Large-$N_c$ constraints for elastic dark matter-light nucleus scattering in pionless effective field theory

TL;DR

This paper combines pionless effective field theory and large-$N_c$ expansion to derive constraints on dark matter interactions with light nuclei, providing predictions for scattering cross sections relevant for direct detection experiments.

Contribution

It introduces a novel approach integrating large-$N_c$ constraints with pionless EFT to analyze dark matter-light nucleus scattering, including two-nucleon contact currents.

Findings

Constraints on dark matter couplings to nucleon currents derived from large-$N_c$ expansion.

Predictions for spin-dependent and spin-independent cross sections for various light nuclei.

Quantitative estimates of scattering cross sections relevant for dark matter detection.

Abstract

Recent proposals for the use of light nuclei as dark matter direct detection targets necessitate a strong theoretical understanding of the nuclear physics involved. We perform relevant calculations for dark matter-light nucleus scattering in a combined pionless effective field theory and large-$N_c$ expansion, where $N_c$ is the number of quark colors. We include a general set of one-nucleon currents that have been used in other effective theories, as well as novel two-nucleon contact currents. First, we obtain constraints for the relative sizes of the dark matter couplings to the one- and two-nucleon currents through the large-$N_c$ expansion. Then, we use these constraints to make predictions for the relative sizes of spin-dependent and spin-independent cross sections for dark matter scattering off of a nucleon, a deuteron, a triton, and helium-3.