What is a glueball?

This question, that seems rather innocuous, is indeed exposed to a lot of prejudices and you will rarely find some expert in the field that will not claim that is just a bound state of gluons that originates from the well known fact that gluons carry color charge. This situation is to be compared to the case of photons that, carrying no electric charge, cannot interact each other (indeed a small effect exists and is called Delbruck scattering and can be obtained from a fully formulation of quantum electrodynamics). Of course one should expect that such states will carry no color charge due to confinement.

Here we see that our current understanding of quantum field theory is just cheating us. We are able to manage quantum field theory for any interaction just with small perturbation theory and almost all our knowledge about comes from such computations. It is not difficult to see that this is a very limited view of the full landscape and we could be easily making mistakes when we try to extend such a small view to the full reality. The question on glueballs is indeed all founded in the infrared limit when small perturbation theory does not apply anymore. In this limit we can rely just on lattice computations and this is already a big limitation notwithstanding the present computational resources.

The right question to be asked here is: Are gluons still the right excitations of the Yang-Mills field in the low energy limit? So far nobody asked this and so nobody has an answer at hand ( I have but this is not the place to discuss it now). So, we are free to call such excitations as glueballs without nobody complaining about.  So, are these bound states of gluons? The answer is no. We are talking about different particles belonging to the spectrum of the same Hamiltonian in a different limit. We can see gluons coming back to reality in the high energy limit due to asymptotic freedom.

Curiously enough, condensed matter theorists seem to be smarter of people like me that worked just on particle physics with the only tool of small perturbation theory. Also condensed matter theorists use such a tool but they, some time ago, asked themselves the right question: What are the right excitations in the given limit? Once you have answered to this question you can safely do ordinary perturbation theory and be happy.

The most important lesson to be learned from all this is that one should not content herself with a theory when it has strong computational limitations. Rather, one should recognize that here there is a serious problem in need of a significant effort to be solved. Of course quantum gravity may be more rewarding but, what if one has a tool to solve any differential equation in physics in a strong coupling regime? Should you call this a scientific revolution?

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