Finite Symmetry of Leptonic Mass Matrices

TL;DR

This paper investigates finite symmetries in leptonic mass matrices using SU(3) subgroups, identifying specific groups that can reproduce parts of the leptonic mixing matrix and predicting mixing angles consistent with experimental data.

Contribution

It systematically searches for finite symmetry groups capable of explaining leptonic mixing data, highlighting the unique role of the group (150) in fitting the third column.

Findings

No single finite group explains all mixing data without free parameters.

Several groups can fit individual columns of the mixing matrix.

(150) accurately predicts 2213 and 2223 mixing angles.

Abstract

We search for possible symmetries present in the leptonic mixing data from SU(3) subgroups of order up to 511. Theoretical results based on symmetry are compared with global fits of experimental data in a chi-squared analysis, yielding the following results. There is no longer a group that can produce all the mixing data without a free parameter, but a number of them can accommodate the first or the second column of the mixing matrix. The only group that fits the third column is $\Delta(150)$. It predicts $\sin^22\theta_{13}=0.11$ and $\sin^22\theta_{23}=0.94$, in good agreement with experimental results.