Chiral and deconfinement transition from correlation functions: SU(2) vs. SU(3)

We study a gauge-invariant order parameter for deconfinement and the chiral condensate in SU(2) and SU(3) Yang–Mills theory in the vicinity of the deconfinement phase transition using the Landau gauge quark and gluon propagators. We determine the gluon propagator from lattice calculations and the quark propagator from its Dyson–Schwinger equation, using the gluon propagator as input. The critical temperature and a deconfinement order parameter are extracted from the gluon propagator and from the dependency of the quark propagator on the temporal boundary conditions. The chiral transition is determined using the quark condensate as order parameter. We investigate whether and how a difference in the chiral and deconfinement transition between SU(2) and SU(3) is manifest.     

The gluon propagator at finite temperature

The Landau gauge gluon propagator at finite temperature above and below the deconfinement transition is measured using lattice Monte Carlo simulation. The color electric and magnetic masses are determined. The most striking result of the calculation is that the time component of the gluon field appears to acquire a vacuum expected value in the deconfined region.     

A Gauge and Lorentz covariant approximation for the quark propagator in an arbitrary gluon field

We decompose the quark propagator in the presence of an arbitrary gluon field with respect to a set of Dirac matrices. The four-dimensional integrals which arise in first order perturbation theory are rewritten as line-integrals along certain field lines, together with a weighted integration over the various field lines. It is then easy to transform the propagator into a form involving path ordered exponentials. The resulting expression is non-perturbative and has the correct behavior under Lorentz transformations, gauge transformations and charge conjugation. Furthermore it coincides with the exact propagator in first order of the coupling g. No expansion with respect to the inverse quark mass is involved, the expression can even be used for vanishing mass. For large mass the field lines concentrate near the straight line connection and simple results can be obtained immediately. Received: 31 March 2001 / Revised version: 3 May 2001 / Published online: 8 June 2001     

Constituent quark masses from modified perturbative QCD

A recently proposed modified perturbative expansion for QCD incorporating gluon condensation is employed to evaluate the quark and gluon self-energy corrections in first approximation. The results predict mass values of 1/3 of the nucleon mass for the light quarks u, d, and s and a monotonously growing variation with the current mass. The only phenomenological input is that is evaluated up to order as a function of the unique parameter C defining the modified propagator, and then C is fixed to give a current estimate of . The light quarks u and d as a result are found to be confined and the s, c, b and t ones show damped propagation modes, suggesting a model for the large differences in stability between the nucleons and the higher resonances. The above properties of quark modes diverge from the fully confinement result following from the similar gluon propagator previously considered by Munczek and Nemirovski. On the other hand, the condensate effects on the gluon self-energy furnish a tachyonic mass shell as predicted by the Fukuda analysis of gluon condensation in QCD. Received: 28 September 2001 / Revised version: 15 November 2001 / Published online: 8 February 2002     

The Color Gauge Invariance and a Possible Origin of Mass in QCD

The general scale parameter, having the dimensions of mass squared, is dynamically generated in the QCD gluon sector. It is introduced through the difference between the regularized full gluon self-energy and its value at some finite point. It violates transversality of the full gluon self-energy. The Slavnov-Taylor identity for the full gluon propagator, when it is given by the corresponding equation of motion, is also violated by it. So in order to maintain both transversality and the identity it should be disregarded from the very beginning, i.e., put formally zero everywhere. However, we have shown how to preserve the above-mentioned identity at non-zero mass squared parameter. This allows one to establish the structure of the full gluon propagator when it is explicitly present. Its contribution does not survive in the perturbation theory regime, when the gluon momentum goes to infinity. At the same time, its contribution dominates the structure of the full gluon propagator when the gluon momentum goes to zero. We have also proposed a method how to restore transversality of the relevant gluon propagator in a gauge invariant way, while keeping the mass squared parameter “alive”.     

Hot gluon propagator

In order to match two complementary approaches to quark gluon plasma, namely the classical hamiltonian lattice gauge field simulation which uses the temporal axial gauge, and hot perturbative QCD which rather uses the Coulomb or the covariant gauge, we obtain a general expression for the hard thermal loop gluon propagator for a variety of non-background gauge fixing conditions. The Coulomb energy is shown to be independent of the gauge fixing condition.     

Quark Loop Effects on Dressed Gluon Propagator in Framework of Global Color Symmetry Model

Based on the global color symmetry model (GCM), a method for obtaining the quark loop effects on the dressed gluon propagator in GCM is developed. In the chiral limit, it is found that the dressed gluon propagator containing the quark loop effects in the Nambu-Goldstone and Wigner phases are quite different. In solving the quark self-energy functions in the two different phases and subsequent study of bag constant one should use the above dressed gluon propagator as input. The above approach for obtaining the current quark mass effects on the dressed gluon propagator is quite general and can also be used to calculate the chemical potential dependence of the dressed gluon propagator.     

Center flux correlation in SU(2) Yang-Mills theory

By using the method of center projection, the center vortex part of the gauge field is isolated and its propagator is evaluated in the center Landau gauge, which minimizes the open 3-dimensional Dirac volumes of nontrivial center links bounded by the closed 2-dimensional center vortex surfaces. The center field propagator is found to dominate the gluon propagator (in the Landau gauge) in the low momentum regime and to give rise to a power-law correction proportional to p(-2.9(1)) at high momentum. The screening mass of the center vortex field vanishes above the critical temperature of the deconfinement phase transition, which naturally explains the second order nature of this transition consistent with the vortex picture. Finally, the ghost propagator of the maximal center gauge is found to be infrared finite and, thus, shows that the coset fields play no role for confinement.     

The Effective Gluon Propagator in the Global Color Symmetry Model

It is shown that the effective gluon propagator in the global color symmetry model can be calculated in the instanton dilute liquid approximation. The calculated effective gluon propagator is consistent with the general command on the qualitative features of the gluon propagator, i.e., (i) the gluon propagator is significantly enhanced at small space-like k², and (ii) for k² > 1.5 GeV² the perturbative results are quantitatively reliable.     

Gluon Propagator and Heavy Quark Potential in an Anisotropic QCD Plasma

The hard-loop resummed propagator in an anisotropic QCD plasma in general linear gauges are computed. We get the explicit expressions of the gluon propagator in covariant gauge, Coulomb gauge and temporal axial gauge. Considering one gluon exchange, the potential between heavy quarks is defined through the Fourier transform of the static propagator. We find that the potential exhibits angular dependence and that there is stronger attraction on distance scales on the order of the inverse Debye mass for quark pairs aligned along the direction of anisotropy than for transverse alignment.     

Numerically Solving Quark-Loop Effects on Dressed Gluon Propagator in Chiral Limit

We do a numerical calculation on the quark-loop effects on the dressed gluon propagator in the chiral limit. It is found that the quark-loop effects on the dressed gluon propagator are significant in solving the quark propagator in the rainbow approximation of the Dyson-Schwinger equation. The approach we used here is quite general and can also be used to calculate both the chemical potential and current quark mass dependence of the dressed gluon propagator.     

Quarks and gluons in dense two-colour QCD

We compute quark and gluon propagators in 2-colour QCD at large baryon chemical potential μ. The gluon propagator is found to be antiscreened at intermediate μ and screened at large μ. The quark propagator is drastically modified in the superfluid region as a result of the formation of a superfluid gap.     

The Mixed Quark-Gluon Condensate from the Global Color Symmetry Model

［1］R.T. Cahill and C.D. Roberts, Phys. Rev. D32 (1985)2419. ［2］P.C. Tandy, Prog. Part. Nucl. Phys. 39 (1997) 117; C.D.Roberts, R.T. Chill, and J. Praschiflca, Ann. Phys. (N.Y.)188 (1988) 20; M.R. Frank, P.C. Tandy, and G. Fai, Phys.Rev. C43 (1991) 2808; M.R. Frank and P.C. Tandy, Phys.Rev. C49 (1994) 478; M.R. Frank and C.D. Roberts,Phys. Rev. C53 (1996) 390; P. Maris and C.D. Roberts,Phys. Rev. C56 (1997) 3369; C.W. Johnson and G. Fai,Phys. Rev C56 (1997) 3353; P. Maris, C.D. Roberts,and P.C. Tandy, Phys. Lett B420 (1998) 267; XiaoFu LU, Yu-Xin LIU, Hong-Shi ZONG and En-Guang ZHAO, Phys. Rev. C58 (1998) 1195; Hong-Shi ZONG,Xiao-Fu LU, Jian-Zhong GU, Chao-Hsi CHANG, and EnGuang ZHAO, Phys. Rev. C60 (.1999) 055208; Hong-Shi ZONG, Yu-Xin LIU, Xiao-Fu LU, Fan WANG, and EnGuang ZHAO, Commun. Theor. Phys. (Beijing, China)36 (2001) 187. ［3］M.R. Frank and T. Meissner, Phys. Rev. C53 (1996)2410. ［4］T. Meissner, Phys. Lett. B405 (1997) 8. ［5］C.D. Roberts and A.G. Williams, Prog. Part. Nucl. Phys.33 (1994) 477, and the references therein. ［6］H.B. Tang and R. J. Furnstahl, hep-ph/9502326. ［7］M. Shifman, A. Vainshtein, and V. Zakharov, Nucl. Phys.B147 (1979) 385. ［8］L. Reinders, H. Rubinstein, and S. Yazaki, Phys. Rep.127 (1985) 1; S. Narison, QCD Spectral Sum Rules, World Scientific, Singapore (1989), and the rererences therein. ［9］Hong-Shi ZONG, Jia-Lun PING, Hong-Ting YANG,Xiao-Fu LU, and Fan WANG, nuth-th/0201001. ［10］C.D. Roberts, A.G. Williams, and G. Krein, Int. J. Mod.Phys. A7 (1992) 5607.     

The Mixed Quark-Gluon Condensate from the Global Color Symmetry Model

The mixed quark-gluon condensate from the global color symmetry model is derived. It is shown that the mixed quark-gluon condensate depends explicitly on the gluon propagator. This interesting feature may be regarded as an additional constraint on the model of gluon propagator. The values of the mixed quark-gluon condensate from some ansatz for the gluon propagator are compared with those determined from QCD sum rules.     

Probing Quark Loop Effects on Dressed Gluon Propagator

We study the quark loop effects on the dressed gluon propagator and also on the quark propagator itself. We find that the gluon propagators are different in two phases. The quark mass effects on the gluon propagator are small but not negligible. We also study the current quark mass dependence on the bag constant.     

Infrared properties of the gauge theory coupling constant III

In previous papers we have outlined a program for deriving the infrared behavior of the axial gauge gluon propagator in a pure Yang-Mills theory. The program is based on an integral equation for the gluon propagator derived from the Dyson equation and the Ward identities. Here we present a solution to this equation, obtained numerically. The solution exhibits a Singularity in the infrared, and therefore presumably predicts confinement of color. The method is supposed to be exact in the infrared. Away from the infrared, therefore, our solution is only approximate. Nevertheless, even in the ultraviolet, our solution for the propagator is not very different from the known asymptotic freedom result, so it may be that it is a reasonable approximation over the entire range of momentum.     

Quark Gluon Condensate,Virtuality and Susceptibility of QCD Vacuum

We study vacuum of QCD in this work. The structure of non-local quark vacuum condensate, values of various local quark and gluon vacuum condensates, quark-gluon mixed vacuum condensate, quark and gluon virtuality in QCD vacuum state, quark dynamical mass and susceptibility of QCD vacuum state to external field are predicted by use of the solutions of Dyson-Schwinger equations in “rainbow” approximation with a modeling gluon propagator and three different sets of quark-quark interaction parameters. Our theoretical predictions are in good agreement with the correspondent empirical values used widely in literature, and many other theoretical calculations. The quark propagator and self-energy functions are also obtained from the numerical solutions of Dyson-Schwinger equations. This work is centrally important for studying non-perturbative QCD, and has many important applications both in particle and nuclear physics.     

Infrared gluon and ghost propagators from lattice QCD

We report on the infrared limit of the quenched lattice Landau gauge gluon and ghost propagators as well as the strong-coupling constant computed from large asymmetric lattices. The infrared lattice propagators are compared with the pure power law solutions from Dyson-Schwinger equations (DSE). For the gluon propagator, the lattice data is compatible with the DSE solution. The preferred measured gluon exponent being ∼0.52, favouring a vanishing propagator at zero momentum. The lattice ghost propagator shows finite-volume effects and, for the volumes considered, the propagator does not follow a pure power law. Furthermore, the strong-coupling constant is computed and its infrared behaviour investigated.     

Gravity’s Rainbow induces topology change

In this paper the Gribov gap equation at finite temperature is analyzed. The solutions of the gap equation (which depend explicitly on the temperature) determine the structure of the gluon propagator within the semi-classical Gribov approach. The present analysis is consistent with the standard confinement scenario for low temperatures, while for high enough temperatures, deconfinement takes place and a free gluon propagator is obtained. An intermediate regime in between the confined and free phases can be read off from the resulting gluon propagator, which appears to be closely related to partial deconfinement.     

Constraints on the infrared behavior of the gluon propagator in Yang-Mills theories

We present rigorous upper and lower bounds for the zero-momentum gluon propagator D(0) of Yang-Mills theories in terms of the average value of the gluon field. This allows us to perform a controlled extrapolation of lattice data to infinite volume, showing that the infrared limit of the Landau-gauge gluon propagator in SU(2) gauge theory is finite and nonzero in three and in four space-time dimensions. In the two-dimensional case, we find D(0)=0, in agreement with Maas. We suggest an explanation for these results. We note that our discussion is general, although we apply our analysis only to pure gauge theory in the Landau gauge. Simulations have been performed on the IBM supercomputer at the University of S?o Paulo.