# Gluon-quark-string interaction

We know "asymptotic freedom" says that the interaction between particles, such as quarks, becomes arbitrarily weak at ever shorter distances
and stronger with range

The quarks are connected like being on a rubber band: (string)

I have the following questions:

1) While the quarks get more seperated on their stretching string,
can you say (theoretical) that this string is really getting thinner,
or getting narrower, just like real elastic?

2) If you compare, theoretical, the situation of 1) increasing distance
and 2) decreasing distance between quarks, what can you say about
the amount of energie in between them:

a) Does this amount of energie depend on the number of interactions
between the quarks and the gluons, and when the answer is yes, which are the most important? And when no, where does it depend on really?

And when the answer is Yes, that means less reactions when the distance get's shorter. But at shorter distance the thermal pressure will rise enormously
Can we say that this thermal pressure "from outside" has no effect on the quarks?
Has this pressure effect on something else? ( I always learnt: more pressure
means more particle-movement, but the quarks seem to move in total
freedom, does their movement only depend on their own gluon-string-energy?)
Cn we maybe say that the energy on the quantum-gluon-elastic
is negative related with the pressure outside?

Kind regards, maxmax.

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maxmax said:
We know "asymptotic freedom" says that the interaction between particles, such as quarks, becomes arbitrarily weak at ever shorter distances
and stronger with range

The quarks are connected like being on a rubber band: (string)

I have the following questions:

1) While the quarks get more seperated on their stretching string,
can you say (theoretical) that this string is really getting thinner,
or getting narrower, just like real elastic?

2) If you compare, theoretical, the situation of 1) increasing distance
and 2) decreasing distance between quarks, what can you say about
the amount of energie in between them:
Euuh string ???

Let me explain to you how quarks interact with each other by exchange of gluons and pions (for the residual strong force). A quark and and anti-quark have a socalled "colour" electric field between them, going from one quark to the other (just like two charged particles). When this quarkpair is placed into a magnetic field, the dual Meissner-effect will occur. this means that the magnetic field lines will circle around the electric field which leads to a constraint of the electric field lines. Basically the electric field is reduced to a very narrow tube (the flux-tube) that connects the two quarks along which a linear potential describes the interaction between the quarks. This potential needs to be linear because of asymptotic freedom. The closer the quarks are together, the more "stable" the quark-configuration becomes. This is the confinement. This does NOT mean that quarks are very close together. No, because this linear potential becomes dominant only in the long range where the strong force is indeed very strong. So basically, this potential means that in the long range (great distances) it will become more difficult to tear the quarks apart. This is quark-confinement.

Why the long range ??? Well, great distances correspond to low energies and the big "mystery" is that in "normal" vaccuum conditions (this is low energy-scale) the quarks are more and more difficult to tear apart. At higher energy-scales the strong force becomes weaker and thus quarks are easier to separate.

When two quarks (at low energy-scales or in the socalled long range) are pulled away from each other the linear potential rises and thus energy rises. At some point this energy will become so big that it is enough to create two new quarks out of the vaccuum. So, at some point the original fluxtube gets cut off and the available potential energy is used for a pair-creation. The result is two quarkpairs (the original one and the new one) with a lower potential energy each (they are closer together then the length of the original "stretched" flux tube). The dimensions of the fluxtube can be modified by implementing external light quarks. Even so, these external quarks can stretch the fluxtube of a static quark anti-quarkpair , following the above description. This is the socalled screening effect. A distortion of a given physical situation by the incorporation of extra "surrounding" particles. There is a nice analogon to explain this better. Suppose you wanna study the electric field between some positive and negative particle. Now we insert extra charged particles around this pair. The extra charges will influence the electric field between the two original particles, due to polarization. So basically, the extra particles disturbe the original physical state.

An other way to modify this fluxtube length is by replacing the vaccuum by some dielectric that influences electric and magnetic fields. In QFT this effect is expressed by the polarization-insertion.

regards
marlon

There are still some points I can't see explained explicite in "popular literature"
Maybe my questions are not relevant, or are the answers hidden in formula's
for insiders?

We do know 3 quarks make up a Baryon.
I never hear about the number of gluons

1) Suppose we could "freeze" a picture of what is happening in this Baryon.

a) How many gluons would we see at work simultanously;
Does the theorie give answer to this, I do suppose there is a maximum or minimum, somewhere between 0 and 3, and does this amount relate with distance?

When the strong interaction force gets weaker (and the range is shortening), and we would "freeze" the same Baryon-picture:

b) will we see the same amount of gluons? Or less, or the same?

c) Will we see less interactions between quarks and gluons?
(Cause I always read that these interactions make up the strong force)

d) will we see less interactions between gluons in between?

2) I do suppose that when 2 gluons are interacting, there is no direct influence on the strong interaction force, is that correct?
(maybe very clear to you, but never made explicite sure in the texts I did read)

regards, marcel, amsterdam

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The usual expression for the interior of a nucleon (proton or neutron) is "Sea of gluons". Asking how many gluons is like asking how many photons in a beam of light. Lots! Skillions!

Gluons attact and repel quarks, but they also attract and repel each other, which makes their interactions very complicated and hard to model mathematically.

maxmax said:
We do know 3 quarks make up a Baryon.
I never hear about the number of gluons
Both of them have a distribution of probability, generally parameterized with respect to the so-called "momentum fraction". In a referential in which the Baryon moves with infinite speed, all the constituents (called "partons" in this context = quarks of all sorts + gluons of all sorts) share a certain amount of the total momentum. This gets easily tricky.
1) Suppose we could "freeze" a picture of what is happening in this Baryon.

a) How many gluons would we see at work simultanously;
Does the theorie give answer to this, I do suppose there is a maximum or minimum, somewhere between 0 and 3, and does this amount relate with distance?
You would see infinitely many of them !
More precisely : from far away (large distance, large scale in length) you will see none. When you get closer (smaller scale in length) you will see more and more, ad infinitum.
When the strong interaction force gets weaker (and the range is shortening), and we would "freeze" the same Baryon-picture:

b) will we see the same amount of gluons? Or less, or the same?
Better question ! As I said : you will see more at short range. This is the same for quarks by the way : the distribution's most probable value will be around 1/3 (for typical scale, of the order 1/10 of the Baryon "size") which is interpreted as the fact that there are 3 valence quarks. But there is a whole continous distribution with respect to the momentum fraction. When the scale of the observation goes down in length (up in energy) this distribution will blow up at low momentum fraction : by looking very close, you will see more and more quarks carrying a very small fraction of impulsion.
c) Will we see less interactions between quarks and gluons?
(Cause I always read that these interactions make up the strong force)

d) will we see less interactions between gluons in between?
The coupling constant goes to zero at higher energy (smaller scale in length). This is asymptotic freedom ! We are really running into difficulties here : the more gluons around, the easiest to exchange color charge, so the "weakest" the interaction.
2) I do suppose that when 2 gluons are interacting, there is no direct influence on the strong interaction force, is that correct?
(maybe very clear to you, but never made explicite sure in the texts I did read)
I am not certain I understand you
The fact that gluons interact with each other is what causes this interaction to be "non-linear" and thus so complicated.

vanesch
Staff Emeritus
Gold Member
humanino said:
Both of them have a distribution of probability, generally parameterized with respect to the so-called "momentum fraction". In a referential in which the Baryon moves with infinite speed, all the constituents (called "partons" in this context = quarks of all sorts + gluons of all sorts) share a certain amount of the total momentum. This gets easily tricky.
(I suppose by infinite speed, you mean: light speed :-))

I agree with humanino. In fact, at high momentum, you can consider all constituents of the proton as being essentially massless (as compared to their kinetic energy), with their momentum to be lightlike 4-vectors parallel to the momentum 4-vector of the proton. This fraction (between 0 and 1) is usually called Bjorken-x. Although you cannot of course distinguish individual quarks or so, you can think of a population of "up-quark" which has a probability distribution as a function of Bjorken-x to be the "interacting parton". You have another distribution of "down quark", still another one of "s-quark". If you have an electromagnetically interacting probe, such as an electron, you're not sensitive to the distribution of "gluon". But you can work out that in order to have the full proton momentum, these distributions have to satisfy certain sum rules. From the other distributions, you can then extract the gluon density as a function of bjorken-x.
If the particles in the proton where fully free, these distributions would be independent of the incident energy of the probe. However, because they are of course interacting through the strong force, there is for instance a higher probability of having a low momentum gluon at higher energies, than at low energies (because there is more "phase space" for a quark-> quark+gluon reaction). So once you know the initial distribution at a given energy, you can calculate how these distributions (as a function of bjorken-x) change with respect to the incident energy. These evolution equations (which can be calculated out of QCD) are called the Altarelli-Parisi equations.
Because of the naivity of the model, people thought that this "toy model" would get corrections, but it turns out that they work extremely well!
(I worked on such an experiment, H1, at Hera - Desy).
So the evolution of the parton densities (which is not very strong, btw, because of the asymptotic freedom, the particles _are_ almost free, so that the distributions are almost independent of incident energy) is well described by QCD. However, the _initial densities_ can, to my knowledge, only be found from experiment. Maybe the lattice people get further now on this issue, I don't know.

cheers,
Patrick.

Thank you Partick for the precisions.
vanesch said:
(I suppose by infinite speed, you mean: light speed :-))
yes

The best introduction I know to deep inelastic scattering by Aneesh V. Manohar. It dates back to 1992, but still arXiv never says "please wait while we generate the file"
I agree with humanino. In fact, at high momentum, you can consider all constituents of the proton as being essentially massless
that is indeed very much of the tricky part
If you have an electromagnetically interacting probe, such as an electron, you're not sensitive to the distribution of "gluon". But you can work out that in order to have the full proton momentum, these distributions have to satisfy certain sum rules. From the other distributions, you can then extract the gluon density as a function of bjorken-x.
This is not entirely correct.
See COMPASS proposal (this is a gzip compressed postcript file)
COMPASS publication page

In any case, you can see this diagram. This is called "open charm leptoproduction" and this is sensitive to the gluons. Of course, it is not a direct interaction with gluons since they do not carry electric charge.

I worked on such an experiment, H1, at Hera - Desy.
Really ! It seems we work in the same field.
I hope it was not about the pentaquarks :tongue:
Maybe the lattice people get further now on this issue, I don't know.
They will render experiments obsolete, hopefully not in the too near future

vanesch
Staff Emeritus
Gold Member
humanino said:
In any case, you can see this diagram. This is called "open charm leptoproduction" and this is sensitive to the gluons.
That's what I call cheating ! :tongue:
In fact, part of the QCD diagram has been moved from the target into the probe part. You can say that you're not looking at the gluon, but at the charm quark which evolved out of the gluon part.

Really ! It seems we work in the same field.
I left it after my PhD in 1997, and the subject was extremely obscure, because of course all the other PhD students before me had extracted what was extractable from the data concerning proton structure. So I did... Pomeron structure :yuck:.

cheers,
Patrick.

vanesch said:
Maybe the lattice people get further now on this issue, I don't know.
Indeed, they do manage to find much on the LO/NLO/NNLO evolution of partons densities, but it seems they are unable to compute them from scartch. That is, they always start from a clever fit of data at a given $$Q^2$$.

For instance : NNLO global parton analysis

However, remember of http://int.phys.washington.edu/PROGRAMS/03-2.html [Broken] ?
Those lattice guys compute here from first principles, not using data :
Generalized Parton Distributions from Lattice QCD
and they can extract partons densities from GPDs. So far, they can only compute moments of the functions, but of course, knowledge of all moments would allow one to recover the full function.

Also : A lattice determination of moments of unpolarised nucleon structure functions using improved Wilson fermions

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vanesch said:
So I did... Pomeron structure :yuck:.
:rofl: Why do you :yuck: ?
Any theorem called "Pomeranchuk" cannot be a bad idea !
Doubtlessely you must know Eugene's paper : An introduction to Pomerons
This is an excellent paper, I think.

vanesch
Staff Emeritus
Gold Member
humanino said:
:rofl: Why do you :yuck: ?
Any theorem called "Pomeranchuk" cannot be a bad idea !
Doubtlessely you must know Eugene's paper : An introduction to Pomerons
This is an excellent paper, I think.
I didn't know about it. It's date is 1998, just after I left. Would probably have helped me writing up my script !!!

cheers,
Patrick.

You would see infinitely many of them !
More precisely : from far away (large distance, large scale in length) you will see none. When you get closer (smaller scale in length) you will see more and more, ad infinitum
Well, it seems that one "sea of gluons", at short range, is bigger and more ad infinitum than the other sea which is at long range, what a great picture!?

1) So, reading this all I can conclude that the linear potential (and thus the strong force)
between 2 quarks will get weaker at short range, because the sea of quarks is getting
bigger, and it will be easier to exchange color charge (humanino)
Is that correct?

2) Is this a valid conclusion: shorter range- more gluons - easier color charge exchange
- and the strong force will get weaker? Or is this picture not the whole?

3) This is not a question, but more some remarks you will not read often at this place, but I feel sometimes it's good to go "outside" your territory.
I know I do belong more at the philosophical side of this forum (or totally outside), but I guess in the forum where I am now, I will find the persons with more knowledge about physics!.

Praise you all, with your knowledge you enriched our language (not only your own!)
and you did change the meaning/contents of our words and worlds

(temperature has now a different meaning than 80 years ago, and who can say the word "dead" means the same since we do know that proton decay is so rare?)

And the Quantum experiments evocate more religion to me than the ones in
"normal life" Love to read the "popular writing", I read between the formula's, skipping them, just very interested in their spin-off-effects to the real world outside and to our language and thinking

There is no border between art, language and science, and we have to tear them down. In fact, when I do write poetry, I want to involve important scientific information/subjects.
That's the reason why I do want to know something about Quantumworlds
Are the important questions in the quantumworld parralel to the questions in our life?

Can we see the picture that "confinement" or "asymptotic freedom" delivers back on life on larger scale?

Ragards, Maxmax