Connes’ approach has an important application in physics as the author and his collaborators were able to show that the Standard Model of elementary particles can be completely derived in terms of noncommutative geometry. There has been some tension due to the observed mass of the Higgs particle that did not seem to fit the prevision by Connes et al. but so far, as I heard directly from him, this point seems to be fixed. Here would help some expert comments from people well aware of this matter.

I used the Connes’ ideas mostly in the realm of non-relativistic quantum mechanics as you can judge by my paper but the insights they contain are wide-ranging and I hope more success to them. Surely, they represent a sound starting point to approach quantum gravity but most as to be said yet.

Cheers,

Marco

]]>I am not a physicist but interested in the fundamental questions. Most of NCG is beyond my skills but I have tried to understand parts of it. I agree that the work by Connes is unique in that it seems to capture fundamental aspects of the SM. I wonder why this work does not get more attention. Maybe the failure of string theory will make alternative approaches more popular.

]]>Your question is clearly off-topic for the post but surely on-topic for the blog. Some readers could miss both it and my answer. Anyhow, I will try to yield an answer from my take about the matter.

As you may know, if pure Yang-Mills theory is concerned (just glueballs and nothing else in the world), the propagator I have found addresses correctly the values obtained on the lattice for the states of the theory. I addressed the question here and was on 2008 in Montpellier. My recent exact solution of the theory keeps the identical spectrum. If in the world quarks would not exist we will be happy with this and can claim to have found glueballs. Unfortunately, things do not stay this way and a pure Yang-Mills theory is not realized in nature. Yang-Mills theory, as any other known gauge theory, comes always coupled to fermion fields and for a good reason. A Yang-Mills theory appears to behave trivially in a low-energy limit. Interaction with quarks makes it not trivial as also happens to the Higgs field (siblings as they are). This fact is not yet accepted by the community even if all the evidences take to this. Most colleagues just claim that the definition of the running coupling in the low-energy limit is not an assessed matter and can hide a non-trivial infrared fixed point just in a new definition. As recently shown by Deur (see here), the fact that the theory shows a trivial propagator but is confining yet is due to the running coupling. Deur just shows that a scalar field theory is able to recover the Cornell potential obtained in lattice computations in this way! So, the idea of mapping between scalar fields and Yang-Mills theory is correct as already proved elsewhere but this evidence is definitely striking.

So, what happens when quarks are introduced in this scenario? The low-energy limit of QCD turns out to be a Nambu-Jona-Lasinio (NJL) model. In a very low-energy limit, just the lowest excitation of the Yang-Mills field enters and produces the meson currently observed in accelerator facilities and marked as f0(500) on PDG. This is a glueball but NJL says us that it mixes up with quarks. This fixes correctly the mass (see here). Going to higher energies, also the higher excited states computed in a pure Yang-Mills theory come into play and, yes, again they will mix up inexorably with the quark fields. But now we can be able to identify them because these computations can be accomplished. I have to confess that I have not done them and I am not particularly interested in doing this.

About NJL I would like to point out an interesting argument. This theory is known to be non-confining. But if you check the states of the theory they are all bounded states. The question is, yes the theory is not confining, but what if it generates just bounded states of quarks in its spectrum?

Ciao,

Marco

]]>I’d love to hear what you have to say about why glueballs, one of the earliest prediction of QCD, have been so elusive experimentally.

The familiar pat explanations that glueballs are hard to see due to mixing with quarkonia doesn’t seem to be holding up. At a minimum, it seems as if glueballs are suppressed relative to naive expectations about their branching fractions in decays, by some unknown mechanism, even if they are not outright non-existent.

For example, “oddballs” (glueballs which can’t mix with quarkonia) ought to be possible to seen in current experiments, but are not, and it appears that most or all scalar and tensor mesons can be explained a “molecules” of vector mesons. See my post & comments at http://dispatchesfromturtleisland.blogspot.com/2016/11/glueballs-still-elusive.html

Experiment seems to increasingly support that hypothesis that glueballs don’t exist or are highly suppressed, but nobody seems to know why. Is there any elegant way that QCD could be modified to have this rifleshot effect of preventing or suppressing glueballs without screwing up the rest of the remarkably successful edifice of QCD?

Indeed, is anyone making BSM proposals for modifications of QCD at all? There are lots of experimental anomalies in QCD compared to the rest of the Standard Model (many probably due to flawed theoretical modeling of approximations of pure QCD), yet the amount of BSM QCD proposals in arXiv seems negligible compared to almost any other part of the Standard Model or General Relativity.

]]>Let us wait them to be published as planned, and the heroic published to benefit from his courage. ]]>