First observation of the decay $B_s^0 \rightarrow \phi \bar{K}^{*0}$

A first observation of the decay $B_s^0 \rightarrow \phi \bar{K}^{*0}$ is reported from an analysis based on a data sample, corresponding to an integrated luminosity of 1.0 fb$^{-1}$ of $pp$ collisions at $\sqrt{s} = 7 TeV$, collected with the LHCb detector. A yield of $30 \pm 6$ $B_s^0 \to (KK)(K\pi)$ candidates is found in the mass windows $1012.5 < M(KK) < 1026.5 MeV/c^2$ and $746 < M(K\pi)< 1046 MeV/c^2$, corresponding to a signal significance of 6.1 standard deviations. The candidates are found to be dominated by $B_s^0 \rightarrow \phi \bar{K}^{*0}$ decays, and the branching fraction is measured to be $BF( B_s^0 \rightarrow \phi \bar{K}^{*0} ) = (1.10 \pm 0.24 (stat) \pm 0.14 (syst) \pm 0.08 (f_d/f_s ) ) \times 10^{-6}$, where the uncertainties are statistical, systematic and from the ratio of fragmentation fractions $f_d/f_s$ which accounts for the different production rate of $B^0$ and $B_s^0$ mesons. The fraction of longitudinal polarization in $B_s^0 \rightarrow \phi \bar{K}^{*0}$ decays is found to be $f_0 = 0.51 \pm 0.15 (stat) \pm 0.07 (syst)$.