Spectral and Transport Properties of Quark-Gluon Plasma in a Nonperturbative Approach

TL;DR

This paper investigates the spectral and transport properties of the quark-gluon plasma using a nonperturbative approach based on the Luttinger-Ward functional, revealing two distinct scenarios with different coupling strengths and their implications for transport coefficients.

Contribution

The study introduces a nonperturbative method employing the Luttinger-Ward functional to compute the QGP's equation of state and distinguishes strongly and weakly coupled scenarios through transport property analysis.

Findings

Identified two solutions: strongly coupled and weakly coupled scenarios.

Transport coefficients differ significantly between the two scenarios at low temperatures.

The ratio of shear viscosity to diffusion coefficient can distinguish coupling regimes.

Abstract

Nonperturbative methods play an important role in quantum many-body systems, especially in situations with an interplay of continuum and bound states and/or large coupling strengths between the constituents. Employing the Luttinger-Ward functional (LWF) we have computed the equation of state (EoS) of the quark-gluon plasma (QGP) using fully dressed selfconsistent 1- and 2-body propagators. We first give an alternative derivation of our previously reported results for resumming the ladder diagram series of the LWF using a "matrix log" technique which accounts for dynamically formed bound and resonant states. Two types of solutions were found in selfconsistent fits to lattice-QCD data for the EoS, heavy-quark free energy and quarkonium correlators: a strongly coupled scenario (SCS) with broad parton spectral functions and strong meson resonances near the transition temperature vs. a weakly coupled scenario (WCS) with well-defined parton quasiparticles and weak meson resonances. Here, we discuss how these solutions can be distinguished by analyzing the pertinent transport properties. We focus on the specific shear viscosity, $(4\pi )\eta/s$, and the heavy-quark diffusion coefficient, $(2\pi T) {\cal D}_s$, including its mass dependence. At low temperatures, in the SCS, they turn out to be a factor of 2 within their conjectured quantum lower bound, while they are a factor of 2-5 larger in the WCS. At higher temperatures, the transport parameters of the two scenarios approach each other. We propose the ratio $ (4\pi\eta/s)/(2\pi T {\cal D}_s )$ as a measure to distinguish the perturbative and strong-coupling limits of 5/2 and 1, respectively.