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We describe multiquark clusters in quark matter within a Beth-Uhlenbeckapproach in a background gluon field coupled to the underlying chiral quarkdynamics using the Polyakov gauge which establishes the center symmetry ofcolor SU(3) that suppresses colored states as an aspect of confinement. Quarkconfinement is modeled by a large quark mass in vacuum motivated by a confiningdensity functional approach. A multiquark cluster containing $n$ quarks andantiquarks is described as a binary composite of smaller subclusters $n_1$ and$n_2$ ($n_1+n_2=n$). It has a spectrum consisting of a bound state and ascattering state continuum. For the corresponding cluster-cluster phase shiftswe discuss simple ans\"atze that capture the Mott dissociation of clusters as afunction of temperature and chemical potential. We go beyond the simple"step-up-step-down" model that ignores continuum correlations and introduce animproved model that includes them in a generic form. In order to explain themodel, we restrict ourselves here to the cases where the cluster size is $1 \len \le 6$. A striking result is the suppression of the abundance of coloredmultiquark clusters at low temperatures by the coupling to the Polyakov loopand their importance for a quantitative description of lattice QCDthermodynamics at non-vanishing baryochemical potentials. An importantingredient are Polyakov-loop generalized distribution functions of $n$-quarkclusters which are derived here for the first time. Within our approach wecalculate thermodynamic properties such as baryon density and entropy. Wedemonstrate that the limits of a hadron resonance gas at low temperatures and$\mathcal{O}(g^2)$ perturbative QCD at high temperatures are correctlyreproduced. A comparison with lattice calculations shows that our model is ableto give a unified, systematic approach to describe properties of thequark-gluon-hadron system.

Thermodynamics of quark matter with multiquark clusters in an effective Beth-Uhlenbeck type approach