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

Abstract

We consider a cluster expansion for strongly correlated quark matter where the clusters are baryons with spectral properties that are described within the generalized Beth–Uhlenbeck approach by a medium dependent phase shift. We employ a simple ansatz for the phase shift which describes an on-shell bound state with an effective mass and models the continuum by an anti-bound state located at the mass of the three-quark continuum threshold, so that the Levinson theorem is fulfilled by construction. The quark and baryon interactions are accounted for by the coupling to scalar and vector meson mean fields modelled by density functionals. At increasing density and temperature, due to the different medium-dependence of quark and baryon masses, the Mott dissociation of baryons occurs and its contributions to the thermodynamics vanish. It is demonstrated on this simple example that this unified approach to quark-hadron matter is capable of describing crossover as well as first order phase transition behaviour in the phase diagram with a critical endpoint. Changing the meson mean field, the case of a “crossover all over” in the phase diagram is also obtained.

Quark Cluster Expansion Model for Interpreting Finite-T Lattice QCD Thermodynamics

“…Another important aspect of the present approach is that it leads to a relativistic density functional theory for QCD matter in the QCD phase diagram, with the known limits of the HRG and pQCD manifestly implemented. Such an approach allows us to predict the existence and location of critical endpoints in the QCD phase diagram, as has been demonstrated, e.g., in [41], where a dependence on a free parameter could have-besides the critical endpoint of the liquid-gas transition in the nuclear matter phase-another endpoint for the deconfinement transition or none. This "crossover all over" case of the QCD phase diagram is impossible to address with two-phase approaches that use a Maxwell construction for the phase transition.…”

Unified Quark–Hadron EoS and Critical Endpoint in the QCD Phase Diagram

“…In developing the approach further, both regions of the QCD phase diagram shall be described with the same model assumptions and an extension to finite isospin asymmetries as well as inclusion of the parity doubling aspects in the HRG component of the EoS shall be accomplished. These aspects are Liquid-Gas Abridged from [27].…”

“…In the low-temperature case (T < 100 MeV) that has been discussed in Ref. [27], the same ansatz (4) for the hadronic phase shifts has been made, but the number of relevant components in the HRG is reduced to that of the nucleons, since no mesons get excited at this low T and we restrict ourselves to chemical potentials below the hyperon threshold. With similar arguments the Polyakov-loop potential and perturbative QCD corrections are neglected in this first step calculation.…”

“…The lower left panel shows the concentration of hadrons and quarks from the cluster expansion, where the dashed lines are the modifications due to Maxwell construction. Abridged from [27].…”

“…The green dashed line represents a crossover all over scenario without critical endpoint. The dashed lines show the crossover transition, retrieved from the inflection point in chemical potential over density.Abridged from[27].…”