Non-factorizable contributions to $\overline{B_d^0}\to D_s^{(\ast )}\overline{D_s^{(\ast )}}$ from chiral loops and tree level $1\mathrm{/}{N}_c$ terms

We point out that the amplitudes for the decays ${\bar{B}}^0\to D_s^{+}{D}_s^{-}$ and ${\bar{B}}_s^0\to D^{+}{D}^{-}$ have no factorizable contributions. If one or two of the $D$-mesons in the final state are vectors (i.e $D^{\ast }$ 's) there are relatively small factorizable contributions through the annihilation mechanism. The dominant contributions to the decay amplitudes arise from chiral loop contributions and $1\mathrm{/}{N}_c$ suppressed tree level. We predict that the branching ratios for the processes ${\bar{B}}_d^0\to D_s^{+}{D}_s^{-}$, ${\bar{B}}_d^0\to D_s^{+\ast }{D}_s^{-}$ and ${\bar{B}}_d^0\to D_s^{+}{D}_s^{-\ast }$ are all of order $(2-3)\times {10}^{-4}$, while ${\bar{B}}_s^0\to D_d^{+}{D}_d^{-}$, ${\bar{B}}_s^0\to D_d^{+\ast }{D}_d^{-}$ and ${\bar{B}}_s^0\to D_d^{+}{D}_d^{-\ast }$ are of order $(4-7)\times {10}^{-3}$. If {\em both} $D$-mesons in the final state are $D^{\ast }$'s, we obtain branching ratios of order two times bigger.