Majorana dark matter cross sections with nucleons at high energies

Abstract

Nonrelativistic dark matter scattering with nucleons is constrained by direct detection experiments. We use the XENON constraints on the spin-independent and spin-dependent cross section for dark matter scattering with nucleons to constrain a hypothetical Majorana fermionic dark matter particle's couplings to the Higgs boson and $Z$ boson. In this paper, we illustrate the change in the dark matter nucleon cross section as one goes from nonrelativistic, coherent scattering to relativistic, incoherent scattering. While the $Z$ invisible decay width excludes directly couplings of dark matter to ordinary matter, by introducing a light ${Z}^{\ensuremath{'}}$ portal to the dark sector, a relatively large dark matter nucleon cross section can be preserved even with accelerator experiment constraints for dark matter with a mass of $\ensuremath{\sim}10\text{ }\text{ }\mathrm{GeV}$.