Possible textures of the fermion mass matrices

TL;DR

This paper reviews all possible textures of fermion mass matrices, analyzing their structures and implications for quark and lepton masses, including hierarchies and phases, to understand fermion mixing patterns.

Contribution

It provides a comprehensive overview of all Fritzsch-like and non Fritzsch-like texture 6, 5, and 4 zero fermion mass matrices, including their hierarchies and phase roles.

Findings

Analysis of texture 6 and 5 zero matrices

Discussion of hierarchy in texture 4 zero matrices

Implications for neutrino mass hierarchies

Abstract

Texture specific fermion mass matrices have played an important role in understanding several features of fermion masses and mixings. In the present work, we have given an overview of all possible cases of Fritzsch-like as well as non Fritzsch-like texture 6 and 5 zero fermion mass matrices. Further, for the case of texture 4 zero Fritzsch-like quark mass matrices, the issue of the hierarchy of the elements of the mass matrices and the role of their phases have been discussed. Furthermore, the case of texture 4 zero Fritzsch-like lepton mass matrices has also been discussed with an emphasis on the hierarchy of neutrino masses for both Majorana and Dirac neutrinos.