Discrete symmetries and model-independent patterns of lepton mixing

TL;DR

This paper introduces a model-independent method using discrete flavor symmetries, particularly von Dyck groups, to predict lepton mixing patterns and matches these predictions with experimental data.

Contribution

It develops a general formalism linking discrete flavor symmetries to lepton mixing parameters, applicable to both finite and infinite groups like modular groups.

Findings

Certain von Dyck groups predict mixing angles consistent with experimental data.

The Klein group as residual symmetry explains permutation properties in the mixing matrix.

The method applies to finite subgroups of modular groups, providing new insights into lepton flavor structure.

Abstract

In the context of discrete flavor symmetries, we elaborate a method that allows one to obtain relations between the mixing parameters in a model-independent way. Under very general conditions, we show that flavor groups of the von Dyck type, that are not necessarily finite, determine the absolute values of the entries of one column of the mixing matrix. We apply our formalism to finite subgroups of the infinite von Dyck groups, such as the modular groups, and find cases that yield an excellent agreement with the best fit values for the mixing angles. We explore the Klein group as the residual symmetry of the neutrino sector and explain the permutation property that appears between the elements of the mixing matrix in this case.