https://doi.org/10.1140/epja/s10050-023-01229-8
Regular Article - Theoretical Physics
Thermodynamics of quark matter with multiquark clusters in an effective Beth-Uhlenbeck type approach
1
Institute of Theoretical Physics, University of Wroclaw, Max Born place 9, 50-204, Wroclaw, Poland
2
Helmholtz-Zentrum Dresden-Rossendorf (HZDR), Bautzner Landstrasse 400, 01328, Dresden, Germany
3
Center for Advanced Systems Understanding (CASUS), Untermarkt 20, 02826, Görlitz, Germany
4
Incubator of Scientific Excellence—Centre for Simulations of Superdense Fluids, University of Wrocław, Max Born place 9, 50-254, Wroclaw, Poland
5
Institute of Physics, University of Rostock, Albert-Einstein Str. 23-24, 18059, Rostock, Germany
Received:
15
August
2023
Accepted:
22
December
2023
Published online:
24
January
2024
We describe multiquark clusters in quark matter within a Beth-Uhlenbeck approach in a background gluon field coupled to the underlying chiral quark dynamics using the Polyakov gauge. An effective potential for the traced Polyakov loop is used to establish the center symmetry of the SU(3) color which suppresses colored states and its dynamical breaking as an aspect of the confinement/deconfinement transition. Quark confinement is modeled by a large quark mass in vacuum which is motivated by a confining density functional approach. A multiquark cluster containing n quarks and antiquarks is described as a binary composite of smaller subclusters 
and 
(
). It has a spectrum consisting of a bound state and a scattering state continuum. For the corresponding cluster-cluster phase shifts we use simple ansätze that capture the Mott dissociation of clusters as a function of temperature and chemical potential. We go beyond the simple “step-up-step-down” model that ignores continuum correlations and introduce an improved model that includes them in a generic form. In order to explain the model, we restrict ourselves here to the cases where the cluster size is 
. A striking result is the suppression of the abundance of colored multiquark clusters at low temperatures by the coupling to the Polyakov loop and their importance for a quantitative description of lattice QCD thermodynamics at non-vanishing baryochemical potentials. An important ingredient are Polyakov-loop generalized distribution functions of n-quark clusters which are derived here for the first time. Within our approach we calculate thermodynamic properties such as baryon density and entropy. We demonstrate that the limits of a hadron resonance gas at low temperatures and 
perturbative QCD at high temperatures are correctly reproduced. A comparison with lattice calculations shows that our model is able to give a unified, systematic approach to describe properties of the quark-gluon-hadron system.
This work has been initiated by Peter Schuck in discussions during the Workshop on “Light Clusters in Nuclei and Nuclear Matter: Nuclear Structure and Decay, Heavy Ion Collisions and Astrophysics”, at the ECT* Trento, September 2–6, 2019.
© The Author(s) 2024
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