Effects of the Running of the QCD Coupling on the Energy Loss in the Quark-Gluon Plasma

Finite temperature modifies the running of the QCD coupling alpha_s(k,T) with resolution k. After calculating the thermal quark and gluon masses selfconsistently, we determine the quark-quark and quark-gluon cross sections in the plasma based on the running coupling. We find that the running coupling enhances these cross sections by factors of two to four depending on the temperature. We also compute the energy loss dE/dx of a high-energy quark in the plasma as a function of temperature. Our study suggests that, beside t-channel processes, inverse Compton scattering is a relevant process for a quantitative understanding of the energy loss of an incident quark in a hot plasma.Comment: 14 pages, 6 figure

Thermodynamics of Constituent Quarks

We investigate the thermal behavior of quarks and antiquarks interacting via a temperature-dependent linear potential. The quarks are constituent quarks with dynamically generated masses from the background linear $\sigma$-model.We find a transition from a system of bound mesons to a correlated quark gas at the same temperature as the chiral transition temperature.Comment: 24 pages, 5 Postscript figures, uses article.sty, epsf.sty, epsfig.st

Volume Dependence of the Pion Mass in the Quark-Meson-Model

We consider the quark-meson-model in a finite three-dimensional volume using the Schwinger proper-time renormalization group. We derive and solve the flow equations for finite volume in local potential approximation. In order to break chiral symmetry in the finite volume, we introduce a small current quark mass. The corresponding effective meson potential breaks chiral O(4) symmetry explicitly, depending on sigma and pion fields separately. We calculate the volume dependence of the pion mass and of the pion decay constant with the renormalization group flow equations and compare with recent results from chiral perturbation theory in a finite volume.Comment: 28 pages, 5 figures, v2: minor changes, references updated, final version published in Phys. Rev.

Renormalization Group Flow Equation at Finite Density

For the linear sigma model with quarks we derive renormalization group flow equations for finite temperature and finite baryon density using the heat kernel cutoff. At zero temperature we evolve the effective potential to the Fermi momentum and compare the solutions of the full evolution equation with those in the mean field approximation. We find a first order phase transition either from a massive constituent quark phase to a mixed phase, where both massive and massless quarks are present, or from a metastable constituent quark phase at low density to a stable massless quark phase at high density. In the latter solution, the formation of droplets of massless quarks is realized even at low density.Comment: 30 pages, 9 figures; typos corrected, section 3 revised, one reference added, two references updated, submitted to Phys. Rev.

Formulating Light Cone QCD on the Lattice

We present the near light cone Hamiltonian $H$ in lattice QCD depending on the parameter $\eta$, which gives the distance to the light cone. Since the vacuum has zero momentum we can derive an effective Hamiltonian $H_{eff}$ from $H$ which is only quadratic in the momenta and therefore solvable by standard methods. An approximate ground state wave functional is determined variationally in the limit $\eta \to 0$.Comment: 48 pages, 8 figure

Statistical Physics and Light-Front Quantization

Light-front quantization has important advantages for describing relativistic statistical systems, particularly systems for which boost invariance is essential, such as the fireball created in a heavy ion collisions. In this paper we develop light-front field theory at finite temperature and density with special attention to quantum chromodynamics. We construct the most general form of the statistical operator allowed by the Poincare algebra and show that there are no zero-mode related problems when describing phase transitions. We then demonstrate a direct connection between densities in light-front thermal field theory and the parton distributions measured in hard scattering experiments. Our approach thus generalizes the concept of a parton distribution to finite temperature. In light-front quantization, the gauge-invariant Green's functions of a quark in a medium can be defined in terms of just 2-component spinors and have a much simpler spinor structure than the equal-time fermion propagator. From the Green's function, we introduce the new concept of a light-front density matrix, whose matrix elements are related to forward and to off-diagonal parton distributions. Furthermore, we explain how thermodynamic quantities can be calculated in discretized light-cone quantization, which is applicable at high chemical potential and is not plagued by the fermion-doubling problem.Comment: 30 pages, 3 figures; v2: Refs. added, minor changes, accepted for publication in PR