Quark cluster expansion model for interpreting finite-T lattice QCD thermodynamics

TL;DR

This paper introduces a unified quark cluster expansion model to interpret finite-temperature lattice QCD thermodynamics, capturing the transition from hadron resonance gas to quark-gluon plasma with high accuracy.

Contribution

It develops a generalized Beth-Uhlenbeck approach with a novel ansatz for phase shifts, incorporating chiral symmetry restoration and Polyakov loop dynamics to model QCD thermodynamics.

Findings

Pressure matches lattice QCD results up to high temperatures.

Models the hadron-quark transition within 150-185 MeV.

Includes a virial correction to improve accuracy.

Abstract

We present a unified approach to the thermodynamics of hadron-quark-gluon matter at finite temperatures on the basis of a quark cluster expansion in the form of a generalized Beth-Uhlenbeck approach with a generic ansatz for the hadronic phase shifts that fulfills the Levinson theorem. The change in the composition of the system from a hadron resonance gas to a quark-gluon plasma takes place in the narrow temperature interval of $150 - 185$ MeV where the Mott dissociation of hadrons is triggered by the dropping quark mass as a result of the restoration of chiral symmetry. The deconfinement of quark and gluon degrees of freedom is regulated by the Polyakov loop variable that signals the breaking of the $Z(3)$ center symmetry of the color $SU(3)$ group of QCD. We suggest a Polyakov-loop quark-gluon plasma model with $\mathcal{O}(\alpha_s)$ virial correction and solve the stationarity condition of the thermodynamic potential (gap equation) for the Polyakov loop. The resulting pressure is in excellent agreement with lattice QCD simulations up to high temperatures.