taken as $C< 4\pi$. For the axial $\chi$ current with $\Lambda = $ TeV, the CMS limit and eqn (\[plage\]) give 3 independent bounds on $\{ c_{qL,A},  c_{uR,A}, c_{dR,A}\}$: 4\
4 |C\_[uR,A]{} - C\_[Z,A]{}|               \
4 |C\_[dR,A]{} + C\_[Z,A]{}|                \[lim3\] where the first line is the summed contributions of $u_L$ and $d_L$, the fractions are approximations $gg_X^Q s_{\rm w}/2c_{\rm w}$, and the $d$ to $u$ pdf ratio is taken 1/2. Similar limits apply for the vector operator of eqn (\[qDMd6\]).

It can be seen already from eqn (\[lim3\]), that including the interactions with the $Z$ will make little differences to the LHC limits on the $C_{QX,A}$: for the doublet quarks, the $Z$ contribution cannot cancel simultaneously against the $u_L$ and $d_L$ contributions, and the $Z$ contribution is irrelevant for the singlet quarks, because also $C_{Z,A}$ must be $\lsim 4\pi$. The parameters ruled out by the first and second eqns of (\[lim3\]) are represented as the central regions in figure \[fig2\].

From the TeV to the MeV {#sec:DD}
=======================

In direct detection, the dark matter scatters non-relativistically off nuclei. Therefore, to translate the EFT from the TeV to the MeV, the $Z$ must be removed, the effects of QCD loops in 