Generalised CP and $\Delta (6n^2)$ Family Symmetry in Semi-Direct Models of Leptons

TL;DR

This paper analyzes how $ ext{Delta}(6n^2)$ family symmetry combined with generalized CP symmetry constrains lepton mixing and mass predictions in semi-direct models, providing specific predictions for PMNS parameters and neutrinoless double beta decay.

Contribution

It introduces a comprehensive analysis of $ ext{Delta}(6n^2)$ combined with generalized CP symmetry in semi-direct lepton models, detailing how different residual symmetries influence predictions.

Findings

Predictions depend on a single undetermined parameter affecting reactor angle.

Five phenomenologically viable cases with specific PMNS parameter predictions.

Predictions for neutrinoless double beta decay vary with the symmetry breaking patterns.

Abstract

We perform a detailed analysis of $\Delta (6n^2)$ family symmetry combined with a generalised CP symmetry in the lepton sector, breaking to different remnant symmetries $G_{\nu}$ in the neutrino and $G_{l}$ in the charged lepton sector, together with different remnant CP symmetries in each sector. We discuss the resulting mass and mixing predictions for $G_{\nu}=Z_2$ with $G_{l}=K_4,Z_p,p>2$ and $G_{\nu}=K_4$ with $G_{l}=Z_2$. All cases correspond to the preserved symmetry smaller than the full Klein symmetry, as in the semi-direct approach, leading to predictions which depend on a single undetermined real parameter, which mainly determines the reactor angle. We focus on five phenomenologically allowed cases for which we present the resulting predictions for the PMNS parameters as a function of $n$, as well as the predictions for neutrinoless double beta decay.