Pion dissociation by the Mott effect in quark plasma is described within the generalized Beth-Uhlenbeck approach on the basis of the PNJL model which allows for a unified description of bound, resonant and scattering states. As a first approximation, we utilize the Breit-Wigner ansatz for the spectral function and clarify its relation to the complex mass pole solution of the pion Bethe-Salpeter equation. Application of the Levinson theorem proves that describing the pion Mott dissociation solely by means of spectral broadening of the pion bound state beyond T Mott leaves out a significant aspect. Thus we acknowledge the importance of the continuum of scattering states and show its role for the thermodynamics of pion dissociation.

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The 2-flavor Polyakov-loop extended model is generalized by taking into account the effective fourquark vector-type interaction with the coupling strengths, which are endowed with a dependence on the Polyakov field Φ. The effective vertex generates entanglement interaction between the Polyakov loop and the chiral condensate. We investigate the influence of an additional quark vector interaction and the entanglement interaction on the location of the critical end-point at the given chemical potential or quark density. It is shown that the finite value of the vector interaction strength Gv improves the model agreement with the lattice data. The influence of the non-zero Gv and entanglement on the thermodynamic observables and the curvature of the crossover boundary in the T − µ plane is also examined.

The thermodynamic behavior of the two-flavor (Nf = 2) three-color (Nc = 3) Polyakov-loop-extended Nambu–Jona-Lasinio (PNJL) model at the finite chemical potential is investigated. New lattice gluon data for gluon thermodynamics are used defining the effective potential within polynomial and logarithmic forms of its approximation. We study the effects of using different sets of data and different forms of the potential on thermodynamic properties of hot and dense matter. It is found that the PNJL thermodynamics depends stronger on the form of the effective potential than on the used lattice data set. Particular attention is paid to the phase diagram in the (T, μ) plane.

The behavior of strange matter in the frame of the SU(3) Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model including the U A (1) anomaly is considered. We discuss the appearance of a peak in the ratio of the number of strange mesons to nonstrange mesons known as the "horn." The PNJL model gives a schematic description of the chiral phase transition and meson properties at finite temperature and density. By using the model, we can show that the splitting of kaon and antikaon masses appears as a result of the introduction of density. This may explain the difference in the K + /π + ratio and the K − /π − ratio at low √ s NN and their tendency to the same value at high √ s NN. We also show that the rise in the ratio K + /π + appears near the critical endpoint when we build the K + /π + ratio along the phase-transition diagram and it can be considered as a critical region signal.