The non-relativistic effective field theory of dark matter-electron interactions

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.. Authors: Krnjaic, Gordan [Fermilab; Chicago U., Astron. Astrophys. Ctr.; Chicago U., KICP] (ORCID:0000000174209577); Rocha, Duncan [Fermilab; Chicago U., KICP; Chicago U., EFI] (ORCID:0000000282637982); Trickle, Tanner [Fermilab] (ORCID:0000000313714988). DOE Contract: 89243024CSC000002. Subjects: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 79 ASTRONOMY AND ASTROPHYSICS; Effective Field Theories; New Light Particles; Specific BSM Phenomenology