Texture Zeros for the Standard Model Quark Mass Matrices

TL;DR

This paper analyzes the role of texture zeros in the quark mass matrices of the standard model, clarifying their physical significance and identifying a viable five-zero texture ansatz consistent with experimental data.

Contribution

It introduces a method to count free parameters considering weak basis transformations and explains the physical meaning of texture zeros, ruling out six-zero textures and proposing a five-zero texture model.

Findings

Six texture zeros are incompatible with experimental constraints.

A five-zero texture ansatz successfully fits all current data.

The analysis clarifies the physical interpretation of texture zeros.

Abstract

A way of counting free parameters in the quark mass matrices of the standard model, including the constraints coming from weak basis transformations, is presented; this allow to understand the exact physical meaning of the parallel and non-parallel texture zeros which appear in some "ans\"{a}tz" of the $3\times 3$ quark mass matrices, including the CP violation phenomena in the analysis, it is shown why the six texture zeros are ruled out. Finally, a five texture zeros "ans\"{a}tze" which properly copes with all experimental constrains, including the angles of the unitary triangle, is presented.