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Matrix element analyses of dark matter scattering and annihilation

We provide a compendium of results at the level of matrix elements for a systematic study of dark matter scattering and annihilation. We identify interactions that yield spin-dependent and spin-independent scattering and specify whether the interactions are velocity- and/or momentum-suppressed. We identify the interactions that lead to s-wave or p-wave annihilation, and those that are chirality-suppressed. We also list the interaction structures that can interfere in scattering and annihilation processes. Using these results, we point out situations in which deviations from the standard lore are obtained.