Lepton Mixing Predictions from Infinite Group Series $D^{(1)}_{9n, 3n}$ with Generalized CP

TL;DR

This paper analyzes the flavor symmetry group series $D^{(1)}_{9n, 3n}$ combined with generalized CP symmetry to predict lepton mixing parameters, identifying viable mixing patterns consistent with experimental data.

Contribution

It provides a comprehensive analysis of the $D^{(1)}_{9n, 3n}$ groups as flavor symmetries with generalized CP, identifying specific mixing patterns that fit experimental observations.

Findings

Only one mixing pattern fits measured angles in both approaches.

Four mixing patterns are viable in the semidirect approach.

Smallest groups with n=1,2 fit data very well.

Abstract

We have performed a comprehensive analysis of the type D group $D^{(1)}_{9n, 3n}$ as flavor symmetry and the generalized CP symmetry. All possible residual symmetries and their consequences for the prediction of the mixing parameters are studied. We find that only one type of mixing pattern is able to accommodate the measured values of the mixing angles in both "direct" and "variant of semidirect" approaches, and four types of mixing patterns are phenomenologically viable in the "semidirect" approach. The admissible values of the mixing angles as well as CP violating phases are studied in detail for each case. It is remarkable that the first two smallest $D^{(1)}_{9n,3n}$ groups with $n=1, 2$ can fits the experimental data very well. The phenomenological predictions for neutrinoless double beta decay are discussed.