QCD Puzzle: Unsolved Equations at Atomic Nuclei Energy Scales

[Deepak247]

Thanks guys for your responses on my last thread...It was very informative for me...This time I also have some unsolved problem on which I want to have your opinions and discussion

I've heard that The equations of QCD remain unsolved at energy scales relevant for describing atomic nuclei, why so?

 

[alsey42147]

basically the interesting properties of QCD exist because the gluons interact with each other. one of these properties is that the strong force becomes stronger with increasing distance, or equivalently, with decreasing energy. in a nucleus you have relatively low energies/large distances, so the strong force is very strong. this means when you try to calculate something, your equations diverge to infinity.

to explain this in more detail, first consider QED.

in QED, 'bare charges' (e.g. an electron) are screened by virtual processes - emission of virtual photons, e+e- loops - effectively reducing the electromagnetic coupling constant. if you increase energy of whatever measuring system you have, equivalently decreasing distance, you are seeing less of this screening and so the coupling constant is larger. This is why the electromagnetic coupling increases with energy.

in QCD, you have an SU(3) gauge symmetry which gives rise to properties different to the U(1) symmetry of QED. importantly here, it means that the gluons interact with each other (photons do not interact with each other). as a result, the virtual screening in QCD has the opposite effect to QED; with increasing energy/decreasing distance, you are seeing more screening of the 'bare' color charge.

The result is that the strong force gets stronger with increasing distance. So at low energies/large distances, you actually have a very strong QCD coupling. These are the conditions that exist in atomic nuclei among other things.

now since any process in a QFT can be written as an expansion in terms of these coupling constants, and there are infinite terms, if the coupling is ~1 (as it is for QCD at low energy) then the expansion diverges and the process cannot be calculated in the normal way. With QED, or with QCD at high energy, this is not a problem since is the coupling is << 1 and so the terms in the expansion become smaller and smaller can be neglected.

 

[tom.stoer]

Looking at perturbative QCD one finds that the strength of the coupling becomes energy-dependent. At (infinitly) high energies the theory becomes asymptotically free, that means quarks behave like free particles. At low energies perturbation theory shows that the strength of the coupling is controlled by a new energy scale which emerges from the renormalization. Near his scale (~ 200 MeV) the perturbative approximation itself breaks down!

Below this scale we do not know how to treat the equations of QCD analytically. All what we have are computer simulations like lattice gauge theories which are quite successful in calculating hadron masses, form factors, dipole moments and things like that. But they are computer simulatons only and are not backed up by analytical calculations unfortunately.

 

[jal]

There are a lot of people trying to get a better understanding of QCD, confinement, deconfinement and perfect liquid.

I found two recent conferences.

QCHS IX

from 30 August 2010 to 03 September 2010This conference is the ninth in a biennial series whose aim is to bring together people working in QCD and strong-interaction dynamics, both theoreticians and experimentalists.
http://147.96.27.42//conferenceTimeTable.py?confId=0

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http://theor.jinr.ru/cpod/Dubna_2010_program2.htm
The 6th workshop on "Critical Point and Onset of Deconfinement" will take place in the period August 23-29, 2010 in the Conference Hall of the Bogoliubov Laboratory for Theoretical Physics at the JINR Dubna.
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If anyone wants to do some more explanation ... I'm listening.
jal

 

[Deepak247]

. one of these properties is that the strong force becomes stronger with increasing distance, or equivalently, with decreasing energy. in a nucleus you have relatively low energies/large distances

Guys...please clear one thing


Ive heard that in quarks, we need to increase energy to increase distance, and when they do separate further then a new particle- antiparticle pair is created...but


I don't get this notion of "INCREASING DISTANCE/DECREASING ENERGY" Please clear this one