Cutting rules for non-relativistic dark matter in solids based on Kohn-Sham orbitals

TL;DR

This paper develops a theoretical framework for applying cutting rules to non-relativistic dark matter interactions in solids, utilizing Kohn-Sham orbitals from density functional theory to connect loop amplitudes with observable quantities.

Contribution

It introduces a novel formulation of cutting rules based on Kohn-Sham orbitals, bridging quantum field theory techniques with density functional theory for condensed matter dark matter studies.

Findings

Framework connects loop amplitudes to physical observables in solids.

Formulation applicable to DM-electron interactions and Coulomb potential.

Provides a basis for future experimental and theoretical research in DM detection in materials.

Abstract

The Cutkosky cutting rules establish a direct connection between the imaginary parts of loop amplitudes and physical observables such as decay rates and cross sections, providing heuristic insights into the underlying processes. This work lays a robust theoretical foundation for the application of cutting rules in solid-state systems involving instantaneous dark matter (DM)-electron Yukawa interaction as well as the Coulomb potential. The cutting rules are formulated using the single-electron wavefunctions and corresponding energy eigenvalues obtained from the Kohn-Sham equations within density functional theory (DFT). This framework is not only of considerable theoretical interest but also holds significant practical relevance for studying DM phenomenology in condensed matter systems.