delta(24)=S_4$. I present results of several extensive studies of lepton mixing predictions obtained in models with a $\Delta(6n^2)$ flavour group that preserve either the full residual $Z_2\times Z_2$ or a $Z_2$ subgroup for neutrinos and can include a generalised CP symmetry. Predictions include mixing angles and Dirac CP phase generally; and if invariance under a generalised CP symmetry is included, also Majorana phases. For this, the interplay of flavour group and generalised CP symmetry has to be studied carefully.