Branching Ratios of $B\to D_{s}K$ Decays in Perturbative QCD Approach

The rare decays $B^0\to D_s^{-}{K}^{+}$ and $B^{+}\to D_s^{+}{\bar{K}}^0$ can occur only via annihilation type diagrams in the standard model. We calculate these decays in perturbative QCD approach. We found that the calculated branching ratio of $B^0\to D_s^{-}{K}^{+}$ agreed with the data which had been observed in the KEK and SLAC $B$ factories. While the decay $B^{+}\to D_s^{+}{\bar{K}}^0$ has a very small branching ratio at $\mathcal{O}({10}^{-8})$, due to the suppression from CKM matrix elements $\mathrm{\mid }{V}_{ub}^{\ast }{V}_{cd}\mathrm{\mid }$.