and low energy EFTs, as done in this note, suggests that the LHC constrains several combinations of operator coefficients that are different from direct detection, as can be seen by comparing eqns (\[lim3\]) and (\[SD\]). However, the contribution of the $Z$ is relatively unimportant, because its couplings to singlet quarks are small, and it interferes with opposite sign with $u_L$ and $d_L$. The LHC limits on the dark matter couplings to quarks and the $Z$ are represented as the central exclusion areas of figure \[fig2\]: the coupling to quarks is more constrained than the coupling to the $Z$, and arbitrary axial current dark matter interactions to quarks cannot be allowed by tuning the dark matter coupling to the $Z$. This is because there is a self-consistency upper bound on contact interaction coefficients at colliders $C/\Lambda^2 < 4\pi/\hat{s}$ (see eqn (\[plage\])). It is important to notice that this upper bound also implies that the LHC limits do not exclude the parameter space probed by spin dependent direct detect experiments.

Second, an interesting difference between direct detection and collider experiments, is that quarks of different chirality and flavour interfere in direct detection, whereas the LHC can constrain the interactions of dark matter 