Rare Decays $B^0 \to D_s^{(*)+} D_s^{(*)-}$ and $B_s^0 \to D^{(*)+} D^{(*)-}$ in Perturbative QCD Approach

In decay modes $B^0 \to D_s^{(*)+} D_s^{(*)-}$ and $B_s^0 \to D^{(*)+} D^{(*)-}$, none of quarks in final states is the same as one of $B$ meson. They can occur only via annihilation diagrams in the Standard Model. In the heavy quark limit, we try to calculate the branching ratios of these decays in perturbative QCD approach without considering the soft final state interaction. We found branching ratios of $B^0 \to D_s^{(*)+} D_s^{(*)-}$ are at the order of $ 10^{-5}$, and branching ratios of $B_s^0 \to D^{(*)+} D^{(*)-}$ are of $10^{-3}$. Those decay modes will be measured in $B$ factories and LHC-b experiments.