A search for new physics in events with a Z boson produced in association with large missing transverse momentum with the CMS experiment at the LHC is presented. The search is based on the 2016 data sample of proton-proton collisions at \sqrt{s} = 13~\mathrm{TeV} corresponding to an integrated luminosity of 35.9~\mathrm{fb}^{-1}. The results of this search are interpreted in terms of a simplified model of dark matter production with spin-0 or spin-1 mediators, a standard model Higgs boson decaying invisibly and produced in association with the Z boson, as well as a model with large extra spatial dimensions. For all models, no significant deviation from the background expectation is found, and limits are set with respect to relevant model parameters.

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