Lepton mixing and discrete symmetries

TL;DR

This paper explores how discrete flavor symmetries like A4, S4, and A5 influence lepton mixing patterns, deriving conditions that relate mixing angles and CP phases, and predicting a specific range for the CP phase delta.

Contribution

It provides a systematic derivation of constraints on lepton mixing parameters from von Dyck type discrete symmetries, including predictions for the CP phase delta.

Findings

Constraints reduce to two equations for mixing parameters.

Predicted CP phase delta is between 60° and 90°.

Compatible with non-zero 13 mixing and deviations from maximal 2-3 mixing.

Abstract

The pattern of lepton mixing can emerge from breaking a flavor symmetry in different ways in the neutrino and charged lepton Yukawa sectors. In this framework, we derive the conditions imposed on the mixing matrix by the structure of discrete groups of the von Dyck type which include A4, S4 and A5. We show that, in general, these conditions reduce to two equations for the mixing parameters (angles and CP phase \delta). These constraints, which correspond to unbroken residual symmetries, are consistent with non-zero 13 mixing and deviations from maximal 2-3 mixing. For the allowed values of mixing angles we predict \delta = 60 - 90^{\circ}.