Wolfenstein Parametrization at Higher Order: Seeming Discrepancies and Their Resolution

TL;DR

This paper investigates apparent discrepancies in higher-order Wolfenstein parametrizations of the CKM matrix and proposes a systematic redefinition of small parameters to resolve these issues, enhancing the consistency of different parametrizations.

Contribution

It introduces a systematic method to resolve discrepancies in higher-order Wolfenstein parametrizations by redefining small parameters, applicable to various parametrizations including Qin-Ma.

Findings

Most discrepancies are resolved by redefinition of small parameters.

The approach is applicable to Wolfenstein-like parametrizations.

Provides a clearer understanding of higher-order effects in CKM matrix parametrizations.

Abstract

In different Wolfenstein parametrizations derived from different exact parametrizations of the Cabibbo-Kobayashi-Maskawa matrix, we explicitly study seeming discrepancies between the matrix elements at the higher order of the expansion parameter $\lambda$. A systematic way of resolving the seeming discrepancies is proposed. We find that most of the discrepancies can be naturally resolved by a proper redefinition of the numerically small (of order $\lambda$) parameters. Our approach is further applied to the cases for the Wolfenstein-{\it like} parametrizations, such as the Qin-Ma parametrization.