A Model Independent Approach to Inelastic Dark Matter Scattering

Abstract: We present a model independent analysis of inelastic dark matter transitions at direct detection experiments by modifying the elastic methodology of Fitzpatrick, et al. By analyzing the kinematics of inelastic transitions, we find the relevant variables to describe these scattering processes, the primary change being a modification of the $\vec{v}^\perp$ variable. Taking this into account, we list the relevant scattering matrix elements and modify the Mathematica package of Anand, et al. to calculate the necessary form factors. As an application, we determine the matrix elements of inelastic scattering for spin transitions between a fermion to fermion, scalar to vector, and scalar to scalar. Finally, we consider fits to the DAMA/LIBRA annual modulation signal for the magnetic inelastic dark matter scenario as well as a model independent scan over relativistic operators, constraining them with limits from direct detection experiments. In the magnetic inelastic dark matter scenario or if the dark matter couples through relativistic operators involving only protons, we find that experiments with xenon and germanium targets can have consistently small rates. However, limits from iodine experiments are much more constraining, leaving small regions of allowed parameter space. We point out that existing uncertainties in the iodine quenching factor strongly affects the constraints, motivating further study to pin down the correct values.