epsf

$^1$[*IPNL, CNRS/IN2P3, 4 rue E. Fermi, 69622 Villeurbanne cedex, France; Université Lyon 1, Villeurbanne; Université de Lyon, F-69622, Lyon, France* ]{}\

> An Effective Field Theory for dark matter at a TeV-scale hadron collider should include contact interactions of dark matter with the partons, the Higgs and the $Z$. This note estimates the impact of including dark matter-$Z$ interactions on the complementarity of spin dependent direct detection and LHC monojet searches for dark matter. The effect of the $Z$ is small, because it interacts with quarks via small electroweak couplings, and the contact interaction self-consistency condition $C/\Lambda^2 < 4\pi/\hat{s}$ restricts the coupling to dark matter. In this note, the contact interactions between the $Z$ and dark matter are parametrised by derivative operators; this is convenient at colliders because such interactions do not match onto low energy quark-dark matter contact interactions.

Introduction
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Various experiments attempt to detect the particle making up the “dark matter”[@DM] of our Universe. For instance, direct detection(DD) experiments [@EdelCDMS; @Xenon; @SC; @autres], search for $\sim $ MeV energy deposits due to scattering of dark matter particles from the galactic halo on detector nuclei. And the Large Hadron Collider (LHC) searches[@CMS; @ATLAS] for dark matter pairs 