Weak couplings of heavy quarks

Abstract

Formulas relating the transition matrix elements involving the charmed quark, $U_{\mathrm{cd}}$, $U_{\mathrm{cs}}$, and $U_{\mathrm{cb}}$, to experimental data are given. For illustration the existing data are used to estimate or bound $\left|U_{\mathrm{ij}}\right|$. With additional assumption of six quark flavors, $U_{\mathrm{ij}}$ can be related to Kobayashi-Maskawa angles (${\theta }_1$, ${\theta }_2$, ${\theta }_3$, $\delta$), and the allowed regions in a ${sin\theta }_2-{sin\theta }_3$ plane are exhibited. When combined with the constraints from the $K^0-{\overline{K}}^0$ system, an accurate determination of $U_{\mathrm{cs}}$ is shown to lead to unique values for (${\theta }_i$, $\delta$).