The first observation of the decay $B_s^0 rightarrow phi bar{K}^{*0}$ is reported. The analysis is 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 $30 pm 6$ $B_s^0 rightarrow (K^+K^-)(K^-pi^+)$ decays is found in the mass windows $1012.5 < M(K^+K^-) < 1026.5 MeV/c^2$ and $746 < M(K^-pi^+)< 1046 MeV/c^2$. The signal yield is found to be dominated by $B_s^0 rightarrow phi bar{K}^{*0}$ decays, and the corresponding branching fraction is measured to be ${cal B}(B_s^0 rightarrow phi bar{K}^{*0}) = (1.10 pm 0.24 (stat) pm 0.14 (syst) pm 0.08 (f_d/f_s)) times 10^{-6}$, 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 significance of $B_s^0 rightarrow phi bar{K}^{*0}$ signal is 6.1 standard deviations. The fraction of longitudinal polarization in $B_s^0 rightarrow phi bar{K}^{*0}$ decays is found to be $f_0 = 0.51 pm 0.15 (stat) pm 0.07 (syst)$.
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