CP Symmetry and Lepton Mixing from a Scan of Finite Discrete Groups

TL;DR

This paper systematically explores finite discrete groups with order less than 2000, combined with CP symmetry, to classify viable lepton mixing patterns consistent with experimental data, and analyzes their phenomenological implications.

Contribution

It provides a comprehensive classification of lepton mixing matrices from finite discrete groups with CP symmetry, identifying eight categories and detailed analytical and numerical analyses.

Findings

Eight categories of viable mixing patterns identified

All patterns derived from specific finite groups with CP symmetry

Predictions made for lepton parameters, neutrinoless double decay, and leptogenesis

Abstract

Including the generalized CP symmetry, we have performed a comprehensive scan of leptonic mixing patterns which can be obtained from finite discrete groups with order less than 2000. Both the semidirect approach and its variant are considered. The lepton mixing matrices which can admit a good agreement with experimental data can be organized into eight different categories up to possible row and column permutations. These viable mixing patterns can be completely obtained from the discrete flavor groups $\Delta(6n^2)$, $D^{(1)}_{9n,3n}$, $A_5$ and $\Sigma(168)$ combined with CP symmetry. We perform a detailed analytical and numerical analysis for each possible mixing pattern. The resulting predictions for lepton mixing parameter, neutrinoless double decay and flavored leptogenesis are studied.