On CP-violation and quark masses: reducing the number of free parameters

TL;DR

This paper explores how CP-violation constraints, specifically the Jarlskog invariant, reduce the free parameters in quark mass matrices, revealing interdependencies among quark masses.

Contribution

It demonstrates that CP-violation constraints decrease the number of free parameters in quark mass matrices from six to five, linking quark mass eigenvalues.

Findings

CP-violation constraints reduce free parameters in quark mass matrices.

Interdependence among quark mass eigenvalues is explicitly shown.

Nearly democratic texture matrices are used to illustrate the constraints.

Abstract

A physically viable ansatz for quark mass matrices must satisfy certain constraints, like the constraint imposed by CP-violation. In this article we study a concrete example, by looking at some generic matrices with a nearly democratic texture, and the implications of the constraints imposed by CP-violation, specifically the Jarlskog invariant. This constraint reduces the number of parameters from six to five, implying that the six mass eigenvalues of the up-quarks and the down-quarks are interdependent, which in our approach is explicitly demonstrated.