[@CMS] uses the range 400 GeV $\leq \ETm\lsim$ TeV. However, the assumption that the jet emission part of the cross-section is the same as for $\nu$ pairs will fail, if $M_{inv}^2$ is a significant fraction of the energy of the event. With the $M_{inv}$ cutoff ranging from 800 GeV to 2 TeV, requiring that the dark matter contribute $\lsim 1/6$ [@CMS] of the SM background, gives an estimated bound $\Lambda \gsim 880 \to 2200$ GeV, for $c_{uL,A} =c_{uR,A} =c_{dL,A} =c_{dR,A}=1$. This compares favourably to the CMS bound of $\Lambda > 950$ GeV, for $C_{uL,A} =C_{uR,A} =C_{dL,A} =C_{dR,A}=1$. Since the analytical estimate is reasonable, most of the dark matter signal probably comes from $M_{inv}^2 \gg m_Z^2$, and the approximation (\[annuler\]) is consistent. However, the analytic bound is a bit to restrictive (perhaps in part because it includes any number of jets), so in the remainder of the paper, the CMS limit of 950 GeV will be used.

There is also an upper limit on the $C$s which a collider can exclude, eqn (\[plage\]), from requiring that the contact interaction approximation be self-consistent: $C/\Lambda^2 <4\pi/M_{inv}^2$. Since the previous analytic estimate reproduces the CMS bound for $M_{inv}^2 \sim$ TeV$^2$, the consistency condition is 