Classification and Application of Triangular Quark Mass Matrices

TL;DR

This paper classifies hierarchical triangular quark mass matrices to analyze their structure, texture zeros, and compatibility with experimental data, providing a systematic approach to understanding quark masses and mixings.

Contribution

It introduces a classification scheme for triangular quark mass matrices in a minimal parameter basis, linking texture zeros to quark mixing predictions.

Findings

Three texture zero configurations are disfavored by data.

One configuration is marginally acceptable.

One configuration fits the experimental data well.

Abstract

The hierarchical structure in the quark masses and mixings allows its ten physical parameters to be most conveniently encoded in mass matrices of the upper triangular form. We classify these matrices in the hierarchical, minimal parameter basis where the mismatch between the weak and mass eigenstates involves only small mixing angles. Ten such pairs are obtained for the up and down quarks. This analysis can be used to classify texture zeros of general mass matrices. For hermitian mass matrices with five texture zeros, this method yields immediately five pairs of textures with simple, analytic predictions for the quark mixings. Comparison with data indicates that, of the five pairs, three are disfavored, one is marginally acceptable, while the fifth fits well.