Nonabelian Debye Screening in One-Loop Resummed Perturbation Theory

Abstract

Debye screening of static chromoelectric fields at high temperature is investigated at next-to-leading order through one-loop resummed perturbation theory. At this order the gluon propagator appears to give rise to strong deviations from a Yukawa form of screening. Generally, an oscillatory behavior is found which asymptotically becomes repulsive, but in a gauge-dependent manner. However, these features are strongly sensitive to the existence of screening of static magnetic fields. It is shown that a small magnetic screening mass can restore exponential screening with a gauge independent value of the screening mass, which depends logarithmically on the magnitude of the magnetic mass. Recent results obtained in temporal axial gauge, which instead indicate an asymptotic (repulsive) power-law behavior of screening, are also critically discussed. In order to arrive at a gauge-invariant treatment of chromoelectric screening, Polyakov loop correlations are considered, both with and without dynamical gauge symmetry breaking. Again a crucial sensitivity to the scale of magnetic screening is found. A detailed comparison of the perturbative results with recent high-precision lattice simulations of the SU(2) Polyakov loop correlator is made, which are found to agree well with the perturbative result in the symmetric phase when a magnetic mass $\sim g^2T/4$ is included.