First observations of $\bar{B}_s^0\to D^+D^-$, $D_s^+D^-$ and $D^0\bar{D}^0$ decays

First observations and measurements of the branching fractions of the $\bar{B}_s^0\to D^+D^-$, $\bar{B}_s^0\to D_s^+D^-$ and $\bar{B}_s^0\to D^0\bar{D}^0$ decays are presented using $1.0$~fb$^{-1}$ of data collected by the LHCb experiment. These branching fractions are normalized to those of $\bar{B}^0\to D^+D^-$, $B^0\to D_s^+D^-$ and $B^-\to D^0D_s^-$, respectively. An excess of events consistent with the decay $\bar{B}^0\to D^0\bar{D}^0$ is also seen, and its branching fraction is measured relative to that of $B^-\to D^0D_s^-$. Improved measurements of the branching fractions ${\cal{B}}(\bar{B}_s^0\to D_s^+D_s^-)$ and ${\cal{B}}(B^-\to D^0D_s^-)$ are reported, each relative to ${\cal{B}}(B^0\to D_s^+D^-)$. The ratios of branching fractions are \begin{align*} {{\cal{B}}(\bar{B}_s^0\to D^+D^-)\over {\cal{B}}(\bar{B}^0\to D^+D^-)} &= 1.08\pm 0.20\pm0.10, \nonumber \\ {{\cal{B}}(\bar{B}_s^0\to D_s^+D^-)\over {\cal{B}}(B^0\to D_s^+D^-)} &= 0.050\pm 0.008\pm0.004, \nonumber\\ {{\cal{B}}(\bar{B}_s^0\to D^0\bar{D}^0)\over {\cal{B}}(B^-\to D^0D_s^-)} &= 0.019\pm 0.003\pm0.003, \\ {{\cal{B}}(\bar{B}^0\to D^0\bar{D}^0)\over {\cal{B}}(B^-\to D^0D_s^-)} &< 0.0024 \nonumber \\ {{\cal{B}}(\bar{B}_s^0\to D_s^+D_s^-)\over {\cal{B}}(B^0\to D_s^+D^-)} &= 0.56\pm 0.03\pm0.04, \nonumber \\ {{\cal{B}}(B^-\to D^0D_s^-)\over {\cal{B}}(B^0\to D_s^+D^-)} &= 1.22\pm 0.02\pm0.07, \nonumber \end{align*} where the uncertainties are statistical and systematic, respectively.