The Effective Field Theory of Dark Matter Direct Detection

TL;DR

This paper develops a comprehensive non-relativistic effective theory framework for dark matter direct detection, identifying new nuclear responses and providing tools for model-independent analysis of experimental data.

Contribution

It introduces all Galilean-invariant operators up to quadratic order, relates them to nuclear responses, and provides matrix elements for common targets, enabling more accurate dark matter detection analysis.

Findings

Identification of novel nuclear response operators.

Evaluation of response functions for key detector materials.

Provision of matrix elements for model-independent analysis.

Abstract

We extend and explore the general non-relativistic effective theory of dark matter (DM) direct detection. We describe the basic non-relativistic building blocks of operators and discuss their symmetry properties, writing down all Galilean-invariant operators up to quadratic order in momentum transfer arising from exchange of particles of spin 1 or less. Any DM particle theory can be translated into the coefficients of an effective operator and any effective operator can be simply related to most general description of the nuclear response. We find several operators which lead to novel nuclear responses. These responses differ significantly from the standard minimal WIMP cases in their relative coupling strengths to various elements, changing how the results from different experiments should be compared against each other. Response functions are evaluated for common DM targets - F, Na, Ge, I, and Xe - using standard shell model techniques. We point out that each of the nuclear responses is familiar from past studies of semi-leptonic electroweak interactions, and thus potentially testable in weak interaction studies. We provide tables of the full set of required matrix elements at finite momentum transfer for a range of common elements, making a careful and fully model-independent analysis possible. Finally, we discuss embedding non-relativistic effective theory operators into UV models of dark matter.