For fun, one of the two emails the paper to a former colleague, a humble professor still struggling with esoteric research...
Quark-gluon plasma paradox
Gesellschaft fur Schwerionenforschung mbH, Planckstr. 1, 64291 Darmstadt
Based on simple physics arguments it is shown that the concept of quark-gluon plasma, a state of matter consisting of uncorrelated quarks, antiquarks, and gluons, has a fundamental problem.
The result? The following email message.
Dear Dr. Miskowiec,
I read your interesting preprint on a possible QGP paradox. My
comments are below.
In the paper it seems you are discussing a caricature of QGP, indeed a straw man. I don't know whether belief in this straw man is widespread among nuclear theorists; perhaps it is. But QGP is, after all, merely the high temperature phase of QCD.
There *are* correlations (dynamics) that lead to preferential clustering of quarks into color neutral objects. These effects are absent at length scales much smaller than a fermi, due to asymptotic freedom. It is only on these short length scales that one can treat QCD as a (nearly) free gas of quarks and gluons. On sufficiently long length scales (i.e., much larger than a fermi) the system would still prefer to be color neutral. While it is true that at high temperatures the *linear* (confining) potential between color charges is no longer present, there is still an energetic cost for unscreened charge.
It's a standard result in finite temperature QCD that, even at high temperatures, there are still infrared (long distance) nonperturbative effects. These are associated with a scale related to the magnetic screening length of gluons. The resulting dynamics are never fully perturbative, although thermodyamic quantities such as entropy density, pressure, etc. are close to those of a free gas of quarks and gluons. The limit to our ability to compute these thermodynamic quantities beyond a certain level in perturbation theory arises from the nonperturbative effects I mention.
Consider the torus of QGP you discuss in your paper. Suppose I make a single "cut" in the torus, possibly separating quarks from each other in a way that leaves some uncancelled color charge. Once I pull the two faces apart by more than some distance (probably a few fermis), effects such as preferential hadronization into color neutral, integer baryon number, objects come into play. The energy required to make the cut and pull the faces apart is more than enough to create q-qbar pairs from the vacuum that can color neutralize each face. Note this is a *local* phenomenon taking place on fermi lengthscales.
I believe the solution to your paradox is the third possibility you list. See below, taken from the paper, bottom of column 1 p.3. I only disagree with the last sentence: high temperature QCD is *not* best described as a gas of hadrons, but *does* prefer color neutrality. No rigorous calculation ever claimed a lack of correlations except at very short distances (due to asymptotic freedom).
...The third possibility is that local correlations between quarks make some cutting surfaces more probable than the others when it comes to cutting the ring and starting the hadronization. Obviously, in absence of such correlations the QGP ring basically looks like in Fig. 3 and no preferred breaking points can be recognized. If, however, some kind of interactions lead to clustering of quarks and gluons into (white) objects of integer baryon numbers like in Fig. 4 then starting hadronization from several points of the ring at the same time will not lead to any problem. However, this kind of matter would be hadron resonance matter rather than the QGP.