# What is the formal definition of spin-independent vs. spin-dependent scattering?

In the search for WIMPs as the dark matter particle, there is an important distinction between spin-independent and spin-dependent scattering. Roughly, WIMPs scattering from nucleons through a spin-independent coupling are not sensitive to the spin (up or down) of the nucleon, while they are sensitive in this way for spin-dependent couplings. In particular, spin-independent scattering can lead to a boost in the total cross-section due to individual nucleons within a nucleus contributing coherently, while the spin-dependent cross-section is (I think) only proportional to the net spin of the nucleus.

Is this distinction only useful (or unambiguous) for scattering mediated through through weak interaction, or does it have a model-independent definition within quantum field theory?

Also, do the two types correspond to scattering events mediated through a boson with specific properties (e.g. Z vs. W)? For instance, this paper by Barger et al. says that "The spin dependent scattering cross section is largely governed by Z-boson exchange and is sensitive to the Higgsino asymmetry". But, as is suggested by the mention of the Higgsino, this is made in the context of SUSY and it's unclear to me whether this is generally true.

Even if this distinction is only used within the narrow field of WIMP scattering, I would be very appreciative of a mathematical precise definition. Thanks!