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A study of the decay $D^{0}\rightarrow K^{-}\pi^{+}\mu^{+}\mu^{-}$ isperformed using data collected by the LHCb detector in proton-proton collisionsat a centre-of-mass energy of 8 TeV, corresponding to an integrated luminosityof 2.0 fb$^{-1}$. Decay candidates with muon pairs that have an invariant massin the range 675--875 MeV$/c^2$ are considered. This region is dominated by the$\rho^{0}$ and $\omega$ resonances. The branching fraction in this range ismeasured to be ${\cal B}$($D^{0}\rightarrow K^{-}\pi^{+}\mu^{+}\mu^{-}$) =$(4.17 \pm 0.12(stat) \pm 0.40(syst))\times10^{-6}$. This is the firstobservation of the decay $D^{0}\rightarrow K^{-}\pi^{+}\mu^{+}\mu^{-}$. Itsbranching fraction is consistent with the value expected in the Standard Model.

First observation of the decay $D^{0}\rightarrow K^{-}\pi^{+}\mu^{+}\mu^{-}$ in the $\rho^{0}$-$\omega$ region of the dimuon mass spectrum