are [@polonais] D\_B\^= g’y\_H (H\^D\^H - (D\^H)\^H) + g’\_y\_\^\[EoMZ\] where $\psi$ is a SM fermion of hypercharge $y_\psi$. Usually[@polonais], operators containing the double derivative on the left of eqn(\[EoMZ\]) are dropped, and the operators containing the Higgs v.e.v. squared $ \langle H^\dagger \Dlr  H \rangle$ are retained. In this usual basis, $\chi-Z$ interactions could be parametrised by $(\overline{\chi}\gamma^\mu \chi) H^\dagger \Dlr  H$, in which case the matrix element for $Z$ exchange at the LHC is $\propto m_Z^2/(p_Z^2 -m_Z^2)$, so negligeable for $p_Z^2 \gg m_Z^2$. But $Z$ exchange should be included in the quark-$\chi$ contact interaction used in direct detection, so the coefficient of the operators of eqn (\[qDMd6\]) would not be the same in direct detection as at the LHC. To avoid this discrepancy, I retain the derivative operators of eqn (\[inteff\]), and use eq. (\[EoMZ\]) to remove the operator $ \propto \langle H^\dagger \Dlr  H  \rangle$. This means that the $Z$ couples significantly to $\chi$ at the LHC, but negligeably in DD, and the operator coefficients do not change when the $Z$ is matched out of the theory.

In the case of the Higgs, the equation of motion is $$D_\mu D^\mu H = \mu^2 H -\lambda H^\dagger H H 