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We have studied the complete set of dimension 5 and dimension 6 effectiveoperators involving the interaction of scalar, fermion and vector Dark Matter(DM) with SM quarks and gluons, to explore the possibility to distinguish theseoperators and characterise the spin of DM at the LHC. We have found that threefactors - the effective dimension of the operator, the structure of the SM partof the operator and the parton densities of the SM particles connected to theoperator - uniquely define the shape of the (unobservable) invariant massdistribution of the DM pair and, consequently, the shape of the (observable)MET distribution related to it. Using $\chi^2$ analysis, we found that at theLHC, with a luminosity of 300 fb$^{-1}$, certain classes of EFT operators canbe distinguished from each other. Hence, since DM spin is partly correlatedwith the factors defining the shape of MET, the LHC can potentially shed alight also on DM spin. We have also observed a drastic difference in theefficiencies (up to two orders of magnitude) for large MET cuts scenarios withdifferent DM spin, thus indicating that the DM discovery potential stronglydepends on it. The study we perform here can be applied more generally thanwithin the EFT paradigm, where the DM mediator is not producedon-the-mass-shell, such as the case of t-channel mediator or mediator with massbelow $2M_{DM}$, where the invariant mass of the DM pair is not fixed.

Dark Matter characterization at the LHC in the Effective Field Theory approach