Classification of lepton mixing matrices from finite residual symmetries

TL;DR

This paper classifies all possible neutrino mixing matrices derived from finite residual symmetries, identifying one series compatible with experimental data, thus advancing understanding of flavor symmetries in neutrino physics.

Contribution

It provides a complete classification of mixing matrices from finite residual symmetries, including known cases and identifying the only series compatible with current data.

Findings

17 sporadic cases identified

One infinite series compatible with data

Mathematical framework based on roots of unity

Abstract

Assuming that neutrinos are Majorana particles, we perform a complete classification of all possible mixing matrices which are fully determined by residual symmetries in the charged-lepton and neutrino mass matrices. The classification is based on the assumption that the residual symmetries originate from a finite flavour symmetry group. The mathematical tools which allow us to accomplish this classification are theorems on sums of roots of unity. We find 17 sporadic cases plus one infinite series of mixing matrices associated with three-flavour mixing, all of which have already been discussed in the literature. Only the infinite series contains mixing matrices which are compatible with the data at the 3 sigma level.