Minimizing the phase structure of quark mass matrices

TL;DR

This paper demonstrates that Fritzsch-Xing texture 4-zero hermitian quark mass matrices with a single phase parameter are consistent with current data and can predict CP violation parameters, revealing less hierarchical mass matrix elements.

Contribution

It shows that a simplified one-phase Fritzsch-Xing texture 4-zero quark mass matrix aligns with experimental data and predicts CP violation, contrasting with previous two-phase models.

Findings

Single-phase matrices fit quark mixing data

Mass matrix elements show weak hierarchy

Strong correlation between up and down sector elements

Abstract

Fritzsch-Xing matrices are a particular class of texture 4 zero hermitian quark mass matrices, known to be successful in accommodating the quark mixing data. In the present work, it is shown that these texture 4-zero matrices with only one phase parameter, unlike the usually considered two phase parameters, are not only consistent with the latest experimental quark mixing data, but also predict the CP violation parameters, $J$ and corresponding phase $\delta$, in agreement with the recent global analyses. We also show that the mass matrix elements do not exhibit a strong hierarchy and there is a strong correlation between some of the mass matrix elements of up and down sector. A precision measurement of $\delta$ as well as small quark masses would have the potential to constrain the phase structure of the matrices further.