Hadronic Rare $B$ Decays via Exchange or Annihilation Diagrams

The two-body mesonic $B$ decays induced only via a single $W$-exchange or annihilation quark diagram, such as $B^-_u\rightarrow D^{(*)-}_sK^{(*)0}$ and $\bar{B}^0_d\rightarrow D^{(*)+}_sK^{(*)-}$, are analyzed in the factorization approximation. We estimate the branching ratios for those transitions into two pseudoscalar mesons, and find them to be negligibly small. The significant effect of final-state rescattering is illustrated by taking $B^-_u\rightarrow D^-\bar{K}^0$ for example.