Comments on the Parametrization of the Kobayashi-Maskawa Matrix

Abstract

We show that the quark mixing matrix can be parametrized in exactly unitary forms with the imaginary parts present only at the order of ${10}^{\ensuremath{-}3}$. With ${s}_{x}={s}_{1}$ and ${s}_{y}$ well determined, measurements of ${\ensuremath{\epsilon}}^{\ensuremath{'}}$ or other $\mathrm{CP}$-nonconservation effects can determine ${s}_{z}{s}_{\ensuremath{\varphi}}$. Then after $|{V}_{\mathrm{ub}}|\ensuremath{\simeq}{s}_{z}$ is measured, ${s}_{\ensuremath{\varphi}}$ is known. We also give a simple expression for the $\mathrm{CP}$ asymmetry in the ${B}^{0}\ensuremath{-}{B}^{0}$ mixing.