Predicting Neutrino Mixing Angles Using Group Presentations

TL;DR

This paper introduces a group presentation-based method to analyze neutrino mixing and CP violation, reproducing previous results and suggesting a potential group-theoretical origin of CP violation, with implications for future measurements.

Contribution

It develops a novel approach using group presentation rules to study neutrino mixing and CP violation, unifying previous results and exploring the phase's role in Klein symmetry elements.

Findings

Method reproduces all previous results in the literature.

Phase in Klein symmetry elements can be removed in analyzed cases.

Method suggests a possible group-theoretical origin of CP violation.

Abstract

By assuming there exist three massive non-degenerate Majorana neutrinos, it is possible to describe neutrino mixing with a residual, unbroken discrete Klein subgroup of a larger spontaneously broken flavor symmetry group. Motivated by forthcoming measurements of leptonic CP violation, we revisit this framework by applying group presentation rules to it. We develop a method that is able to reproduce all previous results in the literature and may also hint at a possible group theoretical origin of CP violation in the Klein symmetry elements. This is due to the explicit appearance of a phase in them. However, for the cases considered in this analysis, it turns out that this phase can be removed. Still, this new method warrants further study.