One of the fundamental predictions of QCD that has not yet been definitively observed is that there exist bound states of two or three gluons that are color charge neutral. In principle, every property of every excited states of every possible glueball can be determined precisely from first principles using the bare equations QCD and the strong force coupling constant. The first calculations had been completed by 1980 and have only been refined modestly since then. Glueballs should in principle be unstable but decay in precise and predictable ways and there are a great many of them that would have masses of about 1.4 GeV to 5 GeV. The trouble is that despite the fact that there is a very well defined target that we are looking for and we have had colliders powerful enough to generate them since at least the LEP experiment, we have yet to make a definitive sighting of a glueball after decades of looking for them. There are all sorts of plausible reasons why glueballs should be hard to see. While pseudo-scalar mesons (other than the neutral pion and neutral kaon) and vector mesons are well defined entities that neatly fit into their appointed places ordained by a quark theory of hadrons, neutral pions, neutral kaons, scalar mesons and axial vector mesons appear to manifest only as mixtures of different pairs of quarks. There is good reason to think that glueballs may share this property. On the other hand, no experimental data rules out the possibility that glueballs (or other "QCD exotics" such as hybrids of glueballs and quarks, or "true tetraquarks" as opposed to meson molecules, etc. that are permitted by naive application of the rules of QCD) don't exist in nature, even though they are well defined composite particles with well defined properties in the equations of QCD that we can calculate with some precision using lattice methods (at least to the level of precision with which we know the QCD coupling constant, of a bit less than 1%). Give that QCD exotics have been so hard to observe, maybe they really don't exist. And, if that is the case, then some fundamental rule of QCD is missing from the Standard Model. Quite unlike most of the rest of fundamental physics, where there is a rich literature of BSM physics possibilities, and a surprisingly thin (but critical) literature working out the implications of the SM without modification, in the literature of QCD exotics, there is a rich literature of what the SM predicts without modification and very little academic interest in the possibility that the SM must be modified in such a manner that would rule out QCD exotics, despite the fact that this seems much more interesting to me than issues like the strong CP problem (basically a question about why a QCD parameter has a value of zero) that doesn't differ much from the question of why any SM parameter takes its experimentally measured value. But, what subtle modification to the SM would be necessary to prevent QCD exotics from arising and in particular to rule out glueballs? I imagine that such a rule might be similar to the OZI rule which states that "any strongly occurring process will be suppressed if its Feynman diagram can be split in two by cutting only internal gluon lines. An explanation of the OZI rule can be seen from the decrease of the coupling constant in QCD with increasing energy (or momentum transfer). For the OZI suppressed channels, the gluons must have high q2 (at least as much as the rest mass energies of the quarks into which they decay) and so the coupling constant will appear small to these gluons." (per the Wikipedia article on the OZI rule). It might be hiding in plain sight due to an unrecognized feature of the equations governing the strong force, or it might require the addition of a new principle or two. In addition to being important for its own sake, such an obscure issue in QCD might be relevant to quantum gravity, both because gravity has a resemblance to QCD squared, and because any rule relating to glueballs must be intimately related to the fact that QCD is non-abelian and self-interacting, just like gravity. For example, a feature of QCD that ruled out glueballs, might also rule out vacuum solutions of the equations of GR as non-physical even though they are permitted by the equations themselves. It might also provide a more principled approach than an ad hoc Killing vector to remove ghost solutions from quantum gravity equations. Is anyone familiar with any academic literature of BSM modifications of QCD that forbid glueballs or other exotic states (or in the alternative, hypothetical interpretations of SM QCD rules that would have the same effect)? Simple searches of arXiv and Google using combinations of words that I've been able to come up with haven't pinpointed this kind of research, perhaps because I don't know the right buzzwords.