Recursive parametrization of Quark flavour mixing matrices

TL;DR

This paper explores a recursive mathematical approach to parametrizing quark flavor mixing matrices for three and four generations, providing new expressions for invariants and symmetry constraints.

Contribution

It introduces a recursive parametrization method for quark mixing matrices and derives related rephasing invariants and symmetry constraints.

Findings

Derived expressions for rephasing invariants

Identified constraints from mod symmetry

Extended parametrization to four generations

Abstract

We examine quark flavour mixing matrices for three and four generations using the recursive parametrization of $U(n)$ and $SU(n)$ matrices developed by some of us in Refs.[2] and [3]. After a brief summary of the recursive parametrization, we obtain expressions for the independent rephasing invariants and also the constraints on them that arise from the requirement of mod symmetry of the flavour mixing matrix.