Quark Confinement

Could someone please clarify my problem with the subject of quark confinement within hadrons. I understand that from the potential that more and more energy is required to further seperate two quarks (or quark anti-quark) and think i understand why that at a point a quark anti-quark pair is formed (energy converted to mass, right?) and subsequently there is the formation of a baryon and meson and so the quark is still confined and we cannot 'see' a free quark. I know this explanation is a little simplistic but im just not able to grab this explanation i got in the lecture today. Any hints/tips in understanding this or alternate explanations? Thanx

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mathman
The description you gave may be simplistic, but it is reasonable enough without going into the mathematics of the subject.

I would like to add one comment : confinement is NOT undestood ! This is one of the main open question with Yang-Mills SU(3). How is confinement produced is very much linked to the structure of the QCD vacuum and therefore, to the difference between matter and vacuum. If you know a bit about superconductivity, maybe you remember that magnetic field is exluded by superconductive materials. It is "screened". People widely believe the same occurs with color field in empty space : it must be "screened" by vacuum polarization. Indeed, in a geometrical formalism chromo- and electromagnetic-fields are very much similar.
More precisely : take empty space, and distrurb it with a chromomagnetic field : the energy decreases ! (Warning : don't get too much bothered, this is perturbative calculation, so nobody really expect it to work here (^_^) You might still feel a taste of what is going on) In this perspective, we imagine chromo-vacuum similar to 2D Ising model, with drops of "up" and "down" pointing spins. This should represent the structure of chromo-vacuum.

Does the colour force have a 1/ r^2 or a 1/r^4 or a 1/ r^10 dependency as distance changes? Nobody seems sure from what I can make out.Also is the colour force symmetrical - does it get strong again at very short distances such as 10^ -20 metres?

humanino said:

People widely believe the same occurs with color field in empty space : it must be "screened" by vacuum polarization.

Are you talking about space at distances greater than 10 ^- 15 metres or just
over the range of the colour force.And what exactly is vacuum polarization in this context?

As far as I know, color force INCREASE with distance. But the precise divergence law does not really matters, so one usually simply pick a linear growing force. Besides, the color force DISAPEAR at small distance.

Two quarks very close to each other can easily exchange their color, meaning they are for all practical purpose FREE. At large distance, they have to exchange the color in a very narrow tube between them (looking very much like a string !), which is not easy, and the force between them must be strong. This is basically the behavior of strong force.

Vacuum polarization correspond to the "drops" of vacuum with different color orientation, similar to "drops" of polarization occuring in 2D Ising model. The reason why this vacuum polarization is relevant to confinement is really technical. Let's say to sum up (and because I know I can easily go wrong on that subject !) : the fancy up-to-date lattice calculations show that confinement is due to a color Coulomb-like potential, corresponding to the instantaneous part of the 4-4 component of the gluon propagator. This potential is then screened by the vacuum polarization, and this provide an UPPER bound on the potential. This phenomenon is responsible for asymptotic freedom (vanishing of the coupling constant, or negativity of the "beta" function). To provide numbers : at 100 GeV, alpha is of order 0.1 (compare with 1/137 of QED). But the interesting part is the non-perturbative regime, at small energy or large distance. Here, screening is not effective any more, and the coupling grows infinity. Understanding what is screening should provide good clues of what happens when there is no screening anymore.

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ZapperZ
Staff Emeritus
Well, I didn't want to bring this in, but since humanino has introduced a concept from condensed matter (superconductivity), then I thought I might as well add my two-cent in here.

In case any of you missed it, keep in mind that there are a tremendous amount of similarities between the phenomena in condensed matter and that found in elementary particles. There are many who do not think it is a mere coincidence that quarks have basic charge of 1/3 and 2/3. The discovery of the fractional quantum hall effect, and consequently, fractional charge of 1/3 in 2D quantum confinment seems to imply that a fractional charge can arise out of many-body elementary excitations. Similar to the quark confiment, the fractional charge found in those condensed matter phenomena does not exist by themselves, unbounded and devoid of the many-body interactions. So this isn't just a matter of strong confinement potential.

There is a good article written by Bob Laughlin (who, incidentally was a co-Nobel winner for the fractional quantum hall effect) establishing the similarities between a condensed matter phenomena (antiferromagnetism) and the strong interaction:

http://arxiv.org/abs/cond-mat/9802180

Zz.

thank you very much for this excellent reference. As far as I undestand, what is shown here is that antiferromagnetism exhibits both confinement and asymptotic freedom. I suddenly wonder : is this behavior really specific to SU(3) gauge group ? Is it not possible that confinement and asymptotic freedom are two generical properties for any nonabelian Yang-Mills field ? I think I already heard something similar, but I can't figure out where... Besides, I see that SU(2) gauge in the case of isospin does exhibit neither asymptotic freedom nor confinement... Maybe SU(N) fot N>2 ....(^_^)

Haelfix
You are thinking of lattice calculations in strongly coupled regions. Confinement is a general property of all nonabelian fields in this context. The difference is, for say the electro weak force there *seems* to be phase transitions that kills the confinement, whereas for SU(3) color the opposite takes place. These are numerical results, valid to like 4% of what we seem to get in experiment.

In the continuum limit, there is still no analytic proof of such

i don not understant hierarcy problem can somebody tell me ? i have very poor english so kindly use simple english .thanks

i am writing thesis on super symmtry .may some body help me

ZapperZ said:
Well, I didn't want to bring this in, but since humanino has introduced a concept from condensed matter (superconductivity), then I thought I might as well add my two-cent in here.

In case any of you missed it, keep in mind that there are a tremendous amount of similarities between the phenomena in condensed matter and that found in elementary particles. There are many who do not think it is a mere coincidence that quarks have basic charge of 1/3 and 2/3. The discovery of the fractional quantum hall effect, and consequently, fractional charge of 1/3 in 2D quantum confinment seems to imply that a fractional charge can arise out of many-body elementary excitations. Similar to the quark confiment, the fractional charge found in those condensed matter phenomena does not exist by themselves, unbounded and devoid of the many-body interactions. So this isn't just a matter of strong confinement potential.

There is a good article written by Bob Laughlin (who, incidentally was a co-Nobel winner for the fractional quantum hall effect) establishing the similarities between a condensed matter phenomena (antiferromagnetism) and the strong interaction:

http://arxiv.org/abs/cond-mat/9802180

Zz.
You are so right, Laughlin has done some really interesting work. What really is amazing is that the Quark Confinement is based on a potential of Electro-Magnetic-Vacuum quantities outside of Einsteinien Spacetimes. Just as the Virtual Photon eminates from a un-identified Spacetime, so does the energy needed to seperate Quarks. For every positive energy amount we throw at them in seperation, an ample amount of negative energy materials materials out of nowhere and maintains the Quark Hierarchy.

The opposite is true for Quantum Hall systems, there is a definate outpouring of Explosive Nova from deep within certain B-E-C superconductive condensed states.

A good example here is the Bose-Nova, where the confinment is broken from within the condensate, exactly the opposite of what we try to do with seperating Quarks (negative-energy infill?) there is a positive outpouring, thus Nova.

ZapperZ
Staff Emeritus
Olias said:
You are so right, Laughlin has done some really interesting work. What really is amazing is that the Quark Confinement is based on a potential of Electro-Magnetic-Vacuum quantities outside of Einsteinien Spacetimes. Just as the Virtual Photon eminates from a un-identified Spacetime, so does the energy needed to seperate Quarks. For every positive energy amount we throw at them in seperation, an ample amount of negative energy materials materials out of nowhere and maintains the Quark Hierarchy.

The opposite is true for Quantum Hall systems, there is a definate outpouring of Explosive Nova from deep within certain B-E-C superconductive condensed states.

A good example here is the Bose-Nova, where the confinment is broken from within the condensate, exactly the opposite of what we try to do with seperating Quarks (negative-energy infill?) there is a positive outpouring, thus Nova.
Although you appear to agree with me regarding Laughlin, etc., I have absolutely no idea what you have said. For example, "BEC superconductive condensed states"?! What are those? BEC is on the OPPOSITE end of the phase line from the BCS condensation. Till a few months ago, it was thought that these two are separated via a distinct phase transition. It was only the recent discovery of the fermionic condensate that there is a real possibility that there is a smooth transition or a crossover between the two extremes. It still does not make them the same thing.

Zz.

mass hierarchy problem

may some body tell me about mass hierarchy problem .why it is prefered to use supersymmetry to solve this problem. as for as i understan that it can be tackled
by fine tunning i.e by introducing -ive terms in bare mass to cancel the divergence term which coms by radiative corrections .ma i right?

supersymmetry

i am writting thesis on supersymmtry may somebody help me ,may someone send me matrial on this icannot afford to by books due to poor financial conditions

ZapperZ
Staff Emeritus
Olias said:
Like I said there are certain correlations, recognized (speculated) by myself some time ago, verified recently.

Of some interest:http://arxiv.org/abs/cond-mat/0405206

From some time ago, this:http://arxiv.org/abs/cond-mat/0303045

and a recent progression:http://arxiv.org/PS_cache/cond-mat/pdf/0405/0405130.pdf [Broken]
What correlations? How do these things "verify" your "speculations"? I am EXTREMELY familiar with X.J. Zhou's et al. paper on LSCO, since I also did ARPES measurement on high-Tc superconductor. I see nothing in here remotely come close to strenghtening your idea of "BEC superconductor". Be careful to not fool yourself into interpreting things you do not understand. "Coupling to bosonic mode" has a very profound meaning in condensed matter physics. I would certainly not use a result from a still controversial area of high-Tc superconductor to extrapolate my idea into something even more speculative.

Furthermore, K. Levin at U. of Chicago has a whole series of theoretical papers on BCS to BEC crossover regime that showed how these two in fact can be COMPETING phenomena in a superconductor. So there are certainly loads of more different interpretation of this phenomena.

If you have published your speculation, please give citation from the peer-reviewed journals that it was published.

Zz.

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ZapperZ said:
What correlations? How do these things "verify" your "speculations"? I am EXTREMELY familiar with X.J. Zhou's et al. paper on LSCO, since I also did ARPES measurement on high-Tc superconductor. I see nothing in here remotely come close to strenghtening your idea of "BEC superconductor". Be careful to not fool yourself into interpreting things you do not understand. "Coupling to bosonic mode" has a very profound meaning in condensed matter physics. I would certainly not use a result from a still controversial area of high-Tc superconductor to extrapolate my idea into something even more speculative.

Furthermore, K. Levin at U. of Chicago has a whole series of theoretical papers on BCS to BEC crossover regime that showed how these two in fact can be COMPETING phenomena in a superconductor. So there are certainly loads of more different interpretation of this phenomena.

If you have published your speculation, please give citation from the peer-reviewed journals that it was published.

Zz.
Whoa

Lets get one thing straight, I have my own model based a little more than speculation, my interest has led me to a inter-phase(Tri-Coupled-State-Matter) model based on geometry (pure), more than soft-condensed states or other toy replicated 2-D theories.

This being said it is only a sideline interest of mine, and you are certainly correct in that I should not be babbling on about a very little understood area of pioneering hpysics, but forgive me if you will, but the main speculative hand-waving comes from reading a vast quantity of pre-print papers, many of the authors I admire greatly.

I am now going to butt out!

Some might learn from the article

Meanwhile, we have learned that the strong interactions are instead described by quantum chromodynamics (QCD), the field theory in which quarks interact through a "colour" force carried by gluons. Although it is therefore not fundamentally a string theory, numerical simulations of QCD ("lattice QCD"; July p23) have demonstrated that Nambu's conjecture was essentially correct: in chromodynamics, a string-like chromoelectric flux tube forms between distant static colour charges. This leads to quark confinement - the potential energy between a quark and the other quarks to which it is tied increases linearly with the distance between them. The phenomenon of confinement is the most novel and spectacular prediction of QCD - unlike anything seen before.
The ideal experimental test of this new feature of QCD would be to study the flux tube of figure 1 directly by anchoring a quark and antiquark several femtometres apart and examining the flux tube between them. In such ideal circumstances, one of the characteristics of the gluonic flux tube would be the model-independent spectrum shown in figure 2. The excitation energy is p/r because the flux tube's mass is entirely due to its stored energy. There are two initially excited longest wavelength vibrations with identical energies because the motion of the flux tube is in the two symmetrical dimensions perpendicular to its length.

http://www.cerncourier.com/main/article/40/7/16