with each flavour and chirality of quark individually. This is related to the relative unimportance of the $Z$: it cannot cancel separately against the contributions of $u_L, d_L, u_R$ and $d_R$.

In summary, the rules of bottom-up Effective Field Theory say that one should include all operators up to some specified dimension. So to parametrise at dimension six the axial vector interactions of dark matter with quarks, one should include contact interactions of dark matter with the quarks and with the $Z$. Including interactions with the $Z$ that are $\propto p_Z^2$, as done here, suggests that these are not crucial.

Acknowledgements {#acknowledgements .unnumbered}
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I thank J.P. Chou, S Malik, and S. Perries for useful comments.

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