wolram
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Can a single quark exist in isolation ?
Hi ST, this, " strong force" increase with distance has me baffled, quite easy,SpaceTiger said:As I understand it, a free quark can't exist because it has a net "color charge" (red, green, blue, antired, antigreen, or antiblue). Much like systems of electric charges tend to arrange themselves to become chargeless on large scales, systems of quarks tend to arrange themselves to be "colorless" in composite particles (like mesons and baryons). A big difference between this and electromagnetic forces, however, is that the effective "strong force" increases with distance, so a quark couldn't escape the pull of its colored partners as a planet could the solar system. In fact, if you try give a quark energy to make such an escape (as in a decay or collision), the potential energy built up between quark pairs will tend to lead to the creation of more quarks -- a quark jet.
Well, ST, really told you the very essence of the story. Quarks have a net color. Every net color will interact with another colour to become colourless. So if you look at quarks in their most stable state (ie the ground state energy) , the most stable configuration is the colourless quark combination. So, this combination is most likely to occur. Now, suppose you wanna take out one quark and separate it from its original structure. While doing so, the interaction between this quark and it's "collegues" in the colourless combination will increase (this is what asymptotic freedom is all about). The increase in energy will be used for the creation of other quarks. This happens because nature is as lazy as possible : The potential energy from the interaction is converted "automatically" into new quarkpairs...wolram said:Hi ST, this, " strong force" increase with distance has me baffled, quite easy,
but what is the mechanics behind this ?
This is called "infra-red slavery". "Asymptotic freedom" is something else.marlon said:Now, suppose you wanna take out one quark and separate it from its original structure. While doing so, the interaction between this quark and it's "collegues" in the colourless combination will increase (this is what asymptotic freedom is all about).
Asymptotic freedom is the weakening of the coupling between matter and the gauge field at high momenta/small distances.marlon said:While doing so, the interaction between this quark and it's "collegues" in the colourless combination will increase (this is what asymptotic freedom is all about).
First of all, if the strong force coupling constant rises when distance rises than it must lower when distance lowers, so what is your problem ? I never claimed to give the exact definition of asymptotic freedom ("free" quarks at "very" short distances, etc etc), but i wanted to illustrate the consequence of a negative beta function. So what are you objecting against ?Perturbation said:Asymptotic freedom is the weakening of the coupling between matter and the gauge field at high momenta/small distances.
No, because, we believe , the potential energy between quark and antiquark increases with separation [V(r)~ar]. So quarks and gluons can never escape from the colour singlet states (observable particles i.e colourless hadrons). We call this confinement or infrared slavery.wolram said:Can a single quark exist in isolation ?
Yes, confinement(large distance behaviour) is the name .Perturbation said:You are right, the QCD "running coupling constant" decreases with increasing q^2 (the momentum transfer) and therefore becomes small for short-distance interactions i.e the coloured particles (quarks and gluons) behave as if they are free. We say that QCD is "asymptotically free".Asymptotic freedom is the weakening of the coupling between matter and the gauge field at high momenta/small distances.
Asymptotic freedom would be a bit of an odd name for the increase in the strong force with distance.
marlon said:tell me where i went wrong.
You called confinement (or infra-red slavery) asymptotic freedom.
Admit a careless mistake, and move on.
i have to rewrite my master's thesis:uhh:
Then, get to it, if you have that mistake in it.
QUOTE]
Also, the bag model of confinement is unrelated to AF, but is a now superseded mode of confinement. A linearly rising potential at large r is more popular.
Websites are not answers.
He's just talking about the interaction strength increasing with distance, which I believe is true in any limit for the strong force -- it wouldn't necessarily have to refer to confinement.marlon said:Now, suppose you wanna take out one quark and separate it from its original structure. While doing so, the interaction between this quark and it's "collegues" in the colourless combination will increase (this is what asymptotic freedom is all about).
SpaceTiger said:He answered the question correctly but named his answer incorrectlyPerhaps I'm missing something, because I don't see why the distinction is so important for what marlon said. Doesn't "infrared slavery" refer to the divergence of the strong interaction at large distance/small energy, while "asymptotic freedom" refers to the behavior at small distance/large energy? I agree that confinement (that is, the lack of free quarks) is more directly due to infrared slavery, but in the context of marlon's post, it seems either would do:
He's just talking about the interaction strength increasing with distance, which I believe is true in any limit for the strong force -- it wouldn't necessarily have to refer to confinement
Asymptotic freedom is the success story of QCD.
The hypothesis of Quark confinement and its extension "coloure confinement" are an embarressment. As to date no proof exists.
To explain quark confinement various suggestion have been made. The most popular one is to assume a linear potential between a quark and an antiquark at large distances, so that there will be only bound states for the pair.The same picture also shows up in the lattice gauge theory of Wilson, who formulated the condition of "quark" confinement in terms of his loop and showed that it is satisfied in the strong coupling approximation. However, it is extremly difficult to formulate the condition for confinement of gluons, which are also coloured, in the lattice gauge theory.
Eventhough I am not an expert on QCD, I did some work on the "mathematical" problem of coloure confinement based on BRS-algebra.
The idea (originally due to Nishijima) based on an analogy with QED.
Bassically, we let the quarks and gluons have the same fate the scalar and longitudinal photons have in QED.
regards
sam
No, i did not.samalkhaiat said:He answered the question correctly but named his answer incorrectly
Now, YOU are naming things incorrectly. The linear potential is not just assumed, it follows from the model you are using. To give you an example : the dual abelian Higgs model [1] will predict the mentioned linear potential without it "being assumed". The basic idea behind this model is to use the theoretical concept of magnetic dipoles. In low energy QCD the coupling constant is very big. Suppose we are able to make a transformation into a "world" where the transformed coupling constant is small, this would be very good since perturbationtheory can still be used in infra red QCD. The transformation i am talking about is the one defined by replacing the E fields by the B fields. So quarks become magnetic monopoles and gluons become dual (electrical) gauge pairs.To explain quark confinement various suggestion have been made. The most popular one is to assume a linear potential between a quark and an antiquark at large distances, so that there will be only bound states for the pair.
marlon said:1) Asymptotic freedom can not explain our inability to observe coloured particles.No, i did not.
2) Free inside Hadrons does not mean or imply "cann't be free outside Hadrons"
So you are wrong.
READ my post carefully. Didn't I say that the linear potential "shows up" in Wilson's lattice gauge theory?Now, YOU are naming things incorrectly. The linear potential is not just assumed, it follows from the model you are using.
magnetic dipoles? I thought it is monopoles! NAMING THINGS INCORECTLY. You have done it again.:surprisedTo give you an example : the dual abelian Higgs model [1] will predict the mentioned linear potential without it "being assumed". The basic idea behind this model is to use the theoretical concept of magnetic dipoles.
Yes, some modles do derive the linear potential. However, almost all modles make some alternative assumptions in order to derive that form of potential. The model you mentioned (magnetic confinement of quarks [1]-[4]) makes the (rather strange) assumption that gluons do not participate in long range interactions.This is the so-called Abilean dominance cojecture which is necessary for the derivation of the linear potential.
Other crippling features of this model are;
1) QCD coloure group SU(3) is not identical to an "Abilean" Higgs. One can show that Abilean-projection-SU(2) and SU(2) have different behaviour in the ultraviolet region.
2) QCD Lagrangian is based on the exact (unbroken) local group SU(3). So scalar fields are absent and the "superconductor" analogy seems inappropriate.
3) The posibility that quarks carry "magnetic" charge does not mesh well with Asymptotic Freedom.
4) One can not get rid of the unwanted neutral contribution to Wilson loop.
5) Abilean gauge fixing (i.e making QCD an interaction theory of photons, monopoles and matter{quarks & gluons}) requires monopole dominance as well as Abilean dominance conjectures.
6) Lattice gauge theory calculations show that "Abilean dominance" is not universal.
HAVE FUN
sam
[1] Nielsen,H.& Olesen,P.(1973), Nuc. Phys.,B61,45.
[2]Englert,F.(1977). "Electric and magnetic confinement" Lectures given at the Cargese Summer School.
[3]Marciano,W.& Pagels,H.(1978), Phys. Rep. 36C, 3, 137.
[4]Mandelstam,S.(1975), Phys. Rep.23C, 3, 245.
I never said any of this. Please read my posts more carefully prior to reacting in this way.samalkhaiat said:1) Asymptotic freedom can not explain our inability to observe coloured particles.
2) Free inside Hadrons does not mean or imply "cann't be free outside Hadrons"
So you are wrong.
My reaction was to the fact that you stated "the linear potential is assumed..." I never referred to this particular model.READ my post carefully. Didn't I say that the linear potential "shows up" in Wilson's lattice gauge theory?
Yep indeed magnetic monopoles. I made a mistake there.magnetic dipoles? I thought it is monopoles! NAMING THINGS INCORECTLY. You have done it again.:surprised
This is not the same as saying that the linear potential itself is assumed from the beginning (which is what you stated, but i am sure you are gonna deny this).Yes, some modles do derive the linear potential. However, almost all modles make some alternative assumptions in order to derive that form of potential.
Nope, this is NOT the basic assumption. I explained to you what that was. Read the reference, please.The model you mentioned (magnetic confinement of quarks [1]-[4]) makes the (rather strange) assumption that gluons do not participate in long range interactions.
Err, your point being ?This is the so-called Abilean dominance cojecture which is necessary for the derivation of the linear potential.
Why this summation ? Did i ever say this model was completely correct ? Again, read the paper before reacting.Other crippling features of this model are;
No problemoHAVE FUN