Generalized Beth-Uhlenbeck approach to the thermodynamics of quark-hadron matter

We present a unified approach to the transition from hadronic matter to quark matter where hadrons are treated as bound states of quarks which dissociate at high densities due to quark Pauli blocking. The newly developed approach makes use of a cluster virial expansion formulated in terms of a generalized $\Phi$-derivable approach to multi-quark correlations with bound and continuum states in their spectrum encoded in hadron phase shifts. Our model can be used to obtain thermodynamic functions not only at zero and small chemical potentials, where they are consistent with lattice QCD simulations, but also at large chemical potentials where lattice QCD simulations have the sign problem. By applying a reaction-kinetic criterion for the chemical freeze-out of multi-quark clusters in heavy-ion collisions, we demonstrate that the chemical freeze-out coincides with their Mott transition. The approach can be applied to study the effects of the QCD transition on primordial black hole formation in the early Universe and on hybrid neutron star formation in supernova explosions and binary neutron star mergers.