On Invariants of Quark and Lepton Mass Matrices in the Standard Model

TL;DR

This paper discusses the importance and applications of invariant functions of quark and lepton mass matrices within the Standard Model and its extensions, highlighting their role in understanding particle physics.

Contribution

It introduces the concept of invariant functions of mass matrices, reviews their historical development, and explores their extensions beyond the Standard Model.

Findings

Invariant functions help characterize mass matrix properties.

Extensions of invariants provide insights into physics beyond the Standard Model.

The work builds on and summarizes key developments since 1985.

Abstract

In this article I present the motivation for introducing the invariant functions of mass matrices, based on my own work, and give some examples. Since their introduction in 1985, in the framework of the standard electroweak model, they have been used by many authors. Some authors have gone further along this path and have studied the extensions of this concept to frameworks beyond the standard model. I hope, in the near future, to give a more detailed account of this subject, including recent developments.