Quark confinement potentials -- Feedback requested

[izh-21251]

Hello, everyone... I'm starting a new thread (among numerous others) regarding quark confinement and propose a discussion (in case anyone finds it interesting) on some of my considerations.

As we all know, the idea of confinement consists in forbidding free propagation of free color-chagres, instead keeping them inside color-neutral states -- mesons and baryons. This phenomenological property of quarks is true only at low energies, while at high energy scales (>few 100MeV?) quarks acquire (asimtotic) freedom and well described by perturbative methods.

The very interesting and challenging question is: "How we describe quark interaction at low-E regime?"
In quantum mechanical (i.e. non-relativistic) approach one can suggest some phenomenological quark-quark potantials (like V(r)~ar+br³, etc.) and solve some bound state problems or whatnot.
Another (powerful but rather sophisticated) approach is the lattice QCD. It reached some obviuos successes, but has (IMHO) essentially computing destination.

Is it possible in some effective theory to obtain (effective) multy-quark relativistic potentials for low-energy regime?
I was looking for the answer or some attemts to that, but found nothing.
The one idea could be to perform the transformation (different from usual renarmalization) from bare partons to "clothed" ones, which will account for confinement properties.
The idea was inspired by several works of Weinberg, Greenberg, Schweber, Kazes, Shirokov, Shebeko (http://arxiv.org/abs/nucl-th/0102037), Stefanovich (http://arxiv.org/abs/physics/0504062) and others. What they suggest is an alternative approach to QFT, where renormalization procedure is achieved by special unitary transformation of particle operators. This transformation require that only interaction with non-empty energy shell are allowed between physical particles. This idea is not trivial, but describing it will take too much space...

In case of quark-gluon system, the idea of unitary transformation suggests we require only those interactions that transfrom color-neutral states to color-neutral states. New one-quark states are effectively confined in color-neutral multy-quark states. I assume that is such approach the strong coupling will be effectivelyrenormalized and weaken down, while quark-quark (and multy-quark) potantials will have property of confinement (i.e. diverge as positive power of r) at low energy transfer.
I recited the core of these ideas here: http://arxiv.org/abs/1404.4383

In case anyone finds it interesting or has any comments, I'll be extremely grateful.
If someone consider these ideas essentially empty or incorrect, please, let me know!

Thanks a lot!
Ivan

 

[AndyW]

Hello Ivan,

Thank you for starting this discussion on quark confinement. It is a very interesting and challenging topic indeed. As you mentioned, confinement is a phenomenon that occurs at low energies, where quarks are bound together in color-neutral states such as mesons and baryons. At high energies, quarks behave as free particles and can be described using perturbative methods.

As for describing quark interactions at low energy regimes, there are a few different approaches that have been proposed. One is the quantum mechanical approach, where phenomenological quark-quark potentials can be used to solve bound state problems. Another approach is lattice QCD, which has had some success in describing quark interactions, but is primarily used for computing.

Your idea of using an effective theory to obtain relativistic potentials for low-energy regimes is very interesting. The concept of a unitary transformation to account for confinement properties is also intriguing. I am not familiar with this specific approach, but I will definitely take a look at the articles you have mentioned.

I think it's important to explore different approaches and ideas in order to better understand quark confinement. Your proposal could potentially lead to new insights and developments in this area. Thank you for sharing your thoughts and I look forward to hearing more about your ideas.