BRST invariance in Coulomb gauge QCD

In the Coulomb gauge, the Hamiltonian of QCD contains terms of order ?²${?}^2$, identified by Christ and Lee, which are non-local but instantaneous. The question is addressed how do these terms fit in with BRST invariance. Our discussion is confined to the simplest, O(g⁴)$O\left(g^4\right)$, example.     

The Landau gauge gluon propagator in lattice QCD

A Monte Carlo calculation of the gluon propagator in the Landau gauge in SU(3) lattice gauge theory is described. The results of calculations at β = 5.6 (200 4³ × 8 lattices), β = 5.8 (400 4³ × 10 lattices and 100 6³ × 12 lattices), and β = 6.0 (100 4³ × 8 lattices) indicate that the gluon propagator resembles a massive particle propagator in which the mass grows with separation. At the largest distances accessible with these lattices, the mass is about 600 MeV.     

An infrared singularity in the damping rate for longitudinal gluons in hot QCD

We calculate γ_l(0), the damping rate for longitudinal on-shell gluons with zero momentum in hot QCD using the hard-thermal-loop scheme, and find it to be divergent in the infrared. We argue that this result suggests that the scheme may be sensitive in this sector and thus may need to be improved upon. We discuss the validity of our result and emphasize the fact that it depends on the way we perform our calculation. In particular, we do not exclude the possibility that alternative approaches that we briefly comment on may in principle yield infrared-safe results.     

Linear response of the hot QCD plasma from the gluon propagator

Linear response theory is used to express the positions of the physical poles in the finite temperature gluon propagator in terms of the components of the proper self-energy. The analysis is valid in a wide class of covariant and non-covariant gauges, for both transverse and non-transverse self-energies. The formalism is then applied to the calculation at the one loop level of the bare plasma parameters and of Landau ghosts in two classes of gauges: the covariant gauge and a one parameter family of non-covariant gauges which interpolate between the static temporal gauge and the Coulomb gauge.     

Resummation in hot field theories

There has been significant progress in our understanding of finite-temperature field theory over the past decade. In this paper, we review the progress in perturbative thermal field theory focusing on thermodynamic quantities. We first discuss the breakdown of naive perturbation theory at finite temperature and the need for an effective expansion that resums an infinite class of diagrams in the perturbative expansion. This effective expansion which is due to Braaten and Pisarski, can be used to systematically calculate various static and dynamical quantities as a weak-coupling expansion in powers of g. However, it turns out that the weak-coupling expansion for thermodynamic quantities are useless unless the coupling constant is very small. We critically discuss various ways of reorganizing the perturbative series for thermal field theories in order to improve its convergence. These include screened perturbation theory (SPT), hard-thermal-loop perturbation theory, the Φ-derivable approach, dimensionally reduced (DR) SPT, and the DR Φ-derivable approach.     

Resummation in QCD fractional analytic perturbation theory

An analytic approach in the QCD perturbation theory that has its origin in studies by Jones, Solovtsov, and Shirkov is briefly summarized. Basic propositions of the fractional analytic perturbation theory (FAPT) are also briefly taken into account with a fixed number of quark flavors and allowing for heavy-quark thresholds in a global FAPT version. Summation of perturbative series in (F)APT is examined. Application of the developed global FAPT version to calculations of the width of Higgs boson decay H → b $ \bar b $ \bar b is described.     

Relating a gluon mass scale to an infrared fixed point in pure gauge QCD

We show that in pure gauge QCD (or any pure non-Abelian gauge theory) the condition for the existence of a global minimum of energy with a gluon (gauge boson) mass scale also implies the existence of a fixed point of the beta function. We argue that the frozen value of the coupling constant found in some solutions of the Schwinger-Dyson equations of QCD can be related to this fixed point. We also discuss how the inclusion of fermions modifies this property.     

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     

Self-interaction and gauge invariance

A simple unified closed form derivation of the non-linearities of the Einstein, Yang-Mills and spinless (e.g. chiral) meson systems is given. For the first two, the non-linearities are required by locality and consistency; in all cases, they are determined by the conserved currents associated with the initial (linear) gauge invariance of the first kind. Use of first-order formalism leads uniformly to a simple cubic self-interaction.Supported by USAF OAR under Grant AFOSR 70-1864.     

The gluon propagator in temporal gauge

The implementation of Gauss's law in perturbative calculations in temporal gauge is achieved through ana explicit construction of the vacuum state. In this scheme the free gluon propagator is calculated. Terms in addition to the principal value part are found.     

Multiple collisions and induced gluon bremsstrahlung in QCD

Induced soft gluon bremsstrahlung associated with multiple collisions is calculated via perturbative QCD. We derive the non-abelian analog of the Landau-Pomeranchuk effect that suppresses induced soft radiation with formation times exceeding the mean free path. The dependence of the suppression effect on the SU(N) representation of the jet parton as well as the kinematic variables is expressed through a radiation formation factor. The soft radiation with k < μ, where μ is the infrared screening scale in the medium, is shown to lead to an approximately constant radiative energy loss per unit length.