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 = σ 0 v n , 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.

We improve limits on the spin-independent scattering cross section of Dark Matter on nucleons, for DM in the 300 MeV -100 GeV mass range, based on the DAMIC and XQC experiments. Our results close the window which previously existed in 1 -8 GeV mass range, for a DM-nucleon cross section of order ∼ µb, assuming the standard velocity distribution. arXiv:1709.00430v3 [hep-ph]