Hierarchy of CKM matrix elements and implications of unitarity

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.
Comment: 13 pages. arXiv admin note: text overlap with arXiv:2310.11152