Beyond effective field theory for dark matter searches at the LHC

We study the validity of effective field theory (EFT) interpretations of monojet searches for dark matter at the LHC for vector and axial-vector interactions. We show that the EFT approach is valid when the mediator has mass m(med) greater than 2.5 TeV. We find that the current limits on the contact interaction scale Lambda in the EFT apply to theories that are perturbative for dark matter mass m(DM) < 800 GeV. However, for all values of m(DM) in these theories, the mediator width is larger than the mass, so that a particle-like interpretation of the mediator is doubtful. Furthermore, consistency with the thermal relic density occurs only for 170 less than or similar to m(DM) less than or similar to 510 GeV. For lighter mediator masses, the EFT limit either under-estimates the true limit (because the process is resonantly enhanced) or overestimates it (because the missing energy distribution is too soft). We give some 'rules of thumb' that can be used to estimate the limit on Lambda (to an accuracy of similar to 50%) for any m D M and m(med) from knowledge of the EFT limit. We also compare the relative sensitivities of monojet and dark matter direct detection searches finding that both dominate in different regions of the m(DM) - m(med) plane. Comparing only the EFT limit with direct searches is misleading and can lead to incorrect conclusions about the relative sensitivity of the two search approaches.