Constraints on Dark Matter with a moderately large and velocity-dependent DM-nucleon cross-section

We derive constraints on a possible velocity-dependent DM-nucleon scattering cross section, for Dark Matter in the 10 MeV–100 GeV mass range, using the XQC, DAMIC, and CRESST 2017 Surface Run experiments. We report the limits on cross sections of the form σ=σvn, for a range of velocity dependencies with n∊{-4,-2,-1,0,1,2}. We point out the need to measure the efficiency with which nuclear recoil energy in the sub-keV range thermalizes, rather than being stored as Frenkel pairs in the semi-conductor lattice. The possibility of a significant inefficiency leaves open a considerable “hole” in the limits for mass in the ∼ 0.2–2 GeV range, which XQC and CRESST can potentially fill when the thermalization efficiency is measured. We call attention to the asymmetry between a conventional lower limit cross section and the “upper-reach cross section” imposed by attenuation in an overburden—an upper boundary being extremely sharp but quite insensitive to the statistics of the experiment. Considering the recent interest to use dark matter-baryon interaction with velocity dependence n=-4 to explain the EDGES 21 cm anomaly, we also derive the limits on milli-charged DM that scatters off protons and electrons under a Coulomb-like interaction. We find that much but not all of the region of interest for the EDGES anomaly can be excluded.