Nonperturbative Debye Mass in Finite Temperature QCD

Abstract

Employing a nonperturbative gauge invariant definition of the Debye screening mass m D in the effective field theory approach to finite temperature QCD, we use 3D lattice simulations to determine the leading O ͑g 2 ͒ and to estimate the next-to-leading O ͑g 3 ͒ corrections to m D in the high temperature region. The O ͑g 2 ͒ correction is large and modifies qualitatively the standard power-counting hierarchy picture of correlation lengths in high temperature QCD. [S0031-9007(97)04353-6] PACS numbers: 11.10. Wx, 11.15.Ha, 12.38.Mh QCD matter, a spatially and temporally extended system of matter described by the laws of quantum chromodynamics, goes at high temperatures into a quark-gluon plasma phase, in which color is no more confined and chiral symmetry is restored. An essential quantity, describing coherent static interactions in the plasma, is the inverse screening length of color electric fields, the Debye mass m D . The Debye mass enters in many essential characteristics of static properties of the plasma. Its numerical value is important for phenomenological discussions of formation of the quark-gluon plasma, for the analysis of J͞C and Y suppression in heavy ion collisions, for the computation of parton equilibration rates, etc. (see, e.g., [1]).The definition and computation of the Debye mass for Abelian QED plasma is well understood [2]. The electromagnetic current j m is a gauge-invariant quantity, and the Debye mass can be extracted from the two-point gauge invariant correlation function of j 0 in the plasma. There are no massless charged particles in QED, which allows an infrared-safe perturbative computation of the Debye mass in powers of the electromagnetic coupling e. This has been done to order e 5 [3]. The situation in QCD is much more complicated. First, the corresponding current in QCD, j a m , is not a gauge-invariant quantity. Second, there are massless charged gluons which give rise to infrared divergences and prevent the perturbative determination of the Debye mass beyond leading order.A nonperturbative gauge-invariant definition of the Debye mass in vectorlike theories with zero chemical potential was suggested in [4]. According to it, m D can be defined from the large distance exponential falloff of correlators of gauge-invariant time-reflection odd The aim of this Letter is a nonperturbative determination of the high temperature limit of the Debye mass, at T . a few 3 T c . We will see that the effective 3D approach to high temperature gauge theories, developed in [5][6][7] (for a review, see [8]) allows a simple and transparent gauge-invariant definition of the Debye mass [4], while 3D lattice Monte Carlo simulations provide an economical way to determine its value. The corrections to the leading result we shall find are numerically large; thus many computations in the phenomenology of quark-gluon plasma in heavy ion collisions should be reanalyzed.The theory we shall study is QCD with N f massless quark flavors and with the gauge group SU͑N͒ with N 2, 3. At high temperatures and zero...

Effective Monopole Action at Finite Temperature in SU(2) Gluodynamics

“…The details of the relation between the phase diagram and the parameter region of the dimensional reduced (GG) 3D in 2-loop perturbative calculation have been studied in [5]. Using the parameter in 2-loop perturbative calculation, the Debye-screening mass is shown to be a nonperturbative physical quantity in itself [1]. The validity of the dimensional reduction for T ≥ 2T c in (SU(2)) 4D have also been confirmed for the glueball spectrum [6] and the gauge-fixed propagator [7].…”

“…At high temperature, QCD enters the Quark Gluon Plasma (QGP) phase in which colors are deconfined and chiral symmetry is restored. It is known that not only perturbative but also nonperturbative effects such as the spatial string tension and the Debye-screening mass [1] exist even in the deconfinement phase.…”

Notes on the Deconfining Phase Transition

“…This implies that the mixing between Polyakov loops and and plaquette operators are small. This small mixing is found in related problems [7]. )…”

Lattice QCD at High Temperature and Density

“…In fact, for Tc < ∼ T < ∼ 100 Tc one finds that mD is still about three times larger than this leading order value [26]. A consequence of this large value of the screening mass is that also short distance properties of the plasma are strongly influenced by nonperturbative screening effects; the Debye screening length, rD ≡ 1/mD, becomes compatible with the characteristic length scale rSB in a free gas where the main contribution to the Stefan-Boltzmann law originates from particle with momenta p ∼ 3T , i.e.…”