THE α, β AND γ PARAMETRIZATIONS OF CP-VIOLATING CKM PHASE

Abstract

The CKM matrix describing quark mixing with three generations can be parametrized by three mixing angles and one CP-violating phase. In most of the parametrizations, 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, α, β or γ in the unitarity triangle as the phase in the CKM matrix, and construct explicit α, β and γ parametrizations. Approximate Wolfenstein-like expressions are also suggested. Since β is most accurately measured among these three phase angles, we consider β parametrization as the best one to use.