From arxiv today


Today the daily from arxiv is particularly rich. A couple of papers are from my friend Marco Ruggieri, one in collaboration with Raul Gatto (see here) and the other is the contribution to Paris Conference proceedings (see here). Marco is currently using a Nambu-Jona-Lasinio model to understand the behavior of hadronic matter at high temperatures and densities. These works imply the use of a chiral chemical potential that has the benefit to permit an identification of the critical end-point on the lattice without the infamous sign problem, as Marco showed quite recently (see here). These works are well founded as the Nambu-Jona-Lasinio model is the right low-energy limit of QCD (see here and here).

Another theoretical confirmation on my result on the beta function for Yang-Mills theory appeared today (see here). This author works out classical solutions to Yang-Mills theory and derives a “beta function” of the form 4\alpha_s, exactly the one I get (see here). This result marks evidence of an infrared trivial fixed point for this theory and the correctness of the mapping on a scalar field. This paper gives just a clue as the treatment remains at a classical level.

Last but not least, the complete Coleman’s lectures appeared finally on arxiv (see here). We have to give a great thank to Bryan Chen and Yuan-Sen Ting for their excellent work. These lectures are a reference today yet and I hope they will see the light in a book with some addenda from most of Coleman’s famous students.

Raoul Gatto, & Marco Ruggieri (2011). Hot Quark Matter with an Axial Chemical Potential arXiv arXiv: 1110.4904v1

Marco Ruggieri (2011). Quark Matter with a Chiral Chemical Potential arXiv arXiv: 1110.4907v1

Marco Ruggieri (2011). The Critical End Point of Quantum Chromodynamics Detected by Chirally
Imbalanced Quark Matter Phys.Rev.D84:014011,2011 arXiv: 1103.6186v2

Marco Frasca (2008). Infrared QCD Int.J.Mod.Phys.E18:693-703,2009 arXiv: 0803.0319v5

Kei-Ichi Kondo (2010). Toward a first-principle derivation of confinement and chiral-symmetry-breaking crossover transitions in QCD Phys. Rev. D, 82 065024 (2010) arXiv: 1005.0314v2

Ding-fang Zeng (2011). Confinings of QCD at purely classic levels arXiv arXiv: 1110.5054v1

Marco Frasca (2010). Mapping theorem and Green functions in Yang-Mills theory PoS FacesQCD:039,2010 arXiv: 1011.3643v3

Sidney Coleman (2011). Notes from Sidney Coleman’s Physics 253a arXiv arXiv: 1110.5013v1

QCD is confining


At Bari Conference , after I gave my talk, Owe Philipsen asked to me about confinement in my approach. The question came out also in the evening, drinking a beer at a pub in the old Bari. Looking at my propagator, it is not so straightforward to see if the theory is confining or not. But we know, from lattice computations, that this must be so. You can realize this from the following figure (see here)

The scale is given by r_0=0.5\ fm, the so called Sommer’s scale, We note a clear linear rising till about 1.5 fm. A linear rising potential is an evidence of confinement as showed about forty years ago by Kenneth Wilson (see here) with his famous area law. Due to this clear evidence coming from lattice computations, any attempt to explain mass gap must show confinement through a linear rising potential.

Indeed, this is not all the story and going to 1.5 fm cannot be enough to display all the behavior of a Yang-Mills theory. As showed quite recently on the lattice Philippe de Forcrand and Slavo Kratochvila (see here), increasing distance, the potential must saturate. This is an effect of the mass gap that causes screening. This means that, at larger distances, the potential sets on an asymptote becoming horizontal. The linear approximation holds on a finite range.

This is indeed what I observe with my approach. I can prove that the potential has a Yukawa form with a form factor dependent on the distance. The mass scale entering into it is just the mass gap. So, you get a linear fit like the following (see here)

that shows confinement with the area law till 10 fm! If one increases the distance the fit worsens and saturation appears as expected. From this we can easily derive the string tension that is given by (g^2/4\pi)C_2 0.000507/r_0^2. For SU(N), C_2=(N^2-1)/2N. This is a fine proof of confinement for a Yang-Mills theory and so, for QCD too. This also means that my approach is again consistent with lattice data. Just for completeness, and to give a great thank to Arlene Aguilar and Daniele Binosi, I show the fit of my propagator with the one obtained numerically solving Dyson-Schwinger equations (see here)

The agreement is almost perfect.

Gunnar S. Bali (2000). QCD forces and heavy quark bound states Phys.Rept.343:1-136,2001 arXiv: hep-ph/0001312v2

Wilson, K. (1974). Confinement of quarks Physical Review D, 10 (8), 2445-2459 DOI: 10.1103/PhysRevD.10.2445

Slavo Kratochvila, & Philippe de Forcrand (2003). Observing string breaking with Wilson loops Nucl.Phys. B671 (2003) 103-132 arXiv: hep-lat/0306011v2

Marco Frasca (2011). QCD is confining arXiv arXiv: 1110.2297v1

A. C. Aguilar, D. Binosi, & J. Papavassiliou (2008). Gluon and ghost propagators in the Landau gauge: Deriving lattice
results from Schwinger-Dyson equations Phys.Rev.D78:025010,2008 arXiv: 0802.1870v3

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