On the four-zero texture of quark mass matrices and its stability

TL;DR

This paper explores specific four-zero textures in Hermitian quark mass matrices, identifying new parameter spaces, proposing flavor-symmetry models, and demonstrating their stability under energy scale evolution.

Contribution

It uncovers previously missed parameter regions, introduces models for these textures, and analytically proves their stability across energy scales.

Findings

Discovered new four-zero texture patterns with fewer parameters

Proposed toy models for flavor symmetry realization

Proved texture zeros are stable under renormalization-group evolution

Abstract

We carry out a new study of quark mass matrices $M^{}_{\rm u}$ (up-type) and $M^{}_{\rm d}$ (down-type) which are Hermitian and have four zero entries, and find a new part of the parameter space which was missed in the previous works. We identify two more specific four-zero patterns of $M^{}_{\rm u}$ and $M^{}_{\rm d}$ with fewer free parameters, and present two toy flavor-symmetry models which can help realize such special and interesting quark flavor structures. We also show that the texture zeros of $M^{}_{\rm u}$ and $M^{}_{\rm d}$ are essentially stable against the evolution of energy scales in an analytical way by using the one-loop renormalization-group equations.