On Measuring $CP$ Violation in Neutral $B$-meson Decays at the $\Upsilon (4S)$ Resonance

Abstract

Within the standard model we carry out an analysis of $CP$-violating observables in neutral $B$-meson decays at the $\Upsilon (4S)$ resonance. Both time-dependent and time-integrated $CP$ asymmetries are calculated, without special approximations, to meet various possible measurements at symmetric and asymmetric $e^{+}e^{-}$ $B$ factories. We show two ways to distinguish between direct and indirect $CP$-violating effects in the $CP$-eigenstate channels such as $B^{0}_{d}/\bar{B}^{0}_{d}\rightarrow \pi^{+}\pi^{-}$ and $\pi^{0} K_{S}$. Reliable knowledge of the Cabibbo-Kobayashi-Maskawa phase and angles can in principle be extracted from measurements of some non-$CP$-eigenstate channels, e.g. $B^{0}_{d}/\bar{B}^{0}_{d}\rightarrow D^{\pm}\pi^{\mp}$ and $\stackrel{(-)}{D}$$^{(*)0}K_{S}$, even in the presence of significant final-state interactions.