Probing 4 X 4 quark mixing matrix

TL;DR

This paper extends the standard 3x3 CKM quark mixing matrix to a 4x4 matrix without specific model assumptions, analyzing its hierarchy and rephasing invariants to explore potential fourth-generation quark effects.

Contribution

It introduces a model-independent 4x4 quark mixing matrix, derives hierarchy relations, and explicitly calculates nine rephasing invariants for the fourth generation.

Findings

Hierarchy among 4th row and column elements established

Explicit expressions for nine rephasing invariants derived

Numerical estimates of invariants based on phenomenological data

Abstract

Without adhering to any specific model, we have presented 4 X 4 quark mixing matrix as an extension of the 3 X 3 PDG parametrization of the CKM matrix. Using unitarity constraints as well as the hierarchy among the elements of the 3 X 3 CKM matrix, we have found the hierarchy among the 4th row and 4th column elements of the 4 X 4 quark mixing matrix. Further, for the fourth generation case, we have explicitly found the 9 independent rephasing invariant parameters J_4X4. Also, using phenomenological estimates of the 4th row and 4th column elements, we have numerically evaluated these 9 parameters.