First observation of the decay $\bar{B}^0_s \to D^0 K^{*0}$ and measurement of the ratio of branching fractions $\frac{\mathcal{B}(\bar{B}^0_s \to D^0 K^{*0})}{\mathcal{B}(\bar{B}^0 \to D^0\rho^0)}$ with the LHCb experiment at $\sqrt{s}$ = 7 TeV

In 36 pb$^{-1}$ of $pp$ collisions at a centre-of-mass energy $\sqrt{s}$ = 7 TeV, we observe for the first time the decay $\bar{B}^0_s \to D^0 K^{*0}$. The $\bar{B}^0_s \to D^0 K^{*0}$ decay mode is a potentially dangerous background for the Cabibbo suppressed decay $B^0 \to \bar{D}^0 K^{*0}$ used in the measurement of the CKM angle $\gamma$. A clear signal of 34.5$\pm$6.9 events is obtained with a statistical significance over 9 standard deviations and we measure its branching ration relative to the $\bar{B}^0 \to D^0\rho^0$ branching ratio.