followed by $Z\to \bar{\nu}\nu$. The 8 TeV LHC is sensitive to dark matter contact interactions with $C/\Lambda^2 \sim $ TeV$^{-2}$.

Given the operators of eqns (\[qDMd6\]) and (\[inteff\]) at the LHC, the axial vector dark matter current can interact with quarks $Q$ via the diagrams of figure \[figop\], which can be written as a four-fermion interaction of coefficient c\_[QX,A]{} & = & C\_[QX,A]{}+ g\_X\^Q\
& &C\_[QX,A]{}+ g\_X\^Q C\_[Z,A]{}    , \[annuler\] where $g_X^Q  =\{ 1- \frac{4}{3}s_{\rm w}^2,- \frac{4}{3}s_{\rm w}^2,
 -1+ \frac{2}{3}s_{\rm w}^2, \frac{2}{3}s_{\rm w}^2\}$ for $\{u_L,u_R,d_L,d_R\}$ [@PDB]. A similiar expression can be obtained for the vector $\chi$ current. The $Z$ exchange looks like a contact interactions for large $p_Z^2 = M^2_{inv} \gg m_Z^2$, where $M^2_{inv}$ is the invariant mass-squared of the dark matter pair. This is a useful approximation, because the arguments below suggests that most $\chi\bar{\chi}$ events arise at larger $M^2_{inv}$.

The aim here is to analytically estimate the invisible four-momentum-squared $ M^2_{inv} $, by comparing the partonic cross-sections for $\nu\bar{\nu}$ and $\chi\bar{\chi}$ production. I assume that the QCD part of the amplitude is identical in both cases, so it does not need to be calculated. This allows for an arbitrary number of jets, which is more difficult to simulate[@Uli2] 