Dark Matter-Nucleon interaction in the Large-N Limit

We study the contact interactions between nucleons and spin-$\frac{1}{2}$ or scalar dark-matter (DM) particles in the framework of pionless effective field theory (EFT$_{\cancel{\pi}}$). The relatives size of low energy coefficients (LECs) is estimated in the large $N_c$ limit, where $N_c$ is the number of colors in quantum chromodynamics (QCD). We also study deuteron-DM elastic scattering and compute the Helium-3/triton-DM cross section to leading-order (LO) in EFT$_{\cancel{\pi}}$ and next-to-leading-order (NLO) in $1/N_c$. The numerical upper bound is obtained by applying cosmological constraints on LECs.