publication. Concretely, $\Lambda$ will be taken as 1- $2 $ TeV, for reasons discussed above eqn (\[lim3\]). Experimental limits on contact interactions will therefore be presented as limits on the dimensionless coefficient $C^{(n)}_O$.

At dimension six, there are vector and axial vector $\chi$ currents coupled to quarks:   \_ \^P\_X Q\_i    ,    -  \_\_5 \^P\_X Q\_i \[qDMd6\] where the quarks $Q_i$ are first generation SM multiplets $   \{q_L,u_R,d_R\}$, and $P_X$ is the appropriate chiral projector. The contact interactions between the dark matter and the $Z$ boson are taken as - D\^B\_ \_       s\_[w]{} p\_Z\^2 Z\^ \_\
D\^B\_ \_\_5       -s\_[w]{} p\_Z\^2 Z\^ \_\_5 \[inteff\] where to the right of the arrow is the resulting vertex, $B^\mu$ is the hypercharge gauge boson with coupling $g'=e\tan\theta_W \equiv e s_{\rm w}/c_{\rm w}$, $B^{\mu\nu} =  \partial ^\mu B^\nu -  \partial ^\nu B^\mu$, and a term $\propto p_Z\cdot Z$ was dropped after the arrow in the axial current operator, assuming the $Z$ was produced by light quarks. There is in addition a “dipole moment” operator $B^{\mu \nu}\overline{\chi} \sigma_{\mu \nu}\chi $, which is neglected here because it also induces dark matter interactions with the photon [@magmoDM] which are more interesting.

Then at dimension seven, there are four-fermion operators:   