Large-N_c constraints for one- and two-nucleon currents in Pionless Effective Field Theory for dark matter direct detection

The detection of dark matter is a high priority in searches for Beyond the Standard Model physics. One candidate for dark matter is a weakly interacting massive particle (WIMP) with a mass above the GeV scale. Proposals for the use of light nuclei for dark matter direct detection require a strong theoretical understanding of the nuclear matrix elements involved. The momentum transfer in direct detection experiments for light nuclei is at most a few MeV, so these systems are amenable to the techniques of pionless effective field theory (EFT). However, the effective theory contains undetermined low energy coefficients that must be determined either from data or from lattice calculations. Fortunately, theoretical constraints can be obtained from other means. We use the spin-flavor symmetry of nucleons in the large-N_c limit of quantum chromodynamics, where N_c is the number of colors, to constrain the coefficients of one- and two-nucleon currents that are not presently known from data. We also examine the impact of these constraints on the cross sections of WIMP-nucleon and WIMP-deuteron elastic scattering. Lastly, these constraints can be used to organize the currents required in many-body calculations.