Evidence for the decay $B_s^0 \rightarrow J/\psi \overline{K}^{*0}$

A search for the decay $B_s^0 \rightarrow J/\psi \overline{K}^{*0}$ is performed with $\sim 37$ pb$^{-1}$ of $pp$ collisions at $\sqrt{s}$ = 7 TeV collected by the LHCb experiment at the Large Hadron Collider at CERN. Using a mass window of $\pm 150$ MeV$/c^2$ around the nominal $K^{*0}$ mass, the signal $B_s^0 \rightarrow J/\psi K\pi$ is found with a $4.7\sigma$ significance. The branching ratio ${\cal B}(B_s^0 \rightarrow J/\psi \overline{K}^{*0})$ is measured to be $(3.5^{+1.4}_{-1.3})\times10^{-5}$ under the assumption that all the $K\pi$ pairs in the $B_s^0$ mass peak originate from a $K^{*0}$. If the assumption on the nature of the $K^{*0}$ is dropped, the measurement becomes ${\cal B}(B_s^0 \rightarrow J/\psi K^{+}\pi^{-})_{|M(K,\pi)-M_{K^{*0},PDG}|<150 {\rm MeV}/c^2} = (2.21^{+0.97}_{-0.91}) \times 10^{-5}$. Statistical and systematic uncertainties are included in the combined uncertainty.