## A review on proton spin

29/05/2009

As you may know, there is a lot of experimental activity to understand as the spin of the proton can arise from its components, i.e. quarks and gluons. The great difficulties we have to manage low-energy QCD makes this problem fundamental toward an improved comprehension of this limit. In arxiv today an interesting review by Steven Bass is appeared (see here and here). Bass gives a brief  overview of the current situation mostly from the experimental side. As reader from this blog may know (see here), glue contribution to spin is about zero and the proton spin appears mostly due to valence quarks and their interplay with vacuum. Indeed this is Bass’ conclusion and we fully agree with it.

The emerging scenario is really striking. It appears that QCD behavior in a non-perturbative regime goes completely off known tracks. This implies that there is a lot of problems to be solved in the future for us working in this field.

## PHENIX says gluons are not all the story

04/05/2009

PHENIX is a collaboration working with data extracted from RHIC (Relativistic Heavy Ion Collider) located at Brookhaven Labs. In an experiment with proton-antiproton colliding beams and looking at the ejected $\pi^0$ they were able to extract the contribution of the gluons to the proton spin. They did this using Next-to-Leading-Order perturbation theory fixing the theory scale at $4GeV^2$. Their paper is here and will appear shortly in Physical Review Letters. Their result is

$\Delta G^{[0.02,0.3]}_{\rm GRSV}=0.2\pm0.1{\rm (stat)}\pm0.1{\rm (sys)} ^{+0.0}_{-0.4}{\rm (shape)}\pm0.1{\rm (scale)}$

that is consistent with zero. This is an independent confirmation of the results of the COMPASS Collaboration that we discussed here. These results let us know that in a proton no contribution to the spin comes from glue, rather this is mostly orbital angular momentum. So, why is this conclusion so relevant? From our point of view we know that, in the low energy limit, glue carries no spin. Rather, true excitations of the Yang-Mills field are some kind of colorless states that makes the spectrum and having the lower state with a massive glueball that can also be seen in labs. We know that this state is the $\sigma$ resonance. This is the scenario that is emerging from experiments and that whatever theory one can think about should explain.

Update: COMPASS Collaboration confirms small polarization of the gluons inside the nucleon (see here, to appear in Physics Letters B). The current world situation is given in their figure that I put here with their caption (for the refs check their paper).

These results, emerging from several different collaborations, are saying to us a relevant information. Glue seems to carry no spin in the low-energy limit. I think that any sound approach to manage QCD in this case should address this result. The main conclusion to be drawn is that glue excitations seen in this case are different from those seen in the high-energy limit. This is a strong confirmation of our point of view presented here and in published papers. It is a mounting evidence that appears to outline a clear scenario of strong interactions at lower energies.

## Carriers of the strong force

19/09/2008

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.

## What makes the proton spin?

17/09/2008

There is currently a beautiful puzzle to be answered that relies on sound and beautiful experimental results. The question is how the components of a proton, that is quarks and gluons, concur to determine the value one half for the spin of the particle. During the conference QCD 08 at Montpellier I listened to a beatiful presentation of Joerg Pretz of the COMPASS Collaboration (see here and here). Hearing these results was stunning for me. I explain the reasons in a few words. The spin of the proton should be composed by the spin of the quarks, the contributions of gluons (gluons???) and orbital angular momentum. What happens is that the spin of quarks does not contribute too much. People then thought that the contribution of gluons (gluons again???) should have been decisive. The COMPASS Collaboration realized a beautiful experiment using charmed mesons. This experiment has been described by Pretz at QCD 08. They proved in a striking way that the contribution of the glue to proton spin can be zero and cannot be used to account for the particle spin. Of course, there are beautiful papers around that are able to explain how the proton spin comes out. I have found for example a paper by Thomas and Myhrer at Jefferson Lab (see here and here) that describes quite well an understanding of the puzzle and surely is worthwhile reading. But my question is another: Why the glue  does not contribute?

From our preceding posts one should have reached immediately an answer, the same that come out to my mind when I listened Pretz’s talk. The reason is that, in the infrared, gluons that have spin one are not the true carriers of the strong force. The true carriers have no spin unless higher excited states are considered. This explains why COMPASS experiment did not see any contribution consistently with previous expectations.

This is again a strong support to our description of the gluon propagator (see here). No other theory around shows this.