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Within our current limits of observation, dark matter (DM) is nonluminous i.e., it neither absorbs nor gives off electromagnetic (EM) radiation. This tells that DM is electrically neutral having no EM interaction or puts an upper bound on its electric charge (if any) such that its EM interaction is unobservably tiny!

What sort of observations tell us that DM also cannot have strong QCD interactions? Well, if it has QCD interactions, it will interact with quarks (which are charged), and in turn might cause indirect emission of EM radiation. Right? Is that how observations constrain strong interactions of DM, too?

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Well, if it has QCD interactions, it will interact with quarks (which are charged), and in turn might cause indirect emission of EM radiation. Right?

Cannot be so, because QCD interactions happen in the dimensions of a fermi, $1×10^{−15} m$ at most. Very large energies of individual particles are needed for the particles involved in order for QCD effects to dominate, due to the structure of the QCD force.

It is only in the cosmological models that a period where QCD interactions dominate, the quark gluon plasma in the Big Bang model, that such energies can be achieved so that the QCD interactions could dominate. These energies cannot be found in the dark mass needed to explain the galactic rotational curves etc. the energy density is too small:

Dark matter is a form of matter thought to account for approximately 85% of the matter in the universe and about a quarter of its total mass–energy density or about $2.241×10^{−27}$ kg/m3

Discussing within the standard model, energies that allow for QCD direct interactions can be found in neutron stars and supernovas, not in apparent interstellar space, at the end of rotation curves, where dark matter dominates.

Models beyond the standard model propose new particles, but still color neutrality and asymtotic freedom, i.e. no free quarks and gluons, has to be obeyed, so interactions of these particles cannot be strong at the available in space energy level densities.To have effects of free quarks and gluons needs energies over GeV.

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  • $\begingroup$ Indeed, and on your second para I note that the recent paper (Beylin et al arxiv.org/abs/2010.13678) suggest new stable quarks as a possible candidates for Dark Matter. $\endgroup$
    – user104617
    Commented Feb 3, 2021 at 11:29
  • $\begingroup$ But your answer does not address the question how we constrain the QCD interaction of dark matter. @annav $\endgroup$
    – SRS
    Commented Feb 3, 2021 at 14:29
  • $\begingroup$ Sorry, it says that within QCD interactions of the standard model there is no way to have them where dark matter exists, because the energy density is far too low. $\endgroup$
    – anna v
    Commented Feb 3, 2021 at 15:43
  • $\begingroup$ Not sure I agree as it's written. Quark nuggets are a(nother) dark matter model that would have QCD interactions. The cross section for that is small, obviously, otherwise it wouldn't be a dark matter candidate. But as long as you stay below current bounds on the cross section, I don't immediately see how the nature of the interaction comes in. You write "in order for QCD effects to dominate" - well, that's in the standard model, but what if dark matter doesn't have any other interaction, then QCD could be all there was, and explain why it's small, no? $\endgroup$
    – rfl
    Commented Feb 3, 2021 at 20:37
  • $\begingroup$ @rfl added further two paragraphs $\endgroup$
    – anna v
    Commented Feb 4, 2021 at 4:57

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