Generalized Beth-Uhlenbeck approach to the equation of state for quark-hadron matter

TL;DR

This paper develops a unified equation of state for quark-hadron matter using a generalized Beth-Uhlenbeck approach, incorporating correlations and phase shifts, and shows it aligns well with lattice QCD results.

Contribution

It introduces a novel thermodynamic framework combining the Beth-Uhlenbeck approach with a $ ext{Φ}$-derivable method for quark-hadron matter, capturing phase transitions and hadron dissociation.

Findings

Accurately models the transition from hadron resonance gas to quark-gluon plasma.

Reproduces lattice QCD thermodynamics data.

Encodes Mott dissociation of hadrons via phase shifts.

Abstract

A unified equation of state for quark-hadron matter is presented in the generalized Beth-Uhlenbeck form. It follows from a $\Phi-$derivable approach to the thermodynamic potential where the ansatz for the $\Phi$ functional contains all 2PI diagrams at two-loop order formed with quark cluster Green's functions for quark, diquark, meson and baryon propagators. We present numerical results using an effective model for the generic behaviour of hadron masses and phase shifts at finite temperature which shares basic features with recent developments within the PNJL model for correlations in quark matter. We obtain the transition between a hadron resonance gas phase and the quark gluon plasma where the Mott dissociation of hadrons is encoded in the hadronic phase shifts. The resulting thermodynamics is in very good agreement with recent lattice QCD simulations.