The α\alpha, β\beta and γ\gamma parameterizations of CP violating CKM phase

The CKM matrix describing quark mixing with three generations can be parameterized by three mixing angles and one CP violating phase. In most of the parameterizations, the CP violating phase chosen is not a directly measurable quantity and is parametrization dependent. In this work, we propose to use experimentally measurable CP violating quantities, $\alpha$, $\beta$ or $\gamma$ in the unitarity triangle as the phase in the CKM matrix, and construct explicit $\alpha$, $\beta$ and $\gamma$ parameterizations. Approximate Wolfenstein-like expressions are also suggested.Comment: 14 page, 1 figur

The β\beta angle as the CP violating phase in the CKM matrix

The CKM matrix describing quark mixing with three generations can be parameterized by three Euler mixing angles and one CP violating phase. In most of the parameterizations, the CP violating phase chosen is not a directly measurable quantity and is parametrization dependent. In this work, we propose to use the most accurately measured CP violating angle $\beta$ in the unitarity triangleas the phase in the CKM matrix, and construct an explicit $\beta$ parameterization. We also derive an approximate Wolfenstein-like expression for this parameterization.Comment: RevTex 7 pages with one figure. Version to be published in Phys. Lett. B. arXiv admin note: substantial text overlap with arXiv:1204.123