Group-theoretical search for rows or columns of the lepton mixing matrix

TL;DR

This paper employs group theory and computational tools to identify groups that predict specific patterns in the lepton mixing matrix, providing new insights into neutrino mixing phenomenology.

Contribution

It introduces a systematic search method using GAP and Mathematica to find groups with particular eigenvalue degeneracies that predict lepton mixing matrix elements.

Findings

Identified groups predicting specific rows or columns of the lepton mixing matrix.

Produced realistic predictions for certain matrix elements.

Demonstrated the effectiveness of computational group theory in particle physics modeling.

Abstract

We have used the SmallGroups library of groups, together with the computer algebra systems GAP and Mathematica, to search for groups with a three-dimensional irreducible representation in which one of the group generators has a twice-degenerate eigenvalue while another generator has non-degenerate eigenvalues. By assuming one of these group generators to commute with the charged-lepton mass matrix and the other one to commute with the neutrino (Dirac) mass matrix, one derives group-theoretical predictions for the moduli of the matrix elements of either a row or a column of the lepton mixing matrix. Our search has produced several realistic predictions for either the second row, or the third row, or for any of the columns of that matrix.