I am wondering if it makes sense to state that the upper limit is roughly 1012 eV (up to know the physics probed by the LHC seems to be pretty consistent with the SM) and the lower one is ... the upper bound for the photon mass (somewhere between 10-14 and 10-26 eV according to https://arxiv.org/abs/hep-ph/0306245).
If I understand well the argument in this article, one could say the larger value 10-14 eV comes from the Standard Model of particles (the photon would acquire mass by the Higgs mechanism, its large-scale behavior beeing effectively Maxwellian) while the smaller value 10-26 eV would come from the standard model of cosmology (the value of the galactic field today leading to this value from the hypothesis of a "Proca regime for all scales" ??).

Edit 06/12/13: I removed the expression : "domain of validity" that sounds too much like a mathematical closed interval. It is not adapted to the Standard Model because it is not a theory. I have chosen the formulation "phenomenological spectrum" to insist on the fact that this spectrum can be enriched with new particles whose masses are in the same energy range as the old ones.

  • $\begingroup$ Don't forget about the neutrino sector (!). It is also a popular belief that dark matter is described by some field(s) that interact weakly with the usual SM fields, but I couldn't tell you which mass scales are crucial. $\endgroup$
    – Vibert
    Feb 26, 2013 at 23:22
  • $\begingroup$ The neutrino sector is very important of course but as far I understand the issue, and following my line of reasoning (I don't know if it is sound) - looking for upper limits for the unknown masses of very light particles - it seems that for neutrinos the upper limit is much larger than the photon (around 100 meV for an order of magnitude estimate ?). $\endgroup$ Feb 28, 2013 at 9:23
  • $\begingroup$ You're right. Since we only measure differences in neutrino masses, giving solid bounds is difficult. The latest Particle Data Group booklet gives a bound of $m \lesssim 1$ eV. But this does imply that extrapolating the SM to $10^{-26}$ eV without including the neutrinos is a risky business ;) $\endgroup$
    – Vibert
    Feb 28, 2013 at 12:36
  • $\begingroup$ You are right Vibert, such an extrapolation is a risky business but as a school teacher when I ask students to evaluate the number of iron atoms in a nail, starting from a (140pm)^3 volume is it not a wild speculation extrapolating geometric concepts from macroscopic to nanoscopic scales? ;-) $\endgroup$ Jun 12, 2013 at 10:07
  • $\begingroup$ Dear Vibert, if you let me carry on speculation once more, I can add something to your first important comment regarding the neutrino sector. I read very recently about some hypothetical almost-commutative spectral extension of the standard model (arxiv.org/abs/1304.0415) that left neutrino mass scale could be controlled by "a Majorana mass of at least of the order of 10^11Gev" (arxiv.org/abs/1304.8050). The theory is unfortunately not developed enough as far as I konw to make any precise connection to dark matter ... $\endgroup$ Jun 12, 2013 at 10:36


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