Determining Dark Matter-Electron Scattering Rates from the Dielectric Function

TL;DR

This paper presents a novel method to determine dark matter-electron scattering rates using the dielectric function, enabling more accurate predictions and calibration with electromagnetic measurements across various materials.

Contribution

It introduces a formalism linking dark matter-electron scattering rates directly to the dielectric function, incorporating many-body effects and reducing theoretical uncertainties.

Findings

Superconductor detectors have a significantly higher potential reach for light mediators.

The dielectric function approach simplifies the calculation of scattering rates across different materials.

Using experimental dielectric data improves the accuracy of dark matter detection predictions.

Abstract

We show that the rate for dark matter-electron scattering in an arbitrary material is determined by an experimentally measurable quantity, the complex dielectric function, for any dark matter interaction that couples to electron density. This formulation automatically includes many-body effects, eliminates all systematic theoretical uncertainties on the electronic wavefunctions, and allows a direct calibration of the spectrum by electromagnetic probes such as infrared spectroscopy, X-ray scattering, and electron energy-loss spectroscopy (EELS). Our formalism applies for several common benchmark models, including spin-independent interactions through scalar and vector mediators of arbitrary mass. We discuss the consequences for standard semiconductor and superconductor targets, and find that the true reach of superconductor detectors for light mediators exceeds previous estimates by several orders of magnitude, with further enhancements possible due to the low-energy tail of the plasmon. Using a heavy-fermion superconductor as an example, we show how our formulation allows a rapid and systematic investigation of novel electron scattering targets.