Fermion mass matrices, textures and beyond

TL;DR

This paper explores the classification of fermion mass matrices, emphasizing the role of textures, naturalness, and weak basis transformations to identify a minimal set of viable quark mass matrices.

Contribution

It introduces a method combining textures, naturalness, and weak basis transformations to systematically reduce the set of viable quark mass matrices.

Findings

A large number of texture possibilities exist without constraints.

Incorporating naturalness and weak basis transformations reduces viable matrices.

A minimal finite set of quark mass matrices is identified.

Abstract

The issue of texture specific fermion mass matrices have been examined briefly from the `bottom-up' perspective. In case no conditions are imposed, the texture ansatze leads to a large number of viable possibilities. However, besides textures, if in case one incorporates the ideas of `natural mass matrices' and uses the facility of Weak Basis Transformations, then one is able to arrive at a minimal finite set of viable mass matrices in the case of quarks.