On Measuring $CP$ Violation in Neutral $B$-meson Decays at the $\mathrm{{\rm Y}}(4S)$ Resonance

Within the standard model we carry out an analysis of $CP$-violating observables in neutral $B$-meson decays at the $\mathrm{{\rm Y}}(4S)$ 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 $B_d^0\mathrm{/}{\bar{B}}_d^0\to {\pi }^{+}{\pi }^{-}$ 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. $B_d^0\mathrm{/}{\bar{B}}_d^0\to D^{\pm }{\pi }^{\mp }$ and $$${}^{(\ast )0}{K}_S$, even in the presence of significant final-state interactions.