ar X iv : n uc l - th / 9 50 30 03 v 2 8 M ar 1 99 5 Hot gluon propagator 1

One of the recently most developing fields of high energy heavy ion physics is the study of the underlying field theory at high temperatures. Despite of the naive picture of the quark gluon plasma as an ideal gas of quarks and gluons stemming from a given interpretation of early lattice gauge theory simulations it is since long clear that the continuum theory is plagued by serious infrared divergences on the supersoft momentum scale O(gT ) at the temperature T with a coupling constant g [1, 2]. Those effects, however, cannot be seen on small size lattices. Even the behavior of the quark gluon plasma on the intermediate, O(gT ) momentum scale is nontrivial, because in this case a thermal field A ≈ T contributes with the same order to the covariant derivative (or kinetic momentum) as the pure derivative (momentum): D = ∂ − gA ≈ gT − gT. It means that effects of higher order in the T = 0 perturbation theory mixes to effects of lower order in the coupling strength g but higher order in the “gradient expansion” of the thermal background. Therefore a new expansion parameter gT is introduced making possible to resum contributions of high momentum (O(T )) hard loops in the propagators and vertices involving soft (O(gT )) momenta. This method, called “hard thermal loop” expansion, is due to Braaten and Pisarski[3, 4, 6]. As a first application the gluon damping rate, i.e. the imaginary part of the hot gluon self-energy describing loss and gain of gluon numbers in a given momentum bin, has been calculated. This, in contrast to earlier calculations which obtained a gauge dependent result even on the sign of this quantity, became positive and gauge independent for zero momentum. The HTL resummation describes the electric (Debye) screening, inserting a self energy term into the plasmon (low momentum) propagator, which is obtained by integrating over hard (high momentum) thermal loops. This selfenergy is symmetric in color and space-time indices reminding us to the physical mechanism behind it: charges (currents) are screened by fields induced by the charges (currents) themselves in a linear approximation. Self correlation is by definition symmetric. Since there are general considerations showing that the zero momentum (static, long wavelength) behavior of the gluon propagator is gauge invariant,