Analysis of the Bounds on Dark Matter Models from Monojet Searches at the LHC

We analyse the constraints on models of WIMP Dark Matter that can be derived from upper bounds on the "monojet" cross section at the LHC. These constraints were originally interpreted in the context of an effective field theory (EFT) where the Standard Model is extended by a dimension--6 operator whose coefficient is $1/\Lambda^2$. We show that combining the 8 TeV data of the ATLAS and CMS collaborations improves the bounds only slightly. We then analyze this final state in the context of simplified models with $s-$channel mediator. We show that if the decay width of the mediator is small, these simplified models can be accurately modeled by the effective field theory only if the mediator mass is above 5 TeV. Finally, we point out that even if the EFT accurately describes the ${\cal O}(\Lambda^{-2})$ contributions to the matrix element, for values of $\Lambda$ near the current bound it receives significant contributions of order $\Lambda^{-4}$, in the context of simplified models, these correspond to diagrams where two mediators are exchanged. This observation challenges the internal consistency of the EFT description since dimension$-8$ operators, which would also contribute to ${\cal O}(\Lambda^{-4})$ to the matrix element, are not included.