What determines the shape of the WIMP cross-section vs mass limit curves?

Question

In figure 5 of arXiv:1310.8214v1, the experiments all seem to reach the lowest cross-sections when the WIMP is in the $40-100\, \mathrm{GeV}/c^2$ range. What is the physical reason for the scale of this minimum?

Answer 1

This is a competition between two effects. If WIMPs are too light, they don't produce observable nuclear recoils: it's like trying to move a bowling ball by hitting it with a ping-pong ball. It just won't move a noticeable amount. If WIMPs are very heavy, there are fewer of them around. (We know the approximate total mass density of dark matter in our neighborhood, so the number density is smaller at higher mass.) Fewer dark matter particles around means a smaller likelihood of interaction in the detector. So the limit is best when the WIMPs are heavy enough to produce recoils above threshold, and light enough that the number density is not too small.