Observation of $B^0\to \omega K^0$, $B^{+}\to \eta {\pi }^{+}$, and $B^{+}\to \eta K^{+}$ and Study of Related Decays

We present measurements of branching fractions and charge asymmetries for seven $B$-meson decays with an $\eta$, ${\eta }^{\prime }$, or $\omega$ meson in the final state. The data sample corresponds to $89\times {10}^6$ $B\overline{B}$ pairs produced from $e^{+}{e}^{-}$ annihilation at the ${\rm Y}(4S)$ resonance. We measure the following branching fractions in units of ${10}^{-6}$: $\mathcal{B}(B^{+}\to \eta {\pi }^{+})=5.3\pm 1.0\pm 0.3$, $\mathcal{B}(B^{+}\to \eta K^{+})=3.4\pm 0.8\pm 0.2$, $\mathcal{B}(B^0\to \eta K^0)=2.9\pm 1.0\pm 0.2$ ($<5.2$, 90% C.L.), $\mathcal{B}(B^{+}\to {\eta }^{\prime }{\pi }^{+})=2.7\pm 1.2\pm 0.3$ ($<4.5$, 90% C.L.), $\mathcal{B}(B^{+}\to \omega {\pi }^{+})=5.5\pm 0.9\pm 0.5$, $\mathcal{B}(B^{+}\to \omega K^{+})=4.8\pm 0.8\pm 0.4$, and $\mathcal{B}(B^0\to \omega K^0)={5.9}_{-1.3}^{+1.6}\pm 0.5$. The charge asymmetries are ${\mathcal{A}}_{\mathrm{c}\mathrm{h}}(B^{+}\to \eta {\pi }^{+})=-0.44\pm 0.18\pm 0.01$, ${\mathcal{A}}_{\mathrm{c}\mathrm{h}}(B^{+}\to \eta K^{+})=-0.52\pm 0.24\pm 0.01$, ${\mathcal{A}}_{\mathrm{c}\mathrm{h}}(B^{+}\to \omega {\pi }^{+})=0.03\pm 0.16\pm 0.01$, and ${\mathcal{A}}_{\mathrm{c}\mathrm{h}}(B^{+}\to \omega K^{+})=-0.09\pm 0.17\pm 0.01$.