How Can Lone Quarks Exist in a Color-Neutral Quark-Gluon Plasma?

[The_Duck]

I think this is one of the most interesting questions to come up on PF in some time. It's an open question, one that has not yet been satisfactorily resolved, and one that deserves more attention.

If you have not already, I encourage you to take a look at the paper on this subject that I referenced, "Quark Gluon Plasma Paradox" by Dariusz Miskowiec. He points out an apparent contradiction between our belief that isolated quarks are impossible and our present concept of a Quark-Gluon Plasma as an uncorrelated mixture of quarks and gluons. During the hadronization of a QGP of macroscopic extent, the formation of isolated quarks would seem unavoidable without violation of causality.

I think that the argument in the linked paper does not work. The paper imagines that it is possible to split a ring of QGP in two places, giving two chunks of QGP both with nonzero net color charge. I think this will never happen; any color non-neutrality will be corrected before the two disjoint chunks of QGP separate by more than about 1 fm.

Here's why I think so. If each chunk of QGP has nonzero net color charge then there is a color-electric field stretching between them. This is unavoidable; by Gauss's law each chunk is the source of a color-electric field. This color field will take the form of a narrow flux tube connecting the two chunks. Its energy will grow linearly with the length of the gap between the two non-neutral chunks until at a length of order 1 fm a quark-antiquark pair will be created, snapping the flux tube and neutralizing both chunks. It should happen in the same way as when you try to pull apart a quark-antiquark pair.

I think a similar thing will happen in the scenario considered in the original post of this thread. No matter how you set things up, color non-neutrality will be corrected before there is any color charge separation over a length scale longer than 1 fm. The reason is that color charges separated by a macroscopic distance would set up a color field with a truly stupendous amount of energy (compared to quark masses or the QCD energy scale). Restoring color neutrality by creating a quark-antiquark pair costs less energy than letting the color charges separate by more than 1 fm.

 

[Bill_K]

I think that the argument in the linked paper does not work. The paper imagines that it is possible to split a ring of QGP in two places, giving two chunks of QGP both with nonzero net color charge. I think this will never happen; any color non-neutrality will be corrected before the two disjoint chunks of QGP separate by more than about 1 fm.

That isn't what he does. He does not simply pull it apart. He cools it.

I break the QGP ring at one point by allowing the QGP to expand and cool such that the hadronization starts there.

He cools it in two widely separated places, and does nothing more. He let's the QGP decide for itself how to hadronize. Locally there appears to be no problem. But depending on exactly how it chooses to hadronize, color non-neutral parts may or may not have been produced, and without superluminal information transfer, the QGP will not know until much later whether or not color neutrality has been violated.

 

[nikkkom]

I think that the argument in the linked paper does not work. The paper imagines that it is possible to split a ring of QGP in two places, giving two chunks of QGP both with nonzero net color charge. I think this will never happen

Even if the ring is one light-year in diameter, and the locations of the split are on the opposite points on the ring? That would need superluminal transfer of information.

I think a similar thing will happen in the scenario considered in the original post of this thread. No matter how you set things up, color non-neutrality will be corrected before there is any color charge separation over a length scale longer than 1 fm.

Again, in my scenario unpaired quarks *start out* with vastly larger separations. I don't pull them apart. They are already apart by light-days. Correction can't happen faster than light, unless you allow superluminal information transfer.

 

[Vanadium 50]

Again, in my scenario unpaired quarks *start out* with vastly larger separations. I don't pull them apart. They are already apart by light-days.

And this requires absurd energies. The difference in energy between correctly and incorrectly paired energies from just those three quarks is about 10³³ MeV - 10²⁰ joules.

Long before you got to this point, there is enough energy to reheat and re-pair the medium.

 

[nikkkom]

And this requires absurd energies. The difference in energy between correctly and incorrectly paired energies from just those three quarks is about 10³³ MeV - 10²⁰ joules.

Long before you got to this point, there is enough energy to reheat and re-pair the medium.

Did you read the paper, in particular, the setup described there, where QGP is in the shape of giant torus one light-year across?

Do you claim that such torus is physically impossible?

Because if such torus is possible, pinching it in two opposite locations inevitably leads to color imbalance.

What basis is under your claims about energies of three unpaired quarks? I though QCD methods aren't refined yet to make predictions in the limit of low energy?

 

[Vanadium 50]

Well, you were wrong. The strength of the QCD flux tube is well known: 160,000 Newtons.

 

[The_Duck]

That isn't what he does. He does not simply pull it apart. He cools it.

He cools it in two widely separated places, and does nothing more. He let's the QGP decide for itself how to hadronize. Locally there appears to be no problem. But depending on exactly how it chooses to hadronize, color non-neutral parts may or may not have been produced, and without superluminal information transfer, the QGP will not know until much later whether or not color neutrality has been violated.

My argument is independent of how the QGP is separated into two chunks. It doesn't matter that this is accomplished by cooling rather than mechanical pulling, or whatever. If you have two separated color charges, there is necessarily a color field between them by Gauss's law. Gauss's law is satisfied at all times with no need for superluminal information transfer. This color field will have enough energy to pair-produce and neutralize both chunks once it stretches across about 1 fm.

What basis is under your claims about energies of three unpaired quarks? I though QCD methods aren't refined yet to make predictions in the limit of low energy?

Lattice QCD has reached sub-percent precision for a number of observables. Among these is the quark-antiquark potential, which is the energy of the flux tube between a "free" quark and a "free" antiquark. I suspect similar calculations have been done for the three-quark potential, but the quark-antiquark potential is simpler.

 

[nikkkom]

Well, you were wrong. The strength of the QCD flux tube is well known: 160,000 Newtons.

You aren't answering the question.

Do you really think that large toroid-shaped QGP is physically impossible?

 

[mfb]

A toroid-shaped QGP would need nicely balanced color charges, otherwise it is not (or does not stay) empty "inside".

 

[nikkkom]

My argument is independent of how the QGP is separated into two chunks. It doesn't matter that this is accomplished by cooling rather than mechanical pulling, or whatever. If you have two separated color charges, there is necessarily a color field between them by Gauss's law. Gauss's law is satisfied at all times with no need for superluminal information transfer. This color field will have enough energy to pair-produce and neutralize both chunks once it stretches across about 1 fm.

What you somehow unwilling to grasp is that the "naked" color charges in these thought experiments are already separated by vastly more than 1 fm by the way experiment is set up.

Pulling any number of quark-antiquark pairs out of the vacuum can't quickly neutralize anything in this setup, since these pairs are color-neutral.

The fastest way for these quarks to become color neutral is to accelerate towards each other and form a baryon. Since they can't move faster than light in any case (regardless how strong color force is), it means they will be observable as color-charged objects for prolonged period of time.

 

[nikkkom]

A toroid-shaped QGP would need nicely balanced color charges, otherwise it is not (or does not stay) empty "inside".

It *is* perfectly color balanced in the initial configuration. Did you not read the peper?

 

[The_Duck]

What you somehow unwilling to grasp is that the "naked" color charges in these thought experiments are already separated by vastly more than 1 fm by the way experiment is set up.

OK, let's consider the toroid thought experiment. Suppose the toroid gets split so that neither chunk of QGP is color-neutral. What do you think the color field configuration looks like when each chunk has cooled enough that the separation between the two chunks of QGP has grown to, say, 1 meter?

Pulling any number of quark-antiquark pairs out of the vacuum can't quickly neutralize anything in this setup, since these pairs are color-neutral.

I don't agree. Color-neutralization via pair-production works very quickly. For simplicity let me consider the quark-antiquark case rather than the three-quark case. Suppose we have a red quark (R) and an anti-red antiquark (r) separated by 2 fm or so. There is a flux tube of color field connecting them:

R===========r

(the === is the flux tube). From this state it is energetically favorable to produce another Rr pair and go to this state:

R=r_________R=r

(the _'s are just spacing). Each color charge has been neutralized. But suppose we somehow stretched the flux tube to 10 fm or so without this happening:

R=======================================================r

Would it take longer to neutralize these color charges? No. It would be energetically favorable to produce a number of Rr pairs and go to this state:

R=r_________R=r_________R=r_________R=r_________R=r_________R=r

and this process would take about the same amount of time as in the case of a 2 fm separation. In fact, because of pair production the flux tubes never grow longer than about 1 fm.

 

[nikkkom]

OK, let's consider the toroid thought experiment. Suppose the toroid gets split so that neither chunk of QGP is color-neutral.

"Grown"?
Did you read the paper?
In the setup described there, separation doesn't start small and then increase. By the geometry of the experiment, color-charged objects form with already huge - macroscopic - separations.

What do you think the color field configuration looks like when each chunk has cooled enough that the separation between the two chunks of QGP has grown to, say, 1 meter?

I think that field between each chunk at this moment is a normal vacuum and a lot of newly formed hadrons frying through it. Locally, there is no mechanism to know that these two chunks, on the whole of their 1 light-year sizes, may be color-imbalanced. In particular, there are no gluon flux tubes between chunks at this moment.

I don't agree. Color-neutralization via pair-production works very quickly. For simplicity let me consider the quark-antiquark case rather than the three-quark case. Suppose we have a red quark (R) and an anti-red antiquark (r) separated by 2 fm or so. There is a flux tube of color field connecting them:

R===========r

(the === is the flux tube).

The key is that flux tube can't form instantaneously. It can form, at max, as fast as light crosses the distance between these two particles.

If the distance is not 1 or 2 or 10 *fm*, but 10 *light-days*, physical observers will have ample time to observe what essentially is an isolated color charge.

I will repeat it again what I said in my first post: I *understand* how confinement works with *already formed* hadrons. There is no need to explain it to me again. Try to understand how thought experiments described here are different from already formed hadrons case before getting on your high QCD horse.

 

[nikkkom]

Let me describe it with electromagnetic analogy.

Let there be a straight insulated metal wire one light-hour long in an empty space.
It is perfectly electrically neutral.
You are in a spacecraft near its middle point.

Your task: cut the wire into two pieces, each of which is perfectly electrically neutral, in less than 30 minutes.

You are allowed to cut the wire, and then transfer electrons from one half to another to achieve this (i.e. you aren't required to make a "perfect cut" in one operation).

You are allowed to have any devices which measure electric and magnetic fields. You can situate them along the entire length of the wire, as you see fit.
However, you can't have a device which tells you "this half of wire has extra (or missing) electrons" in less than 30 minutes (since such device is physically impossible).

I posit that you can't reliably achieve this task. At best, you can achieve it by chance.

 

[Vanadium 50]

before getting on your high QCD horse.

And we're done here.