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.
The Gauge Connection 
You’ve had a dearth of any level comments recently, so I’m going to supply you with at least a low level one to contemplate…
Suppose that QED had been discovered, perhaps by high energy experiments, before the QM bound states for the atoms. One would then be faced with the problem of guessing the bound states of the hydrogen atom from the QED. And getting that 1/r potential wouldn’t be that obvious. I think that this is the situation faced in QCD.
For example, when one does a Lamb shift calculation using QED, one begins with the wave functions defined by QM and then perturbs these. Bound states are not perturbations and so one cannot bootstrap the whole theory based on its high temperature limit.
Hi Carl,
After the storms, this blog turned back to almost the same number of readers as before (with an increase rather than a decrease). As you may know, who should have conceded defeat did not do that. If you are God Almighty you can decide who lives and who dies.
Cheers,
Marco
Dear Marco, I don’t quite understand why it should be surprising that “a simple gluon exchange” is not the only thing that governs the confined, strongly coupled limit of QCD.
I don’t even understand what it would mean if they were the only factor.
“Gluon exchange”, in the sense that a physicist understands it, is a contribution to an amplitude from a Feynman diagram with intermediate gluons – especially at the tree level. Even if one adds loop diagrams, it’s still just a perturbative treatment, and a strongly coupled QCD surely has a lot of non-perturbative phenomena.
It would be much more interesting if someone showed that, in some new well-defined sense, gluons were everything in all the regimes.
Dear Luboš,
There are a lot of people working in this matter that try to work out properties of bound states in QCD using this kind of bare gluons. They claim that, given the right potential, we can accommodate all the low energy physics through bound state of such gluons and quarks. It is the same way we work in QED treating atoms or molecules. Of course, in QED we are lucky as the coupling is really small and you can work out all your computations with free states. Particles are friendly. But when the coupling becomes large, and we learned this from condensed matter, particles are not properly the same of a free theory. At best they get dressed in some way and there is no perturbation computation we can do to recover them. Rather, we should be able to identify the right states from the start and then we can do perturbation theory with these states.
This paper by Pirjol and Schant points into this direction. COMPASS Collaboration by its side does not see any contribution from glue for the spin of the proton. But already lattice computations, by identifying a gluon mass, are saying to us that gluons seen in high-energy experiments are not quite the same particles that produce the phenomenology at low energies.
The point is that you can exploit your high-energy expansion to whatever order you like and you will not see this. Low energy phenomena require new approaches and new views.
Anyhow, it is quite common to see people working in the infrared limit with a set of Feynman diagrams proper to high energies. Sometime they are lucky and almost (almost emphasized) recover the behavior seen on lattice but, in most cases, they missed completely the right scenario.
Marco
Dear Marco,
I cannot agree with you more that “low energy phenomena require new approaches and new views”. This is why I believe that traditional models that rely on equilibrium field theory, PI methods, generating functionals and so on are ineffective in the infrared limit of QCD and other strongly coupled field theories. I recently submitted a paper to a nonlinear dynamics journal where I show that the spectrum of hadron masses follows from the universal route to chaos in non-equilibrium Yang-Mills-Dirac theory. Results are in close match to experimental data. I plan on sending you a copy after acceptance.
Best regards,
Ervin Goldfain
Dear Ervin,
Are you able to explain the light unflavored meson spectrum? So, what is sigma meson and how do you compute its width? Where does the lowest glueball state lie?
There would be something more to be asked but for the moment this is enough.
So, please, post here your equations and then we will discuss about.
Marco
Dear Marco,
Let me say from the outset that my paper is introductory and is far from being comprehensive. It promotes a less explored view on how to deal with infrared QCD. I focus exclusively on a limited hadron range, from the pi-meson to Y-meson and from nucleons to Lambda baryons. Much more remains to be done in the future to be able to properly answer your questions.
Best regards,
Ervin
Dear Ervin,
If things stay that way, your approach is not helpful. You should answer that questions to be taken seriously as these are matters of everyday experiments at accelerator facilities and something people is trying to understand since a long time.
In order to give you an idea of the importance of all this, the question of the low lying part of the spectrum has involved people as ‘t Hooft and Maiani and is in the agenda of most of the brightest people working in this area. The reason is that an understanding of this implies surely a complete understanding of the whole theory and this is what we want.
So, if you come out claiming that you have got a nice mass formula for a restricted and uninteresting part of the hadron spectrum, I am afraid nobody will stay there listening to you.
Cheers,
Marco
Dear Marco,
Yes, I agree with you that all these questions need to be addressed at some point or another in follow-up papers. But, again, mine is exclusively an introductory research. I do not arrive at a “nice mass formula” as you say in your reply using some speculative, hand-waiving arguments. I start from a different framework and analytic results match experimental data over a good segment of hadron spectrum. I might very well be wrong here but this ought to be intriguing enough to stimulate further developments.
Time will tell.
Take care,
Ervin
Good luck.
Cheers,
Marco
Marco, you picked up another citation rather nicely agreeing with you on gluons today, 0904.2355.
Carl,
Thank you for the link but the right one is
http://arxiv.org/abs/0904.2555
This paper comes from people I met at Montpellier last year at QCD 08 conference. Stephan Narison was the organizer.
Indeed, their computations give strong support to mine.
Marco
[…] are not all the story: An update In a recent post of mine (see here) I have pointed out to you a beautiful paper by Dan Pirjol and Carlos Schat. This paper is now […]
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