Inelastic dark matter reconciles the DAMA anomaly with other null direct detection experiments and points to a non-minimal structure in the dark matter sector. In addition to the dominant inelastic interaction, dark matter scattering may have a subdominant elastic component. If these elastic interactions are suppressed at low momentum transfer, they will have similar nuclear recoil spectra to inelastic scattering events. While upcoming direct detection experiments will see strong signals from such models, they may not be able to unambiguously determine the presence of the subdominant elastic scattering from the recoil spectra alone. We show that directional detection experiments can separate elastic and inelastic scattering events and discover the underlying dynamics of dark matter models.
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