Publications Repository - Helmholtz-Zentrum Dresden-Rossendorf

We describe multi-quark 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 property of color SU(3) center symmetry as an aspect of confinement.
A higher multi-quark cluster of size $a$ is described as a binary composite of smaller subclusters a1 and a2 (where a1+a2=a) with a bound state and a scattering state spectrum. 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 compare the simple "step-up-step-down" model that ignores continuum correlations with 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 largest cluster contains six quarks.
One striking result is the suppression of the abundance of colored multi-quark clusters at low temperatures by the coupling to the Polyakov loop. This is understood in close analogy to the suppression of free quark abundances by the same mechanism. We derive here the corresponding Polyakov-generalized distribution functions of b -quark clusters. Another new result is the effective suppression of free quarks by a large (> 600 MeV) constituent quark mass generated by dynamical breaking of the approximate chiral symmetry in the quark sector and its sudden restoration at the Mott temperature, where all hadronic bound states become dissociated into the multi-quark continuum.
Within our approach we calculate thermodynamic properties such as baryon density and entropy. 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.