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

Abstract

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.

14 page, 1 figure

References in corpus (8)

• Wolfenstein Parametrization at Higher Order: Seeming Discrepancies and Their Resolution
• Triminimal Parametrization of Quark Mixing Matrix
• A new simple form of quark mixing matrix
• Parametrization of fermion mixing matrices in Kobayashi-Maskawa form
• Unified triminimal parametrizations of quark and lepton mixing matrices
• Comment on Reparametrization Invariance of Quark-Lepton Complementarity
• Remarks on the Qin-Ma Parametrization of Quark Mixing Matrix
• The $\beta$ angle as the CP violating phase in the CKM matrix