Conflicting Teachings concerning Quark confinement

[kmarinas86]

I've heard things from lineraly rising potential to linearly rising force. Since the change is over distance... which is it? If dF/dx is constant, then energy, being the product of force times distance, would increase at twice the exponential. That would mean that potential does not rise linearly with distance, assuming that there is only one correct definition of potential (which I think probably isn't the case).

I just found a Wikipedia article which makes this apparent contradiction more visible:

http://en.wikipedia.org/wiki/Colour_confinement

Colour confinement (often just confinement) is the physics phenomenon that colour charged particles (such as quarks) cannot be isolated. The quarks are confined with other quarks by the strong interaction to form pairs or triplets so that the net colour is neutral. The force between quarks increases as the distance between them increases, so no quarks can be found individually.

The reasons for quark confinement are somewhat complicated; there is no analytic proof that quantum chromodynamics should be confining, but intuitively confinement is due to the force-carrying gluons having colour charge. As two electrically-charged particles separate, the electric fields between them diminish quickly, allowing electrons to become unbound from nuclei. However, as two quarks separate, the gluon fields form narrow tubes (or strings) of colour charge. Thus the force experienced by the quark remains constant regardless of its distance from the other quark. Since energy goes as force times distance, the total energy increases linearly with distance.

I see this problem in many places, even among university material, not just Wikipedia. Can anyone solve this condundrum?

 

[kmarinas86]

Somebody has raised this issue before, but not everything I wanted to be addressed was, so I made a response:

http://en.wikipedia.org/wiki/Talk:Colour_confinement#mistake

== mistake ==

Something is wrong here:

> Thus the force experienced by the quark remains constant regardless of its distance from the other quark.

> The force between quarks increases as the distance between them increases, so no quarks can be found individually.

One of these statements is wrong. Which one?

:They're both correct at different scales. As quarks separate, the force between them initially increases and then becomes constant. Could be worded more clearly perhaps. -- [[User:Xerxes314|Xerxes]] 22:12, 13 December 2005 (UTC)

::I've heard that, at some range, the attractive force between quarks increases linearly with distance (i.e. <math>dF/dx=constant</math>). However, when that is true, that would mean that force*distance would be quadratic in nature, like elastic potential energy (i.e. <math>.5kx^2</math>). In contradiction to this, there is the coloumb+linear potential, which does not appear to have the property of linearly increasing force. http://en.wikipedia.org/wiki/Quarkonium#QCD_and_quarkonia In fact, the decreasing of the slope in the line graph of such a potential, suggests to this layman that force decreases with distance (which is obviously wrong). http://images.google.com/images?q="cornell+potential"+OR+"quark+potential"+OR+"qcd+potential" Somebody please clarify this...~~~~

 

[Meir Achuz]

"The force between quarks increases as the distance between them increases, so no quarks can be found individually."

That statement is just a careless mistake, typical of Wikipedia.
The rest of the article is reasonable, but the statement
"there is no analytic proof that quantum chromodynamics should be confining," has to be kept in mind.

 

[Meir Achuz]

I should have mentioned that linear (for the potential) confinement is not the only guess. Many people use a bag model or SHO (force increasing llinearly) without much justification other than ease of calculation.
Most quark model predictions are not sensitive to the confinement mechanism, or even to confinement at all, so it is still an open question.

 

[Haelfix]

Keep in mind we are dealing with a many body calculation, including nontrivial radiative corrections. The form of the potential is thus largely intractable, outside simple analysis of basic diagrams, accessible only at certain regimes. Worse, perturbation series will completely break down at most energies of interest, and so we can only hope to calculate short range potentials b/c of asymptotic freedom.

Already you can see terms that give contributions both to repulsive as well as attractive behaviour (for instance quarks in the color singlet configuration attract strongly, whereas when they are in the octet its repulsive). Naively you can calculate this and see you will get short range potential not unlike the coulomb potential.

You can model long range potentials however you want, but experiment gives results that are too coarse to probe exact details on its structure yet (that will need to come from theory dealing with the many body problem, as well as significant progress in lattice qcd)