In a short time, Physical Review Letters will publish a shocking paper by Dan Pirjol and Carlos Schat with a proof of the fact that a simple gluon exchange model for bound states of QCD does not work. The preprint is here. The conclusions drawn by the authors imply that one cannot expect a simple idea of free gluons exchanged by quarks to work. I think the readers of this blog may be aware of the reason why this conclusion is correct and PRL will publish an important paper.
The idea is that, in the low energy limit, the nonlinearities in the Yang-Mills equations modify completely the properties of the glue. We can call these excitations gluons only in the high energy limit were asymptotic freedom grants that nonlinearities can be treated as small perturbations and gluons are what we are acquainted with. But when we have to cope with bound states, we are in a serious trouble as our knowledge of this regime of QCD is really very few helpful for our understanding.
This result of Pirjol and Schat should be taken together with the measurements of the COMPASS Collaboration (see my post) about the spin of the protons. They proved that glue does not contribute to form the spin of the proton. Collecting together all this a conclusion to be drawn is that the high energy excitations of a Yang-Mills theory cannot be the same of the excitations in the low energy limit.
So, let’s move on and take a better look at our equations.