Interplay of the LHC and non-LHC Dark Matter searches in the Effective Field Theory approach

We present accurate and up-to-date constraints on the complete set of dimension five and six operators with scalar, fermion and vector Dark Matter (DM). We find limits using LHC mono-jet data, spin inde- pendent and spin dependent direct searches, relic density and CMB, and show the interplay between high and low energy data in setting bounds on the parameter space. In order to properly compare data taken at different energies, we take into account the effect of the running and mixing of operators. We also take into account the local density uncertainties affecting direct detection data, and apply EFT validity criteria related to the cut on the invariant mass of DM pair production at the LHC, which turns out to be especially important for the case of vector DM. Finally, we estimate the potential of the future LHC runs to probe DM parameter space.