One of the more questionable points I have discussed so far is: What are QCD asymptotic states at very low momenta? This question is not trivial at all. If you will speak with experts in this matter, a common point they will share is that gluons carry color charge and so must form bound states. A claim like this has a strong implication indeed. The implication is that Yang-Mills Hamiltonian must display the same asymptotic states at both ends of the energy range. But the problem is exactly in the self-interaction of the theory that, at very low momenta, becomes increasingly large and gluons, asymptotic states of Yang-Mills theory in the asymptotic freedom regime, are no more good to describe physics. So, what are good states at low energies? I have already answered to this question a lot of times (recently here) and more and more confirmations are around. I would like just to cite a very nice paper I have seen recently on arxiv (see here) by Stanley Brodsky, Guy de Teramond and Alexandre Deur. These authors have nicely exploited AdS/CFT symmetry obatining striking results in the understanding of low-energy QCD. I would like to cite again the work of these authors as their soft-wall model is indeed a strong support to my view. It would be really interesting to get them working out a pure Yang-Mills model obtaining beta function and all that.
What one has at low end of momenta is a new set of states, glue states or glueballs if you prefer, that permits strong interactions. These states have already been seen in most laboratories around the World and belong to the open question of the understanding of the lower part of the hadronic spectrum.