Non-factorizable contributions to $\bar{B^0_d} \to D_s^{(*)} \bar{D_s^{(*)}}$ from chiral loops and tree level $1/N_c$ terms

Abstract

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