Non-relativistic effective theory of dark matter direct detection

TL;DR

This work develops a non-relativistic effective theory (NR EFT) for dark matter direct detection, capturing DM–nucleus interactions with a minimal, testable operator basis that remains valid across a wide range of high-energy models. By separating mediator regimes into heavy (contact) and light (long-range) cases, it derives explicit NR SI and SD potentials governed by a small set of Wilson coefficients, whose shapes in the recoil spectrum encode the underlying dynamics. The paper maps microscopic relativistic operators to NR operators through nuclear matrix elements and form factors, and provides concrete current-experiment bounds on these coefficients while outlining constraints on the force carriers from collider, flavor, and astrophysical probes. It emphasizes that the recoil spectrum’s morphology, together with nuclear and astrophysical uncertainties, can distinguish interaction types and guide future model-building and experimental analyses. The framework thus enables a model-agnostic interpretation of potential DM signals and clarifies how direct detection data relate to UV completions and collider phenomenology.

Abstract

Dark matter direct detection searches for signals coming from dark matter scattering against nuclei at a very low recoil energy scale ~ 10 keV. In this paper, a simple non-relativistic effective theory is constructed to describe interactions between dark matter and nuclei without referring to any underlying high energy models. It contains the minimal set of operators that will be tested by direct detection. The effective theory approach highlights the set of distinguishable recoil spectra that could arise from different theoretical models. If dark matter is discovered in the near future in direct detection experiments, a measurement of the shape of the recoil spectrum will provide valuable information on the underlying dynamics. We bound the coefficients of the operators in our non-relativistic effective theory by the null results of current dark matter direct detection experiments. We also discuss the mapping between the non-relativistic effective theory and field theory models or operators, including aspects of the matching of quark and gluon operators to nuclear form factors.