Gauge and Lorentz covariant quark propagator in an arbitrary gluon field

The quark propagator in the presence of an arbitrary gluon field is calculated gauge and Lorentz covariantly order by order in terms of powers of the gluon field and its derivatives. The result is independent of the path connecting the ends of the propagator, and the leading order result coincides with the exact propagator in the trivial case of a vanishing gluon field. Received: 5 February 2003 / Published online: 23 May 2003     

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     

Renormalizability of a quark–gluon model with soft BRST breaking in the infrared region

We prove the renormalizability of a quark–gluon model with soft breaking of the BRST symmetry, which accounts for the modification of the large distance behavior of the quark and gluon correlation functions. The proof is valid to all orders of perturbation theory, by making use of softly broken Ward identities.     

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.     

Hadron correlators and the structure of the quark propagator

The structure of the quark propagator of QCD in a confining background is not known. We make an ansatz for it, as hinted by a particular mechanism for confinement, and analyze its implications in the meson and baryon correlators. We connect the various terms in the Källen-Lehmann representation of the quark propagator with appropriate combinations of hadron correlators, which may ultimately be calculated in lattice QCD. Furthermore, using the positivity of the path integral measure for vector like theories, we reanalyze some mass inequalities in our formalism. A curiosity of the analysis is that, the exotic components of the propagator (axial and tensor), produce terms in the hadron correlators which, if not vanishing in the gauge field integration, lead to violations of fundamental symmetries. The non observation of these violations implies restrictions in the space-time structure of the contributing gauge field configurations. In this way, lattice QCD can help us analyze the microscopic structure of the mechanisms for confinement.Supported in part by CICYT (AEN91-0234) and DGICYT grant (PB91-0119-C02-01)     

Transport theory for a scalar quark & gluon model

A model for scalar quarks and gluons that successfully gives rise to a ln s behavior in high-energy qq scattering and which contains a non-trivial three-gluon vertex is used to study collision theory with the following aspects: i) A three-body interaction simulating QCD is present and ii) particle production and annihilation occur naturally. In this paper, the collision term in the model is examined in detail in the quasiparticle approximation. The construction of cross-sections in which self-energy terms are ordered according to a coupling constant expansion is undertaken. It is shown explicitly which terms of second order are required to obtain the scattering amplitudes that are two body in nature. Additional ordering in the number of colors shows that quark loop diagrams are suppressed and gluon production or scattering processes dominate. It is also shown that a consistent calculation of the scattering graphs at the two-loop level also simultaneously yields terms that renormalize one-loop level graphs. This can then be extended to arbitrary m↦n processes. We examine the constraint equation briefly, discussing the appearance of a width. The issue of pinch singularities is also addressed, and examples of the elimination of such singularities in equilibrium are given explicitly. Received: 7 November 2001 / Accepted: 12 June 2001     

Mesonic corrections to the quark propagator in the Nambu-Jona-Lasinio model

Corrections to the chiral condensate and quark mass in the Nambu-Jona-Lasinio model for the four-dimensional cutoff and dimensional-analytical regularizations are calculated within the mean-field expansion in the bilocal quark-source formalism. It is shown that pion corrections to quark masses are zero in both regularizations. This coincidence of the results suggests that the zero pion contribution to the quark mass is a fact of the Nambu-Jona-Lasinio model and is independent of regularization. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 31–36, July, 2006.     

The gluon propagator in the Coulomb gauge

We give the results for all the one-loop propagators, including finite parts, in the Coulomb gauge. In the finite parts we find new non-rational functions in addition to the single logarithms of the Feynman gauge. Of course, the two gauges must agree for any gauge invariant function.Received: 14 November 2003, Revised: 20 July 2004, Published online: 24 September 2004     

Revisiting the quasi-particle model of the quark–gluon plasma

The quasi-particle model of the quark–gluon plasma (QGP) is revisited here with a new method, different from earlier studies, one without the need of a temperature dependent bag constant and other effects such as confinement, effective degrees of freedom etc. Our model has only one system dependent parameter and shows a surprisingly good fit to the lattice results for the gluon plasma, and for 2-flavor, 3-flavor and (2+1)-flavor QGP. The basic idea is first to evaluate the energy density ε from the grand partition function of quasi-particle QGP, and then derive all other thermodynamic functions from ε. Quasi-particles are assumed to have a temperature dependent mass equal to the plasma frequency. Energy density, pressure and speed of sound at zero chemical potential are evaluated and compared with the available lattice data. We further extend the model to a finite chemical potential, without any new parameters, to obtain the quark density, quark susceptibility etc., and the model fits very well with the lattice results on 2-flavor QGP. PACS 12.38.Mh; 12.38.Gc; 05.70.Ce; 52.25.Kn     

Scalar mesons and glueball in a quark model allowing for gluon anomalies

This paper is a sequel of a previous one (Scalar mesons in a chiral quark model with glueball, Eur. Phys. J. A 8, 567 (2000)) where an attempt to construct an effective U(3)×U(3)-symmetric meson Lagrangian with a scalar glueball was made. The glueball was introduced by using the dilaton model on the base of scale invariance. The scale invariance breaking because of current quark masses and the scale anomaly of QCD, reproduced by the dilaton potential, was taken into account. However, in the previous paper, the scale invariance breaking because of the terms like h _φφ² and h _σ , where φ and are the pseudoscalar and scalar isosinglets, was not taken into account. These terms are produced by the part of the 't Hooft interaction that is connected with gluon anomalies. Allowing for the scale invariance breaking by these terms has a decisive effect on the quarkonium-glueball mixing and noticeably changes the widths of glueball strong decays. Taking account of this additional source of the scale invariance breaking and its implications are the subject of the present work. It is also shown that in the decay of a glueball into four pions, the channel with two ρ-resonances dominates. Received: 11 January 2001 / Accepted: 25 January 2001     

Study of the gluon propagator in the axial gauge

It is shown that a non-linear integral equation for the gluon propagator in the axial gauge (Baker et al.) can be simplified considerably. A comparison is made with an approximate equation for the gluon propagator in the Landau gauge (Mandelstam). Both equations have polynomial kernels where the argument is the divisor of the internal and external momenta. A solution which behaves as a double pole for low momenta remains consistent.     

A non-perturbative calculation of the infrared limit of the axial gauge gluon propagator (II)

We show, numerically, that the integral equation for the axial gauge gluon propagator developed in the preceding paper has an explicit solution with the features outlined there. This solution is expected to be exact in the infrared limit. We find, however, that even in the ultraviolet limit it does not differ greatly from the known asymptotic freedom behavior of the propagator. It may, therefore, be a reasonable approximation over the whole range.     

A non-perturbative calculation of the infrared limit of the axial gauge gluon propagator (I)

We describe a non-perturbative study of the infrared behavior of the axial gauge gluon propagator based on the Dyson equation and Ward identities. We conclude that the propagator Δ_μν(q) displays a q^?4 singularity in the infrared limit, and that consequently the axial gauge running coupling constant g_A²)(q) displays a q^?2 singularity in the same limit. The only assumption necessary to obtain this conclusion is that the transverse part of the triple-gluon vertex function does not dominate the longitudinal part in the infrared regime.     

Measurements of the structure of quark and gluon jets in hadronic Z decays

An experimental investigation of the structure of identified quark and gluon jets is presented. Observables related to both the global and internal structure of jets are measured; this allows for tests of QCD over a wide range of transverse momentum scales. The observables include distributions of jet-shape variables, the mean and standard deviation of the subjet multiplicity distribution and the fragmentation function for charged particles. The data are compared with predictions of perturbative QCD as well as QCD-based Monte Carlo models. In certain kinematic regions the measurements are sensitive mainly to perturbatively calculable effects, allowing for a test of QCD. The comparisons are also extended into regions where nonperturbative effects become large, and in this way the transition from hard to soft QCD is investigated. It is found that by including leading and next-to-leading logarithmic contributions in the QCD predictions, the agreement with the data can be extended to lower transverse momentum scales, especially for gluon jets. Received: 2 February 1998 / Published online: August 9, 2000     

Studying pion effects in the quark propagator

Within the framework of Schwinger-Dyson and Bethe-Salpeter equations we investigate the importance of pions for the quark-gluon interaction. To this end we choose a truncation for the quark-gluon vertex that includes intermediate pion degrees of freedom and adjust the interaction such that unquenched lattice results for various current quark masses are reproduced. After extrapolation to the physical point we find a considerable contribution of the pion back reaction to the quark mass function as well as to the chiral condensate.     

Analytic structure of ρ meson propagator at finite temperature

We analyse the structure of one-loop self-energy graphs for the ρ meson in real time formulation of finite temperature field theory. We find the discontinuities of these graphs across the unitary and the Landau cuts. These contributions are identified with different sources of medium modification discussed in the literature. We also calculate numerically the imaginary and the real parts of the self-energies and construct the spectral function of the ρ meson, which are compared with an earlier determination. A significant contribution arises from the unitary cut of the π ω loop, that was ignored so far in the literature.