Simplified Spin Dependence in Dark Matter Direct Detection

TL;DR

This paper simplifies the analysis of dark matter-electron interactions in direct detection experiments by identifying conditions under which certain response functions vanish, reducing computational complexity and aiding diverse material analysis.

Contribution

It introduces a framework that reduces the number of response functions needed to analyze dark matter interactions, especially in symmetric and chiral materials.

Findings

Certain linear combinations of response functions vanish in specific materials.

Response functions simplify in parity-symmetric materials.

The scattering rate formula is extended to anisotropic, chiral detectors.

Abstract

The interactions of dark matter with Standard Model particles can be systematically studied in the language of effective field theories. We investigate dark matter interactions with Standard Model particles, including spin-dependent interactions, for direct detection experiments and demonstrate that, although the scattering rate generally depends on multiple types of material response functions, certain linear combinations of these material response functions vanish if the initial and final electronic states share the same Hamiltonian. We also find that several other response functions vanish in parity-symmetric materials, making these systems as simple as isotropic detectors in some respects. Finally, we present the scattering rate for an anisotropic, possibly chiral detector, for generic dark matter-electron spin interactions. These relations reduce the number of independent response functions needed, thereby simplifying the computational complexity for a broad class of dark matter models. Our results provide a complete and efficient toolkit for analyzing electron recoil signals in diverse detector materials.