Quark-Gluon Plasma: Coupling, Perturbation Theory & Lattice-Gauge Theory

[RedX]

I just finished reading the Wikipedia article on the quark-gluon plasma and it states that because of the large coupling, lattice-gauge theory is used instead of perturbation theory/Feynman diagrams. However, I thought the coupling decreases with increasing energy (asymptotic freedom), so shouldn't perturbation theory work when energies are high enough to produce quark-gluon plasmas? I thought lattice-gauge theory was only useful for showing that quarks are confined at low energies/large couplings.

 

[humanino]

You are right that in few body systems, the strong coupling decreasing at high energy, one may use perturbation methods. But note that wikipedia articles mentions that non-perturbative lattice calculations are used to deal with the plasma because the density if so high that we have a many-body problem. In fact, one even describes things in terms of chemical potential !

 

[Rade2]

Humanino,

I have a question. Consider that the few body system under study is the deuteron [NP], of course we then have 6 quarks with strong coupling. Now, suppose we set up an experiment to allow fusion of matter deuteron [NP] with antimatter deuteron [N^P^], with ^ = anti. Would you predict that such a matter+antimatter reaction would produce enough energy to form a quark-gluon plasma ? If so, how would this reaction then be described in terms of chemical potential ?

 

[humanino]

Yes. At the energies required to search for QGP (or CGC) it would also be described in terms of chemical potential for two nucleon collisions. It has to do with a tremendous number of virtual partons. For instance at the LHC, you can pretty much consider that the protons are mere bags of glue.

 

[RedX]

The quark-gluon plasma is said to be unconfined. Does this result from many-body considerations?

Without taking into account many-body considerations, I've gone through a proof that says Abelian gauge theories are unconfined, and that non-Abelian gauge theories are also unconfined if the gauge coupling is small, and confined if the gauge coupling is large.

But what's confusing is that the book then sends the lattice spacing to zero, and says that the coupling constant then goes to zero (which I guess is asymptotic freedom), but no phase transition is undergone: the phase is still confined! So does this mean that even when the coupling gets very weak at high energies, quarks are still confined? If so, then that proof that non-Abelian gauge theories are unconfined so long as the coupling is weak is wrong?