Determining the transport coefficients of the quark-gluon plasma using a new relaxation time approximation of the Boltzmann equation

Abstract

We investigate the transport properties of a kinetic theory model that is tuned to describe the thermodynamic properties of QCD at zero chemical potential using a new formulation of the relaxation time approximation. In contrast to previous approaches, the latter is constructed to preserve the fundamental properties of the collision term of the Boltzmann equation for any energy-dependence of the relaxation time. A novel choice of matching conditions is implemented to ensure that the background mean-field depends only on the temperature even when the system is out of equilibrium. We provide a consistent analysis of how the transport coefficients of relativistic Navier-Stokes theory vary with the energy dependence of the relaxation time. We also show that the entropy production of this theory is consistent with the second law of thermodynamics and verify that it is independent of the matching conditions employed. We used this fact to calculate the matching independent combination of transport coefficients.

Novel relaxation time approximation: a consistent calculation of transport coefficients with QCD-inspired relaxation times

“…The entropy current for classical quasiparticles is S µ = dP p µ f p (1 − ln f p ). We note that the entropy production does not depend on the choice of matching conditions [3]. To first order in the Chapman-Enskog expansion, one finds…”

“…Plots for B(T ) and M (T ) can be seen in Refs. [2,3]. Qualitatively, M (T )/T is very large at low temperatures and saturates at M (T )/T ≈ 1.1 at high temperatures.…”

“…[5] the conservation laws hold at the microscopic level even when considering momentum-dependent relaxation times and arbitrary matching conditions. In practice, we approximate the collision term as [3]…”

“…In particular, obtaining the transport coefficients of the quark-gluon plasma, throughout the QCD phase diagram, is a very challenging task that is currently beyond the reach of first-principles techniques [1]. In this contribution, we compute the transport coefficients of an effective kinetic model [2,3] with a temperature-dependent mass whose equation of state mimics lattice QCD thermodynamics [4]. We use the new relaxation time approximation (RTA) of the relativistic Boltzmann equation proposed in [5] and impose alternative matching conditions such that the interaction energy [6] depends only on the temperature even out of equilibrium.…”

“…Even though this is not achieved at high temperatures, where M/T → 1.1[3], these expansions serve as estimates.…”