An email from Cosmoquest led me to find Physicists Narrow Range of Potential Masses for Dark Matter Candidate articles. Technical details at Theoretical bounds on dark matter masses and on the Arxiv. The mass range is 10−3eV≲mφ≲107eV. Thus we have a range from neutrino masses (still very uncertain, but nonzero) up to about 1/10 the mass of a muon. This appears to exclude WIMPs, which were already in trouble. This also suggests that finding dark matter is not a justification for building a more powerful particle accelerator than the LHC; 107eV is well within the range of the LHC and other current devices.
We still do not have a complete theory of quantum gravity, but apparently enough is understood to make such calculations possible. I am looking forward to seeing what other theoretical physicists say about this.