Hierarchy of CKM matrix elements and implications of unitarity

TL;DR

This paper revisits the hierarchy of CKM matrix elements using unitarity constraints and examines how different parametrizations affect the calculation of CP violation parameters, revealing inconsistencies linked to hierarchy.

Contribution

It provides a rigorous analysis of CKM hierarchy and explores the impact of unitarity-based parametrizations on CP violation measurements, highlighting limitations in certain approaches.

Findings

Not all unitarity-based parametrizations reproduce _k.

Hierarchy influences the accuracy of CP violation parameters.

Certain parametrizations fail to match the observed _k value.

Abstract

The hierarchy amongst the CKM matrix elements, highlighted recently by Luo and Xing, has been rigorously revisited using the PDG parameterization incorporating unitarity constraints. Further, we have explored the evaluation of the CP violating parameter \epsilon_k for the 9 possible unitarity ensured equivalent independent parametrizations of CKM matrix. Interestingly, we find that not all of these reproduce the value of parameter \epsilon_k, this being presumably due to the hierarchical nature of the CKM matrix elements. This situation is echoing similar conclusions regarding the evaluation of Jarlskog's rephasing invariant parameter J through unitarity ensured equivalent possibilities.