Leptonic Mixing and Group Structure Constants

TL;DR

This paper explores the mathematical structure underlying leptonic mixing matrices, revealing dependencies among parameters and proposing a method to determine valid group-based configurations using finite group structure constants.

Contribution

It identifies dependencies among the six integers parametrizing neutrino mixing and introduces a novel approach using finite group structure constants to find allowed parameter combinations.

Findings

Six integers are not independent in neutrino mixing parametrization.

A method using finite group structure constants to determine valid parameter sets.

Provides a framework for analyzing residual symmetries in leptonic mixing.

Abstract

Hernandez and Smirnov discovered an interesting formula to parametrize each column of a neutrino mixing matrix by six integers related to the residual symmetry. We point out that these six integers are not independent, and propose a way to find the allowed combinations using structure constants of finite groups.