this note, is only marginally consistent, because the contact interactions to which the LHC is sensitive would have to be mediated by strongly coupled particles. As recalled in the next section, this implies that colliders can exclude contact interactions of order their sensitivity, but not much larger.

Effective Field Theory (EFT) is a recipe to get the correct answer in a simple way[@Georgi]. So this note attempts to compare LHC and DD constraints on dark matter, according to the prescriptions of [@Georgi]. An EFT for dark matter at the LHC should parametrise all possible SM-gauge invariant interactions of the dark matter with other on-shell particles. So first, contact interactions between the dark matter and the Higgs or $Z$ should be included at the LHC. These can interfere with the contact interactions studied in previous analyses, but contribute differently at colliders from in direct detection, so the linear combination of operator coefficients constrained at high and low energy will be different. Secondly, an EFT contains in principle a tower of operators[@Porod] organised in increasing powers of the inverse cutoff scale $1/\Lambda$, and higher orders can only be neglected if there is a sufficient hierarchy of scales: $\Lambda_{NP}\gg v$. This hierarchy is 