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

[nikkkom]

I get the idea of confinement, and how it is impossible to separate a lone quark from a baryon: it needs more energy than creation of two more quarks, so the latter happens first, and you end up with having created a (color-neutral) meson.

However, I don't see what prevents free quarks from appearing out of primordial quark-gluon plasma:

Whereas quark-gluon plasma is color-neutral on average, when it cools and "quenches" into baryons, the quarks group into color triplets *randomly*.

Even if a volume of cubic meter (or a cubic light year) of q-g plasma is strictly color neutral (it is possible to pair up (or is it triple-up?) all quarks into baryons with no leftovers), it is extremely unlikely quarks would manage to do that *randomly*.

Imagine that all of quarks successfully combined into baryons except three quarks (one red, one green, one blue) because there is small problem: they are on the order of 100 light days apart from each other. Why? Because quarks aren't sentient, they can't "plan" how to carefully pair up to avoid such a fk-up.

The cubic light year is still perfectly color neutral as a whole. However, it contains three quarks which for all practical purposes are lone quarks.

What am I missing?

 

[phinds]

Hm ... that's an interesting question. I have no idea but your logic seems sound to me. On the other hand, I remember that even Joyce had them in triplets

 

[ViperSRT3g]

oooo very curious as to the possibilities of this question. *follows thread for answers*

 

[PhotonicBoom]

You might find this interesting

https://en.wikipedia.org/wiki/Quark%E2%80%93gluon_plasma#General_introduction

If I understand it correctly, the theory predicted free quarks and gluons but in reality they couldn't do it in modern accelerators due to some ''remnant effects of confinement'', which I guess are still unknown?

 

[mfb]

As long as the quarks are not paired, you still have a plasma. A local imbalance of quark colors (where does it come from?) would quickly get canceled by color flow from other parts of the plasma.

 

[Bill_K]

A local imbalance of quark colors (where does it come from?) would quickly get canceled by color flow from other parts of the plasma.

But "quickly cancelled" does not make "color imbalance" and "color flow" any less interesting!

 

[dauto]

The thing that causes quark confinement is the fact that the attractive force between unpaired (un-tripled) quarks does not drop with the distance. That means that even though quarks are not sentient, they can find each other over extremely large distances. There will be no f--- up.

 

[Bill_K]

The thing that causes quark confinement is the fact that the attractive force between unpaired (un-tripled) quarks does not drop with the distance. That means that even though quarks are not sentient, they can find each other over extremely large distances. There will be no f--- up.

Perhaps, but I remain unconvinced. We're talking about such a high-energy regime for QCD that there's no supporting evidence. I don't dispute that color differences will quickly be resolved, but on a short enough time-scale there may be some interesting things happening.

 

[mfb]

I don't dispute that color differences will quickly be resolved, but on a short enough time-scale there may be some interesting things happening.

Maybe - but nikkkom asked about the low-energetic regime where hadronization happens.

 

[Vanadium 50]

The whole premise is off. Consider the following 1D argument with magnetic poles:

N (S N) (S N) (S N) (S N) (S N) (S N) (S N) (S N) S

you could also say "Look! It's leaving two monopoles unpaired far away!"

But what would actually happen is a re-paring.

[N S] [N S] [N S] [N S] [N S] [N S] [N S] [N S] [N S]

 

[nikkkom]

The whole premise is off. Consider the following 1D argument with magnetic poles:

N (S N) (S N) (S N) (S N) (S N) (S N) (S N) (S N) S

you could also say "Look! It's leaving two monopoles unpaired far away!"

But what would actually happen is a re-paring.

[N S] [N S] [N S] [N S] [N S] [N S] [N S] [N S] [N S]

Yes. But imagine that the line in your pic is very long. Such a re-pairing still cannot propagate faster than light - the particles do not magically know they need to re-pair, and how exactly they need to do that. (edit:) It is analogous to the movement of an electron and a somewhat distant hole in the semiconductor. Holes definitely don't move faster than light.

As long as it did not complete, you will have "free" quarks.

 

[Jilang]

I thought quarks were the ends of strings so couldn't exist on their own. It would be like my shoe lace only having one end! Is this not right?

 

[Bill_K]

This question is discussed (but not resolved!) in this paper. (The author is a member of the ALICE team)

The problem, which does not manifest itself during creation of QGP but only during the transition back to hadrons, consists in the fact that simultaneous hadronization in regions separated by space-like intervals must in some cases lead to single quarks left at the borders between hadronization domains because there is no way to synchronize this process without violating causality.

To me, the third of his possible solutions ("hadron resonance matter") sounds the most likely.

 

[phinds]

I thought quarks were the ends of strings so couldn't exist on their own. It would be like my shoe lace only having one end! Is this not right?

Strings are still a mythical beast, believed by theoretical physicists to exist but never actually seen in the wild, much less in domestication.

 

[dauto]

Strings are still a mythical beast, believed by theoretical physicists to exist but never actually seen in the wild, much less in domestication.

Jilang is not talking about the same kind of string you're thinking about. What Jilang is talking about is a filament of quark-gluon plasma that connects the quarks keeping them from becoming free quarks. You're thinking about string theory. Those are two completely different beasts.

 

[phinds]

Jilang is not talking about the same kind of string you're thinking about. What Jilang is talking about is a filament of quark-gluon plasma that connects the quarks keeping them from becoming free quarks. You're thinking about string theory. Those are two completely different beasts.

Ah ... I didn't realize that. Thank you.

 

[ChrisVer]

But still, the pairing of the magnets is not so weird even if the sides are not spacelike separated. I mean the N and S parts don't connect with each other but with their neighbors... So the endpoint S doesn't look at the other endpoint N, but with its neighbouring N... In order to fill in the separation for a compact thing, you will have to fill in the distances accordingly and you will end up with N... am I wrong?

As for strings, that's the initial use of string theory in physics... (if someone wants to check it out, he can have a look at Prof. G. t'Hoft 's lecture notes on string/superstring theory)

 

[Bill_K]

But still, the pairing of the magnets is not so weird even if the sides are not spacelike separated. I mean the N and S parts don't connect with each other but with their neighbors... So the endpoint S doesn't look at the other endpoint N, but with its neighbouring N... In order to fill in the separation for a compact thing, you will have to fill in the distances accordingly and you will end up with N... am I wrong?

The magnet example is misleading. If it were just a conceptual pairing, the N at the end could easily be regarded as paired with its neighbor. But what we have is a phase transition, from quarks to hadrons. A finite amount of energy is involved in the formation of each hadron, taking a finite amount of time. To "re-pair" the quarks, you have to dissolve and reform many hadrons.

As for strings, that's the initial use of string theory in physics... (if someone wants to check it out, he can have a look at Prof. G. t'Hoft 's lecture notes on string/superstring theory)

The strings of String Theory are not involved. A popular and simple model of quark confinement describes it as the formation of gluon tubes, explaining why the potential energy holding a pair of quarks together grows linearly with distance. But this idea must be understood as a model only, and it relates only to confinement. In a quark-gluon plasma, the quarks are deconfined.

 

[Vanadium 50]

Mathematically, a quark looks more like a magnetic pole than an electric charge: because the color field is strong and charged, a quark acts more like a boundary condition than an actual generator of the charge. It's often a better way to gain insight on behavior than the "color charge" model.

Many-body physics was mentioned, and this is often used to model heavy ion collisions (sometimes in mutually incompatible ways). To take the magnetic picture I discussed, the lower line has both lower energy and higher entropy. (In one dimension) You have the same thing in QCD - re-pairing the quarks has both lower energy and higher entropy. So when a QGP freezes out into hadrons, the phase transition will not leave you with free quarks.

 

[nikkkom]

Mathematically, a quark looks more like a magnetic pole than an electric charge: because the color field is strong and charged, a quark acts more like a boundary condition than an actual generator of the charge. It's often a better way to gain insight on behavior than the "color charge" model.

Many-body physics was mentioned, and this is often used to model heavy ion collisions (sometimes in mutually incompatible ways). To take the magnetic picture I discussed, the lower line has both lower energy and higher entropy. (In one dimension) You have the same thing in QCD - re-pairing the quarks has both lower energy and higher entropy. So when a QGP freezes out into hadrons, the phase transition will not leave you with free quarks.

This still does not explain how quarks in a large volume would magically pick a pairing which does not leave even a single trio of spatially separated unpaired quarks. The "correct" pairing is locally indistinquishable from "incorrect" one (apart from the locations of "leftover" quarks).

Here's an illustration in 1D monopole model. Initial state is a very long but finite line of monopoles. We are looking at microscopic part of it:

...NSNSNSNSNSNSNSNSNSNSNSNSNSNSNSNSN...

Temperature falls to to recombination threshold, particles start to pair randomly, some left unpaired:

...(NS)(NS)(NS) N (SN)(SN)(SN)(SN) S (NS)NS(NS)(NS)(NS)(NS) N (SN)(SN)...

This is not lowest energy state, some local reshuffling happens to eliminate unpaired ones:

...(NS)(NS)(NS)(NS)(NS)(NS)(NS)(NS)(NS)(NS)(NS)(NS)(NS)(NS)(NS)(NS)(N...

All is good, eh? Well, not really, if the global picture is like this! -

S...(NS)(NS)(NS)(NS)(NS)(NS)(NS)(NS)(NS)(NS)(NS)(NS)(NS)(NS)(NS)(NS)(N...N

This particular choice of "locally correct" pairing is in fact the wrong one: globally, it will leave, at a minimum, two unpaired particles.

 

[Vanadium 50]

This is the same question as "how does one atom in a forming crystal know about the position of another atom a million cell spacings away? The answer is that even locally the "right" pairing has lower energy than the wrong one.

 

[nikkkom]

This is the same question as "how does one atom in a forming crystal know about the position of another atom a million cell spacings away? The answer is that even locally the "right" pairing has lower energy than the wrong one.

You actually confirm my point: crystals of macroscopic sizes aren't perfect, they have unfilled vacancies and interstitial atoms as analogues of what I describe.

On another note, if crystal grows slowly, there is an obvios syncronization mechanism for new atoms to take the correct locations on the growth front. If crystallization would happen quickly in a large volume, crystals will be small and randomly oriented - not a lowest energy state, clearly.

 

[Vanadium 50]

You actually confirm my point

Fine. Believe whatever the heck you want. You still don't get free quarks, for precisely the reasons I describe: when the phase transition is occurring, the right pairing is favorable.

 

[ChrisVer]

perfect or not (crystals) we still haven't found an isolated magnetic monopole (unfortunately)

 

[Nugatory]

You actually confirm my point: crystals of macroscopic sizes aren't perfect, they have unfilled vacancies and interstitial atoms as analogues of what I describe.

You're pushing V50's analogy to and beyond the breaking point. Defects in a macroscopic crystal would quickly disappear if the potential barrier between the state with the defect and the lower-energy state without the defect were lower relative to the energy difference.

The interesting question is not why quarks pair up properly; it is why crystals don't form properly.

 

[Bill_K]

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.

He proposes three possible resolutions, the first two of them IMO rather unlikely. (a) instantaneous communication ala quantum entanglement (!) and (b) restriction of hadronization to the surface of the QGP rather than the volume (so that a large QGP must evaporate around the edges, thus taking large amounts of time to fully hadronize).

The third one (c) is the one that to me makes the most sense, namely that a QCP is not really a random collection of quarks after all, rather it's a collection of increasingly large colorless pieces ("hadron resonance matter") so that when the QCP is cooled or decompressed, it will split only into colorless parts, thus avoiding the possibility of creating quarks that are isolated or other colored fragments. Our knowledge of the QGP state is still rather tentative - it's described to be less like a gas and more like a nonviscous liquid. The chain of reasoning that leads to the paradox must be broken somewhere, and I think the QGP itself being the weakest link, that is where we need to modify our understanding.

 

[nikkkom]

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.

I read the paper. The author's final opinion is that q-g plasma isn't really a plasma, it has "baryons" of sorts pre-paired.

I find it physycally nonsensical. Baryons have definite size. If matter is compressed sufficiently, each baryon inevitably has less space to occupy than its volume. At this point, baryons aren't separate particles anymore - it's a soup of quarks now.

How about another possible resolution? - "free quarks *can* exist". What's the problem with such postulate? Yes, such a state will probably be massive due to large quantum corrections, but it may be finite.
I think QCD isn't precise enough to claim with certainty that a free quark has infinite and non-renormalizable mass and thus is not possible?

 

[ChrisVer]

what's the definite size of a Baryon? you can drag a baryon and it will split

 

[mfb]

How about another possible resolution? - "free quarks *can* exist". What's the problem with such postulate? Yes, such a state will probably be massive due to large quantum corrections, but it may be finite.
I think QCD isn't precise enough to claim with certainty that a free quark has infinite and non-renormalizable mass and thus is not possible?

Free quarks of different colors would feel a very strong attraction even over a large distance - so strong that they are not "free" any more.

This might take a while if the QGP starts with a diameter of 1 light year, but I think "in the worst case" you just need more time for hadronization. Alternatively, one of (a) (b) (c) from the paper Bill_K linked applies, then this is not even an issue.

 

[Bill_K]

I read the paper. The author's final opinion is that q-g plasma isn't really a plasma, it has "baryons" of sorts pre-paired.
I find it physycally nonsensical. Baryons have definite size. If matter is compressed sufficiently, each baryon inevitably has less space to occupy than its volume. At this point, baryons aren't separate particles anymore - it's a soup of quarks now.

Your physical intuition may need updating. The author's conclusion is that the QGP is not just a soup of quarks. And in fact that naive idea has been ruled out by experiment at RHIC and CERN. The QGP is shown to be a liquid with close to zero viscosity. The QGP has structure, i.e. long-distance correlations. Quarks are not confined to particular baryons, they slide over one another and change partners, but do not simply fly about at random like molecules in a gas. Recall that the viscosity of a gas is not zero.

How about another possible resolution? - "free quarks *can* exist". What's the problem with such postulate?

Astronomical observations would probably be able to rule it out.

 

[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?