Several extensions of the Standard Model predict associated production of Dark Matter particles with a Higgs boson. Such processes are searched for in final states with missing transverse momentum and a Higgs boson decaying to a $b\bar b$ pair with the ATLAS detector using 36.1~fb$^{-1}$ of $pp$ collisions at a center-of-mass energy of 13~TeV at the LHC. The observed data are in agreement with the Standard Model and limits are placed on the associated production of Dark Matter particles and a Higgs boson for a simplified Dark Matter model and without extra model assumptions.

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