Momentum dependent dark matter scattering

It is usually assumed that WIMPs interact through spin-independent and spin-dependent interactions. Interactions which carry additional powers of the momentum transfer, q(2), are assumed to be too small to be relevant. In theories with new particles at the similar to GeV scale, however, these q(2)-dependent interactions can be large, and, in some cases dominate over the standard interactions. This leads to new phenomenology in direct detection experiments. Recoil spectra peak at non-zero energies, and the relative strengths of different experiments can be significantly altered. We present a simple parameterization for models of this type which captures much of the interesting phenomenology and allows a comparison between experiments. As an application, we find that dark matter with momentum dependent interactions coupling to the spin of the proton can reconcile the DAMA annual modulation results with other experiments.