Thermodynamics of the high-temperature quark-gluon plasma

TL;DR

High-temperature QCD thermodynamics is analyzed through weak-coupling methods, comparing perturbation theory with lattice results. The authors develop and compare resummation schemes, including HTL perturbation theory, screened perturbation theory, dimensional reduction, and Φ-derivable (2PI) approaches, with a focus on entropy as a diagnostic and its quasiparticle interpretation. They show that entropy and quark-number susceptibilities can be described accurately by dressed quasiparticles for $T \gtrsim 2.5\,T_c$, supporting a weakly interacting quasiparticle picture of the quark-gluon plasma, while nonperturbative magnetic effects remain a caveat. The work demonstrates how soft-scale physics can be captured via effective theories and resummations, yielding results that align with lattice benchmarks and informing phenomenology for heavy-ion collisions.

Abstract

We review the various methods which have been employed recently to describe the thermodynamics of the high temperature quark-gluon plasma using weak coupling techniques, and we compare their results with those of most recent lattice gauge calculations. Many of the difficulties encountered with perturbation theory at finite temperature are in fact not specific to QCD but are present in any field theory at finite temperature and will be discussed first in the simple example of the scalar field theory. We discuss the merits and limitations of various techniques which have been used to go beyond perturbation theory in the soft sector, such as dimensional reduction, screened perturbation theory or hard-thermal-loop perturbation theory, and Phi-derivable approximations. In the last part of the review, we focus on the later, which lead to a remarkably simple expression for the entropy of the quark-gluon plasma. When complemented with further, physically motivated, approximations, this approach reproduces accurately the entropy obtained from lattice gauge calculations at temperatures above 2.5 T_c, where T_c is the deconfinement temperature. This calculation thus provides also support to the physical picture of the quark-gluon plasma as a gas of weakly interacting quasiparticles.

Figures (21)

• Figure 1: Weak-coupling expansion through orders $g^2$, $g^3$, $g^4$, and $g^5$ for the pressure normalized to that of an ideal gas as a function of $g(2\pi T)$ in $\phi^4$ theory.
• Figure 2: Weak-coupling expansion to orders $g^2$, $g^3$, and $g^4$ for the screening mass normalized to the temperature as a function of $g(2\pi T)$.
• Figure 3: Lowest order correction to the self-energy in scalar $\phi^4$ theory.
• Figure 4: The lowest order correction to the thermodynamic potential in $\phi^4$ theory.
• Figure 5: Diagrams that are resummed when computing the tadpole in Fig. \ref{['fig:tadpole']} with the dressed propagator in eq. (\ref{['hatD']}).