produced in multi-TeV $pp$ collisions, which would materialise as an excess of events with missing energy and jets. The LHC and DD searches are at very different energy scales, so different Standard Model (SM) particles are present, and also the quantum interferences are different[@PST]. The expected rates can be compared in specific dark matter models [@R], or, in recent years, several studies[@CMS; @tevatron; @toutlmonde; @Z; @unitarity1; @monoH] have compared the LHC and DD sensitivities using a contact interaction parametrisation of the dark matter interactions with the standard model particles.

The LHC bounds obtained in this way are restrictive, and probe smaller couplings than direct detection experiments searching for “spin dependent” interactions between partons and dark matter [@SC]. These contact interaction studies are refered to as “Effective Field Theory” (EFT), and considered to be relatively model independent. However, the particle content is an input in EFT, and the restrictive LHC limits assume that the dark matter particle is the only new particle accessible at the LHC. Relaxing this assumption can significantly modify the experimental sensitivities[@st; @pvz; @toni2]. This has motivated various simplified models for dark matter searches at the LHC [@marcusmodel; @DMLQ; @deSGS]. Retaining this assumption, as will be done in 