Lepton Mixing Patterns from a Scan of Finite Discrete Groups

TL;DR

This study systematically scans finite discrete groups under 1536 to identify those predicting lepton mixing angles consistent with current experimental data, revealing only three promising groups among over a million.

Contribution

It provides a comprehensive scan of finite discrete groups to find those compatible with observed lepton mixing angles, highlighting the rarity of such groups.

Findings

Only 3 groups out of over one million match experimental data within 3-sigma.

Most finite groups do not produce realistic lepton mixing patterns.

A systematic categorization method for these groups is proposed.

Abstract

The recent discovery of a non-zero value of the mixing angle theta_13 has ruled out tri-bimaximal mixing as the correct lepton mixing pattern generated by some discrete flavor symmetry (barring large next-to-leading order corrections in concrete models). In this work we assume that neutrinos are Majorana particles and perform a general scan of all finite discrete groups with order less than 1536 to obtain their predictions for lepton mixing angles. To our surprise, the scan of over one million groups only yields 3 interesting groups that give lepton mixing patterns which lie within 3-sigma of the current best global fit values. A systematic way to categorize such groups and the implications for flavor symmetry are discussed.