H d + \[ H d \]\^    ,    \_5   H d + \[ H d \]\^\
\^   H \_ d + \[ H \_ d \]\^                (and similarly for $u$ quarks, but with a charge conjugate Higgs field), interactions with the gluons: $$\frac{C^{(7)}_{gg,S}  }{\Lambda^3}
\overline{\chi} \chi G_{\mu \nu}^A  G^{\mu \nu, A}
~~~,~~~
\frac{C^{(7)}_{g\tilde{g},P}  }{\Lambda^3}
\overline{\chi}\g_5 \chi G_{\mu \nu}^A  \tilde{G}^{\mu \nu, A}~~~,$$ and double-derivative interactions between dark matter and the Higgs: H\^D\^D\_ H       - m\_W\^2 W\_\^+W\^[-]{} - m\_Z\^2 Z\_Z\^[ ]{} + h\
H\^D\^D\_ H \_5        - m\_W\^2 W\_\^+W\^[- ]{} \_5 - m\_Z\^2 Z\_Z\^[ ]{} \_5 + h \_5\[higgs\] where $\langle H \rangle = v = 174$ GeV, $p_h$ is the four-momentum of the physical Higgs particle $h$, and after the arrow are the interactions induced by the operator.

The $Z$ and Higgs operators are choson $\propto p^2$ so that they are relevant at the LHC where the $Z$ and Higgs are external legs in the EFT, but do not contribute in the low-energy scattering of DD. This choice should be acceptable, because the operator basis can always be reduced by using the equations of motion[@Simma]. Focussing for simplicity on the hypercharge boson $B$, and neglecting gauge-fixing terms, the equations of motion 