  This analysis presents the possibility for the search for Dark Matter (DM)
particles using events with a Z$^{\prime}$ heavy gauge boson and a large
missing transverse momentum at the Large Hadron Collider (LHC). We consider the
muonic decay of Z$^{\prime}$. The analyzed Monte Carlo samples were the Open
simulated files produced by the CMS collaboration for proton-proton collisions
correspond to an integrated luminosity of the LHC run-I with 19.7 fb$^{-1}$ at
$\sqrt{s} = $ 8 TeV. Two scenarios, one simplified benchmark scenario so called
Dark Higgs and the effective field theory (EFT) formalism, were used for
interpretations. Limits are set on both Z$^{\prime}$, dark matter masses and
the cutoff scale of the EFT.
