Parametrization of the CKM matrix

Noting the hierarchy between three mixing angles, θ2,3=O(θ12), we present an exact form of the quark mixing matrix, replacing Wolfenstein's approximate form. In addition, we suggest to rotate the unitarity triangle, using the weak CP phase convention where the phase is located at the (31) element sinθ1sinθ2eiδ while the (13) element sinθ1sinθ3 is real. For the (ab) unitarity triangle, the base line (x-axis) is defined from the product of the first row elements, V1aV1b*, and the angle between two sides at the origin is defined to be the phase δ. This is a useful definition since every Jarlskog triangle has the angle δ at the origin, visible directly in the Cabibbo-Kobayashi-Maskawa matrix. It is argued that δ represents the barometer of the weak CP violation, which can be related to possible Yukawa textures.