Search for rare decays $B^{+}\to D_s^{(\ast )+}\eta$, $D_s^{(\ast )+}{\bar{K}}^0$, $D^{+}\eta$, and $D^{+}{K}^0$

We present a study of rare decay modes $B^{+}\to D_s^{+}{h}^0$, $B^{+}\to D_s^{\ast +}{h}^0$, and $B^{+}\to D^{+}{h}^0$, where $h^0$ denotes the neutral mesons $\eta$ or $K^0$, using a data sample of $(772\pm 10)\times {10}^6$ $B\bar{B}$ events produced at the $\mathrm{{\rm Y}}(4S)$ resonance. The data were collected by the Belle detector operating at the asymmetric-energy KEKB collider. We observe no evidence for these decays, so we provide upper limits at the 90$\mathrm{\%}$ confidence level on the branching fractions of $B^{+}\to D_s^{+}{h}^0$, $D_s^{\ast +}{h}^0$, and $D^{+}{h}^0$ decay modes. Along with rare decay modes, we report improved measurements of the color-suppressed decay branching fractions $\mathcal{B}({\bar{B}}^0\to D^0\eta )$ = (26.6 $\pm$ 1.2 $\pm$ 2.1) $\times$ ${10}^{-5}$ and $\mathcal{B}({\bar{B}}^0\to D^0{\bar{K}}^0)$ = (5.6 $\pm$ 0.5 $\pm$ 0.2) $\times$ ${10}^{-5}$. The first and second uncertainties are statistical and systematic, respectively.