夸克混合矩阵Qin-Ma参数化的注记
Remarks on the Qin-Ma Parametrization of Quark Mixing Matrix
摘要：
最近，Qin和Ma（QM）在Cabibbo-Kobayashi-Maskawa（CKM）参数化的三极小展开的基础上，提出了一种新的类Wolfenstein夸克混合矩阵参数化。QM参数化中的CP-奇相位与CKM参数化中的CP-奇相位一样在$90^\circ$附近。我们指出，在对夸克场进行适当的相位重新定义后，可以从Wolfenstein参数化中得到QM参数化，并且QM和CKM参数化中的相位$δ$都与么正角$α$、$β$和$γ$有关，即$δ= β+γ$或$π-α$ .我们表明，QM和Wolfenstein参数化可以推导出CKM和Chau-Keung-Maiani的。通过从夸克混合矩阵的Fritzsch-Xing（FX）参数化导出QM参数化，我们发现FX形式的相位在$-270^\circ$附近，因此也在$\sinδ\approx 1$附近.我们讨论了在$λ\approx |V_{us}|$的高阶Wolfenstein和QM参数化之间的差异。
英文摘要：
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 $δ$ in both QM and CKM parametrizations is related to the unitarity angles $α$, $β$ and $γ$, namely, $δ= β+γ$ or $π-α$. 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 $\sinδ\approx 1$. We discuss the seeming discrepancy between the Wolfenstein and QM parametrizations at the high order of $λ\approx |V_{us}|$.
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