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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 http://arxiv.org/pdf/hep-ph/0306245v2.pdf).
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" ??).

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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. – Vibert Feb 26 at 23:22
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 ?). – laboussoleestmonpays Feb 28 at 9:23
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 ;) – Vibert Feb 28 at 12:36

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