Remarks on the Qin-Ma parametrization of quark mixing matrix

Recently, Qin and Ma (QM) have advocated a new Wolfenstein-like parametrization of the quark mixing matrix based on the triminimal expansion of the Cabibbo-Kobayashi-Maskawa (CKM) parametrization. The CP-odd phase in the QM parametrization is around 90 degrees just as that in the CKM parametrization. We point out that the QM parametrization can be readily obtained from the Wolfenstein parametrization after appropriate phase redefinition for quark fields and that the phase delta in both QM and CKM parametrizations is related to the unitarity angles alpha, beta and gamma, namely, delta = beta + gamma or pi - alpha. We show that both QM and Wolfenstein parametrizations can be deduced from the CKM and Chau-Keung-Maiani ones. By deriving the QM parametrization from the exact Fritzsch-Xing (FX) parametrization of the quark mixing matrix, we find that the phase of the FX form is in the vicinity of -270 degrees and hence sin delta approximate to 1. We discuss the seeming discrepancy between the Wolfenstein and QM parametrizations at the high order of lambda approximate to vertical bar V-us vertical bar. (C) 2011 Elsevier B.V. All rights reserved.