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The CKM matrix describing quark mixing with three generations can beparameterized by three mixing angles and one CP violating phase. In most of theparameterizations, the CP violating phase chosen is not a directly measurablequantity and is parametrization dependent. In this work, we propose to useexperimentally measurable CP violating quantities, $\alpha$, $\beta$ or$\gamma$ in the unitarity triangle as the phase in the CKM matrix, andconstruct explicit $\alpha$, $\beta$ and $\gamma$ parameterizations.Approximate Wolfenstein-like expressions are also suggested.

The $\alpha$, $\beta$ and $\gamma$ parameterizations of CP violating CKM phase