Coxeter groups and the PMNS matrix

TL;DR

This paper explores how Coxeter group symmetries in the leptonic sector can predict the PMNS matrix structure, analyzing finite and infinite groups to find those consistent with experimental neutrino data.

Contribution

It identifies specific finite and infinite Coxeter groups with 2 to 4 generators that can produce PMNS matrix predictions aligning with experimental observations.

Findings

Certain finite Coxeter groups match experimental PMNS data.

Infinite Coxeter subgroups with 4 generators can also be consistent.

Group structures influence neutrino mixing predictions.

Abstract

We discuss the symmetries of the Lagrangian of the leptonic sector. We consider the case when this symmetry group is a Coxeter group. The number of elements of the PMNS matrix predicted by this group structure would depend on the number of generators of this group. We analyze finite Coxeter groups with 2 to 4 generators and even finite subgroups of infinite Coxeter groups with 4 generators and show which of them can give results that are consistent with experimental data.