The WIMP "miracle" is often used to motivate WIMPs: that a WIMP with a weak-scale mass naturally freezes out of thermal equilibrium after the big bang with the right relic abundance. I understand the "weakly-interacting" part of the "miracle" -- the SM includes a weak interaction cross section -- but I don't understand why the "weak-scale mass" is such a coincidence. It would only be a coincidence if we had a generic independent reason to expect particles at the weak-scale. Do we? 100 GeV doesn't seem to be intrinsic to weakly-interacting particles (after all, neutrinos are weakly interacting, and they are pretty far from 100 GeV).

EDIT: adding two sources that seem to conflict with each other to help explain the source of my confusion.

On page 9 of Ref. 1, Feng tells us that the thermal relic density is proportional to $m^2/G^4$, where m is the WIMP mass and G it's self-coupling. So the WIMP miracle only works for ~100 GeV particles with weak coupling.

But on page 221 of Ref. 2, by Jungman et al, we are told that the thermal relic density is independent of WIMP mass.

Both these papers are by experts in the field and are fairly authoritative. So my question is who is right? Or are both right and what am I misunderstanding?


  1. J. L. Feng, Non-WIMP Candidates, arXiv:1002.3828.
  2. G. Jungman, M. Kamionkowski, K. Griest, Supersymmetric dark matter, Phys. Rep. 267 (1996) 195–373, PDF.
  • $\begingroup$ A large enough mass is needed to act as dark matter. The standard model neutrinos are too light to fit the observations . $\endgroup$
    – anna v
    Nov 11, 2015 at 4:52
  • $\begingroup$ @anna v, I understand that dark matter can't be hot, but that's presumably a separate data point from motivating weak-mass-scale dark matter specifically... $\endgroup$
    – user1247
    Nov 11, 2015 at 4:54
  • $\begingroup$ It has to have a large enough mass to be captured by the gravitational wells that the galaxies are. The neutrinos travel the universe almost at the velocity of light and the gravitational attraction is too weak to bind them to an orbit around a galaxy see the case for WIMPs here astro.caltech.edu/~george/ay20/eaa-wimps-machos.pdf $\endgroup$
    – anna v
    Nov 11, 2015 at 4:57
  • $\begingroup$ @annav, Yes, I know, as I said, I understand that dark matter can't be hot. I'm familiar with the experimental side of things. I'm asking about the WIMP miracle, a supposedly purely theoretical coincidence. $\endgroup$
    – user1247
    Nov 11, 2015 at 5:19
  • $\begingroup$ To see the "width" of the weak scale see en.wikipedia.org/wiki/Electroweak_scale $\endgroup$
    – anna v
    Nov 11, 2015 at 6:35

1 Answer 1


Dark matter has been postulated to explain discrepancies in observations

Astrophysicists hypothesized the existence of dark matter to account for discrepancies between the mass of large astronomical objects determined from their gravitational effects, and their mass as calculated from the observable matter (stars, gas, and dust) that they can be seen to contain. Their gravitational effects suggest that their masses are much greater than the observable matter survey suggests.

To explain the discrepancy with known particles it would require to have them trapped around the gravitational wells of the galaxies to be neutral in charge and to have weak interactions as otherwise they would have been detected from light emitted or absorbed.

The standard model of particle physics does not have weakly interacting massive particles that are stable, except the neutrinos which have a very small mass. To reconcile all astrophysical observations for the existence of dark matter, masses of order of the weak scale or larger are postulated. It is the gravitational trapping that is important , which needs large masses.

Why the weak scale as a lower limit ? because if stable weakly interacting particles with mass of order GeV or tens of GeV existed we would have had a different standard model, they would have been detected in last century's particle physics experiments.

In extensions of the standard model with supersymmetry, and in string theories heavy weakly interacting particles are expected in abundance and they could solve the dark matter problem, though other alternatives proposals also exist .

So it is not a miracle that larger than about 100 GeV masses are needed for WIMPS . W bosons and Z boson are of that order of magnitude, and were detected, but they decay . The thermal equilibrium arguments and crossections will be ironed out if a TeV WIMP is found experimentally. It is the non observation of WIMPs in the experiments that sets the lower limit.

  • $\begingroup$ I'm very familiar with all of the experimental evidence for dark matter. I'm asking specifically about the "WIMP miracle" -- the supposed theoretical coincidence that weak scale particle matter gives the correct thermal relic abundance after freeze out. $\endgroup$
    – user1247
    Nov 11, 2015 at 5:23
  • $\begingroup$ I have edited . $\endgroup$
    – anna v
    Nov 11, 2015 at 5:25
  • $\begingroup$ The "weak scale particle" can give the correct answer. A higher scale can also. it is the lower limit from particle physics experiments presently. Maybe the LHC will surprise us $\endgroup$
    – anna v
    Nov 11, 2015 at 5:27
  • $\begingroup$ You are still not giving a direct answer to my question, but I'm inferring from your response that in your opinion the WIMP miracle is not a "miracle" at all, since theoretically the WIMP mass could be anything (again, I understand the experimental constraints). $\endgroup$
    – user1247
    Nov 11, 2015 at 15:03
  • $\begingroup$ Not anything, there is the lower experimental limit, and the higher limit from the possibilities of models. I am sure that if a good candidate is discovered, they will still be calling it a miracle :) even if it is at 1 TeV $\endgroup$
    – anna v
    Nov 11, 2015 at 15:49

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