In the present work, we search for Dark Matter candidates generated in association
with the Z 0 boson, in events with large missing transverse momentum produced in proton-proton
collisions at the Large Hadron Collider, using Monte Carlo simulation, at total integrated
luminosity of 136.2 f b −1 and center-of-mass energy of 13 TeV. The signal is evaluated from three new
physics scenarios beyond standard model of dark matter with Z' boson as a final-state radiation,
and they are: Dark Higgs model, Light vector model and the light Z' with inelastic effective field theory coupling
model. The three models assume that the Z' is coupled to new dark sector states, which might be a
candidate or decaying to a candidate suitable to be the dark matter. The dark matter candidate is supposed to have
mass of order GeV to few TeV. The Z' boson is considered to decay leptonically. The dileptons invariant mass and the missing transverse momentum distributions
are studied before and after selection conditions of the resonance event. The significances of the three models will be tested.