Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2011-05-02
Physics
High Energy Physics
High Energy Physics - Phenomenology
8 pages, a shortened version accepted by PLB
Scientific paper
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 $90^\circ$ 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 Fritzsch-Xing (FX) parametrization of the quark mixing matrix, we find that the phase of the FX form is in the vicinity of $-270^\circ$ and hence $\sin\delta\approx 1$. We discuss the seeming discrepancy between the Wolfenstein and QM parametrizations at the high order of $\lambda\approx |V_{us}|$.
Ahn Yu-Hwan
Cheng Hai-Yang
Oh Sechul
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