Wolfenstein Parametrization at Higher Order: Seeming Discrepancies and Their Resolution

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.