Finite Modular Groups and Lepton Mixing

TL;DR

This paper explores lepton mixing patterns derived from finite modular groups, identifying key groups and analyzing how subgroup choices influence mixing angles, with implications for neutrino physics and potential quark sector extensions.

Contribution

It systematically analyzes lepton mixing patterns from finite modular groups, highlighting six relevant groups and their subgroup structures, and predicts non-zero theta_13 consistent with experimental data.

Findings

Identifies six relevant finite modular groups for lepton mixing

Predicts non-zero theta_13 in several mixing patterns

Provides a framework for extending to quark sector

Abstract

We study lepton mixing patterns which are derived from finite modular groups Gamma_N, requiring subgroups G_nu and G_e to be preserved in the neutrino and charged lepton sectors, respectively. We show that only six groups Gamma_N with N=3,4,5,7,8,16 are relevant. A comprehensive analysis is presented for G_e arbitrary and G_nu=Z2 x Z2, as demanded if neutrinos are Majorana particles. We discuss interesting patterns arising from both groups G_e and G_nu being arbitrary. Several of the most promising patterns are specific deviations from tri-bimaximal mixing, all predicting theta_13 non-zero as favoured by the latest experimental data. We also comment on prospects to extend this idea to the quark sector.