Today on arxiv it is appeared the contribution to the conference “The many faces of QCD” of my friend Marco Ruggieri. Marco is currently a postdoc student at Yukawa Institute in Tokyo and has been a former student of Raoul Gatto. Gatto is one of the most known Italian physicists that had as students also Gabriele Veneziano and Luciano Maiani. With Marco we have had a lot of fun in Ghent and several interesting discussions about physics. One of the main interests of Marco is to study QCD vacuum under the effect of a strong magnetic field and he pursue this line with Gatto. This is a very rich field of research producing several results that can be compared with lattice computations and LHC findings at last. Marco’s contribution (see here) approaches the question using Nambu-Jona-Lasinio model. Before to enter is some details about Marco’s work, let me explain briefly what is the question here.
As my readers know, there has been so far no widely accepted low-energy limit of QCD rigorously derived from it. Simply, we can do computations of low-energy phenomenology just using some models that we hope, in some approximation, will describe correctly what is going on in this limit. Of course, there have been a number of successful models and Nambu-Jona-Lasinio model is one of this. This model, taken from the original formulation, is not renormalizable and not confining. But it describes fairly well the breaking of chiral symmetry and the way bound states can form from quark fields. Indeed, one is able to get a fine description of the low-energy behavior of QCD notwithstanding the aforementioned shortcomings of this model. In the course of time, this model has been refined and some of its defects have been corrected and today appears a serious way to see the behavior of QCD at very low-energy. But all this success appears somewhat incomprehensible unless someone is able to prove that this model is indeed a low-energy approximation to the QCD quantum field theory. A couple of proofs are around: One is due to Kei-Ichi Kondo (see here) and the other one is due to your humble writer (see here). Kondo’s work does not reach a value for the NJL coupling while I get one through my gluon propagator that I know in a closed form. Anyhow, I was able to get a fully quantum formulation quite recently and this was published in QCD08 and QCD10 proceedings. But, notwithstanding these achievements, I keep my view that, until the community at large does not recognize these results as acquired, we have to continue to take not proved the fact that NJL is obtainable from QCD.
Given this situation, Marco’s approach is to consider a couple of modified NJL models and applies to them a constant magnetic field. Dirac equation with a constant magnetic field is well-known and exactly solvable producing a set of Landau levels and a closed form fermion propagator. This means that, given the mean field approximation, Marco is able to give well defined conclusions through analytical computations. NJL models Marco is considering have been both tuned to agree with lattice computations. What he finds is that the magnetic field has indeed important effects on the temperature of chiral symmetry restoration and for the deconfining phase. But he claims as a weak point a proper determination of the coupling that appears in the NJL models through the Polyakov loop that enters in the way the NJL models are formulated here. This is work for the future. I would like to emphasize the relevance of this kind of research for our understanding of the low-energy behavior of QCD. I will keep my readers up-to-date about this and I will keep on asking to Marco to clarify what the issues are for his research. What I find really striking here is to see the interplay between a magnetic field and strong force vacuum so entangled to produce really non-trivial results. Other groups around the World are working on this and accelerator facilities as LHC can produce important clues for our understanding of the vacuum of QCD. It will be really interesting to see how the results in this area will reach their maturity.
Marco Ruggieri (2011). Chiral symmetry restoration and deconfinement in strong magnetic fields arxiv arXiv: 1102.1832v1
Kondo, K. (2010). Toward a first-principle derivation of confinement and chiral-symmetry-breaking crossover transitions in QCD Physical Review D, 82 (6) DOI: 10.1103/PhysRevD.82.065024
FRASCA, M. (2009). INFRARED QCD International Journal of Modern Physics E, 18 (03) DOI: 10.1142/S0218301309012781