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

TL;DR

This paper develops a non-relativistic effective field theory for dark matter-electron interactions, connecting high-energy models to low-energy experimental phenomenology and providing tools for calculating relevant scattering rates.

Contribution

It derives the NR EFT from high-energy Lagrangians, introduces Feynman rules for calculations, and explains in-medium screening effects in DM-electron interactions.

Findings

Derived Feynman rules for NR EFT of DM-electron interactions.

Connected high-energy theories to low-energy electron excitation experiments.

Calculated absorption, scattering, and Thomson scattering rates for various DM models.

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.