We present measurements of the branching fractions of the decays $B^{+}\to {\mathrm{\eta }}^{\mathrm{\prime }}{K}^{+}$ and $B^0\to {\mathrm{\eta }}^{\mathrm{\prime }}{K}^0$. For $B^0\to {\mathrm{\eta }}^{\mathrm{\prime }}{K}_S^0$ we also measure the time-dependent $CP$-violation parameters $S_{{\mathrm{\eta }}^{\mathrm{\prime }}{K}_S^0}$ and $C_{{\mathrm{\eta }}^{\mathrm{\prime }}{K}_S^0}$, and for $B^{+}\to {\mathrm{\eta }}^{\mathrm{\prime }}{K}^{+}$ the time-integrated charge asymmetry ${\mathcal{A}}_{\mathrm{c}\mathrm{h}}$. The data sample corresponds to $88.9\times {10}^6$ $B\overline{B}$ pairs produced by $e^{+}{e}^{-}$ annihilation at the ${\rm Y}(4S)$. The results are $\mathcal{B}(B^{+}\to {\mathrm{\eta }}^{\mathrm{\prime }}{K}^{+})=(76.9\pm 3.5\pm 4.4)\times {10}^{-6}$, $\mathcal{B}(B^0\to {\mathrm{\eta }}^{\mathrm{\prime }}{K}^0)=(60.6\pm 5.6\pm 4.6)\times {10}^{-6}$, $S_{{\mathrm{\eta }}^{\mathrm{\prime }}{K}_S^0}=0.02\pm 0.34\pm 0.03$, $C_{{\mathrm{\eta }}^{\mathrm{\prime }}{K}_S^0}=0.10\pm 0.22\pm 0.04$, and ${\mathcal{A}}_{\mathrm{c}\mathrm{h}}=0.037\pm 0.045\pm 0.011$.

• Received 31 March 2003

DOI:https://doi.org/10.1103/PhysRevLett.91.161801