In my preceding post I discuss the question of the proton spin, experimental measurements and the relevant conclusion that these measurements are consistent with the fact that there is no glue contribution to spin. Rather, we have a partial contribution by quarks and the remanent should be due to orbital angular momentum. I concluded from this that the infrared carriers of the strong force are not properly gluons but rather spin 0 excitations. In this post I would like to expand on this matter to make clear that all this is plainly obtained from QCD and so, fully consistent with the theory. Anyhow, it should be remembered that the quark sea for nucleons plays a relevant role in this case making quarks dressed.

The question is rather simple. At higher energy QCD tends to become a free theory, that is the coupling becomes increasingly small and the gluon propagator one uses at the tree level is that of a free particle. This in turn means that the non-linear contributions from Yang-Mills theory are small and small perturbation theory applies. In this limit we can identify as the excitations of Yang-Mills theory with ordinary gluons carrying spin one.

In the infrared limit, the case of low energies, the behavior of Yang-Mills theory changes radically. The reason is that in this case the non-linear terms in the equations become so strong that ordinary gluons are no more the fundamental excitations of the theory. In this case one has glueballs and the lower end of the spectrum of the glueballs carries spin zero. This is the reason why COMPASS Collaboration see no spin contributions from glue.

One should see such things in the same way quasi-particles are seen in condensed matter. The free particles that make the theory are not the one of the free theory but will depend upon the way interactions act on them. So, in the ultraviolet limit we can safely call them gluons and in the infrared limit things are quite different. In this light, it would be interesting to try to see similar measurements for charmonium and see in this case what is the contribution of glue. It may happen that this physical situation is radically different from that of the nucleon.

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The idea seems indeed intriguing: infrared QCD transforms spin 1 gluons into spinless glueballs through a transition that is reminiscent of BE condensation. If I understand your argument correctly, Yang-Mills theory effectively becomes a scalar phi^4 model in the infrared limit.

I might be missing something here, but I think that there are some challenges that need to be resolved for this idea to gain ground. If you take the viewpoint that glueball self-interaction is very weak (while the glue coupling to quarks remain strong to preserve confinement), then a fraction of glueballs must be free to flow through space and they should have been detected as free objects so far. By contrast, if you assume that both gluon self-interaction and gluon-quark coupling are strong, then you have a strongly coupled self-interacting scalar field theory (similar to a Higgs background) in interavtion with quarks. But then what prevents gluons to gain large mass via unsuppressed quantum corrections? (Higgs mass is protected to gain quadrative mass corrections through SUSY).
Besides, a strongly coupled glue theory in the infrared may be far different from an equilibrium quantum field model. One may need to apply non-equilibrium field theory that leads to completely different results from what the standard theory of propagators yields.

My approach work in the strong coupling limit and then your argument does not apply. Indeed, there is a conceptual mistake when such things are approached and it is to believe that just small perturbation theory apply ( being a coupling constant). Indeed, also the case does exist and it is the one for which I have developed a lot of new approaches in twenty years of research in physics. See

What has been missed so far with QCD is the great chance to make a substantial change of paradigm in mathematical-physics that is overdue when one met with difficulties like these. I hope to have given some hints to the community in this direction and this is also the main reason why I opened up this blog.

Marco,

The idea seems indeed intriguing: infrared QCD transforms spin 1 gluons into spinless glueballs through a transition that is reminiscent of BE condensation. If I understand your argument correctly, Yang-Mills theory effectively becomes a scalar phi^4 model in the infrared limit.

I might be missing something here, but I think that there are some challenges that need to be resolved for this idea to gain ground. If you take the viewpoint that glueball self-interaction is very weak (while the glue coupling to quarks remain strong to preserve confinement), then a fraction of glueballs must be free to flow through space and they should have been detected as free objects so far. By contrast, if you assume that both gluon self-interaction and gluon-quark coupling are strong, then you have a strongly coupled self-interacting scalar field theory (similar to a Higgs background) in interavtion with quarks. But then what prevents gluons to gain large mass via unsuppressed quantum corrections? (Higgs mass is protected to gain quadrative mass corrections through SUSY).

Besides, a strongly coupled glue theory in the infrared may be far different from an equilibrium quantum field model. One may need to apply non-equilibrium field theory that leads to completely different results from what the standard theory of propagators yields.

Yours,

Ervin

My approach work in the strong coupling limit and then your argument does not apply. Indeed, there is a conceptual mistake when such things are approached and it is to believe that just small perturbation theory apply ( being a coupling constant). Indeed, also the case does exist and it is the one for which I have developed a lot of new approaches in twenty years of research in physics. See

http://prola.aps.org/abstract/PRA/v58/i5/p3439_1 (or the preprint http://arxiv.org/abs/hep-th/9801069 if you do not have a subscription to PROLA).

You can also read my post about this matter that explains plainly what is going on here

https://marcofrasca.wordpress.com/2008/06/26/strong-perturbation-theory/

What has been missed so far with QCD is the great chance to make a substantial change of paradigm in mathematical-physics that is overdue when one met with difficulties like these. I hope to have given some hints to the community in this direction and this is also the main reason why I opened up this blog.

Ciao,

Marco