CP Violation and Flavour Mixing in the Standard Model

Abstract

We review and update the constraints on the parameters of the quark flavour mixing matrix $V_{CKM}$ in the standard model and estimate the resulting CP asymmetries in $B$ decays, taking into account recent experimental and theoretical developments. In performing our fits, we use inputs from the measurements of the following quantities: (i) $\abseps$, the CP-violating parameter in $K$ decays, (ii) $\delmd$, the mass difference due to the \bdbdbar\ mixing, (iii) the matrix elements $\absvcb$ and $\absvub$, (iv) $B$-hadron lifetimes, and (v) the top quark mass. The experimental input in points (ii) - (v) has improved compared to our previous fits. With the updated CKM matrix we present the currently-allowed range of the ratios $|V_{td}/V_{ts}|$ and $|V_{td}/V_{ub}|$, as well as the standard model predictions for the \bsbsbar\ mixing parameter $\xs$ (or, equivalently, $\delms$) and the quantities $\sin 2\alpha$, $\sin 2\beta$ and $\sin^2\gamma$, which characterize the CP-asymmetries in $B$-decays. Various theoretical issues related to the so-called ``penguin-pollution," are of importance for the determination of the phases $\alpha$ and $\gamma$ from the CP-asymmetries in $B$ decays, are also discussed. (to be published in the proc. of the Pisa heavy flavour physics conference.)