Dyson-Schwinger Studies Research Articles

Quark susceptibilities, transport properties and heavy quark production in an extended Quasi-Particle Model with Nf = 2 + 1 + 1 flavors

The quark susceptibilities are a very useful tool to understand the nature of the degrees of freedom in the vicinity of the QCD phase transition while Heavy-Quarks (HQs) transport coefficients give us information on their thermalization time in the Quark-Gluon Plasma (QGP). Recently, new lattice results for the equation of state of QCD with 2 + 1 + 1 dynamical flavors have become available. Therefore, we extend our QPM approach for Nf = 2 + 1 to Nf = 2 + 1 + 1 where the charm quark is included. We also explore the extension of QPM approach to a more realistic model in which partonic propagators explicitly depend on the three-momentum with respect to the partonic matter at rest in order to match pQCD at high momenta following Dyson-Schwinger studies in the vacuum. In this context, we evaluate and correctly reproduce both EoS and quark susceptibilities which are understimated in the simple QPM approach. Therefore, we study the impact of the extended QPM approach on the spatial diffusion coefficient Ds of charm quark making a comparison with the results in the standard QPM approach.

Effects of anisotropy in QED3from Dyson-Schwinger equations in a box

We investigate the effect of anisotropies in the fermion velocities of 2+1 dimensional QED on the critical number N_f^c of fermions for dynamical mass generation. Our framework are the Dyson-Schwinger equations for the gauge boson and fermion propagators formulated in a finite volume. In contrast to previous Dyson-Schwinger studies we do not rely on an expansion in small anisotropies but keep the full velocity dependence of fermion equations intact. As result we find sizable variations of N_f^c away from the isotropic point in agreement with other approaches. We discuss the relevance of our findings for models of high-T_c superconductors.

From Euclidean to Minkowski space with the Cauchy–Riemann equations

We present an elementary method to obtain Green’s functions in non-perturbative quantum field theory in Minkowski space from Green’s functions calculated in Euclidean space. Since in non-perturbative field theory the analytical structure of amplitudes often is unknown, especially in the presence of confined fields, dispersive representations suffer from systematic uncertainties. Therefore, we suggest to use the Cauchy–Riemann equations, which perform the analytical continuation without assuming global information on the function in the entire complex plane, but only in the region through which the equations are solved. We use as example the quark propagator in Landau gauge quantum chromodynamics, which is known from lattice and Dyson–Schwinger studies in Euclidean space. The drawback of the method is the instability of the Cauchy–Riemann equations against high-frequency noise,which makes it difficult to achieve good accuracy. We also point out a few curious details related to the Wick rotation.

Extraction of spectral functions from Dyson–Schwinger studies via the maximum entropy method

It is shown how to apply the Maximum Entropy Method (MEM) to numerical Dyson–Schwinger studies for the extraction of spectral functions of correlators from their corresponding Euclidean propagators. Differences to the application in lattice QCD are emphasized and, as an example, the spectral functions of massless quarks in cold and dense matter are presented.

GLUONS AT FINITE TEMPERATURE IN LANDAU GAUGE YANG–MILLS THEORY

The infrared behavior of Yang–Mills theory at finite temperature provides access to the role of confinement. In this review recent results on this topic from lattice calculations and especially Dyson–Schwinger studies are discussed. These indicate persistence of a residual confinement even in the high-temperature phase. The confinement mechanism is very similar to the one in the vacuum for the chromomagnetic sector. In the chromoelectric sector screening occurs at the soft scale g2T, although not leading to a perturbative behavior.

Multiplicative renormalizability and quark propagator

The renormalized Dyson-Schwinger equation for the quark propagator is studied, in Landau gauge, in a novel truncation which preserves multiplicative renormalizability. The renormalization constants are formally eliminated from the integral equations, and the running coupling explicitly enters the kernels of the new equations. To construct a truncation which preserves multiplicative renormalizability, and reproduces the correct leading order perturbative behavior, non-trivial cancellations involving the full quark-gluon vertex are assumed in the quark self-energy loop. A model for the running coupling is introduced, with infrared fixed point in agreement with previous Dyson-Schwinger studies of the gauge sector, and with correct logarithmic tail. Dynamical chiral symmetry breaking is investigated, and the generated quark mass is of the order of the extension of the infrared plateau of the coupling, and about three times larger than in the Abelian approximation, which violates multiplicative renormalizability. The generated scale is of the right size for hadronic phenomenology, without requiring an infrared enhancement of the running coupling.