Search for dark matter produced in association with a Z boson in proton-proton collisions at $\sqrt{s}=13~\mathrm{TeV}$

A search for dark matter (DM) particles is performed using events with a Z boson candidate and large missing transverse momentum. The analysis is based on proton-proton collision data at a center-of-mass energy of $13~\mathrm{TeV}$ collected by the CMS experiment at the LHC in $2016-2018$, corresponding to an integrated luminosity of $137~\mathrm{fb}^{-1}$. The search uses the decay channels $\mathrm{Z}\to\mathrm{e}\mathrm{e}$ and $\mathrm{Z}\to\mu\mu$. No significant excess of events is observed over the background expected from standard model processes. Limits are set on DM production in the context of simplified models with vector, axial-vector, scalar, and pseudoscalar mediators, as well as a two-Higgs-doublet model with an additional pseudoscalar mediator. The limits are also provided for spin-dependent and spin-independent scattering cross sections and are compared to those from direct-detection experiments. The results are also interpreted in the context of models of invisible Higgs boson decays, unparticles, and large extra dimensions.