The Non-Relativistic Effective Field Theory Of Dark Matter-Electron Interactions

Abstract: Electronic excitations in atomic, molecular, and crystal targets are at the forefront of the ongoing search for light, sub-GeV dark matter (DM). In many light DM-electron interactions the energy and momentum deposited is much smaller than the electron mass, motivating a non-relativistic (NR) description of the electron. Thus, for any target, light DM-electron phenomenology relies on understanding the interactions between the DM and electron in the NR limit. In this work we derive the NR effective field theory (EFT) of general DM-electron interactions from a top-down perspective, starting from general high-energy DM-electron interaction Lagrangians. This provides an explicit connection between high-energy theories and their low-energy phenomenology in electron excitation based experiments. Furthermore, we derive Feynman rules for the DM-electron NR EFT, allowing observables to be computed diagrammatically, which can systematically explain the presence of in-medium screening effects in general DM models. We use these Feynman rules to compute absorption, scattering, and dark Thomson scattering rates for a wide variety of high-energy DM models.