The CDMS collaboration has put out a paper on dark matter effective field theory and possible implications for direct detection experiments. Most reported dark matter limits are based on a very specific model of Majorana fermion dark matter that interacts with nucleons through either scalar (spin-independent) or axial vector (spin-dependent) interactions.
These two channels are nice since they yield cross sections that are, for the purposes of direct detection where Q2 is very small, independent of the incoming WIMP’s energy. However, there are additional possible interactions, such as pseudoscalar interactions that yield cross sections proportional to the WIMP velocity. These are usually ignored because the WIMPs are quite nonrelativistic, so these terms are suppressed by a factor of at least v/c. If the fundamental couplings are all similar, then a v/c suppression will make this interaction very small compared to the scalar or axial vector interaction.
The Majorana fermion assumption is potentially more problematic because this assumes that the WIMP is in a particular class of particles and thus implicitly sets limits on the types of operators allowed. The effective field theory approach ignores fundamental questions like this and simply utilizes all the possible operators built from things like spin and momentum operators combined using dot and cross products. With this expanded set of operators, they see how the inclusion of more than just the canonical spin-independent and spin-dependent operators can affect limits. These new operators can interfere, either enhancing or suppressing the cross section used in the standard limit analysis. They can also change the shape of the recoil energy spectrum. Some methods, such as the “maximum gap” method from Yellin utilize spectral shape to get a stronger limit than just counting events in some range of event phase space, so deviation from the model can have a big effect on those kinds of limits.
The paper shows CDMS limits on the coefficients of these different interactions and also looks at things like limits in an isoscalar/isovector space where proton and neutron interactions with dark matter are allowed to be different. Finally, they also look at how possible spectral shape differences can affect current limits.