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We consider a cluster expansion for strongly correlated quark matter wherethe clusters are baryons with spectral properties that are described within thegeneralized Beth-Uhlenbeck approach by a medium dependent phase shift. Weemploy a simple ansatz for the phase shift which fulfils the Levinson theoremby describing an on-shell bound state with an effective mass and models thecontinuum by an anti-bound state located at the mass of the three-quarkthreshold. The quark and baryon interactions are accounted for by the couplingto scalar and vector meson mean fields modelled by density functionals. Atincreasing density and temperature, due to the different medium-dependence ofquark and baryon masses, the Mott dissociation of baryons occurs and thenuclear cluster contributions to the thermodynamics vanish. It is demonstratedon this simple example that this unified approach to quark-nuclear matter iscapable of describing crossover as well as first order phase transitionbehaviour in the phase diagram with a critical endpoint. Changing the mesonmean field, the case of a "crossover all over" in the phase diagram is alsoobtained.

A unified quark-nuclear matter equation of state from the cluster virial expansion within the generalized Beth-Uhlenbeck approach