Wolfenstein parametrization at higher order: Seeming discrepancies and their resolution

Abstract

The precise determination of the Cabibbo–Kobayashi–Maskawa (CKM) matrix elements is extremely important towards the understanding of CP violation. We explicitly study seeming discrepancies between the CKM matrix elements at the higher order of the expansion parameter λ in different Wolfenstein parametrizations derived from different exact parametrizations. 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 λ) parameters. Our approach is further applied to the cases for the Wolfenstein-like parametrizations, such as the Qin–Ma parametrization.