Phase transitions in hot and dense matter and the in-medium behavior of pseudoscalar mesons (π ± , π 0 , K ± , K 0 ,K 0 , η and η ′ ) are investigated, in the framework of the three flavor NambuJona-Lasinio model, including the 't Hooft interaction, which breaks the U A (1) symmetry. Three different scenarios are considered: zero density and finite temperature, zero temperature and finite density in quark matter with different degrees of strangeness, and finite temperature and density.At T = 0, the role of strange valence quarks in the medium is discussed, in connection with the phase transition and the mesonic behavior. It is found that the appearance of strange quarks, above certain densities, leads to meaningful changes in different observables, especially in matter with β -equilibrium. The behavior of mesons in the T − ρ plane is analyzed in connection with possible signatures of restoration of symmetries.

The modification of mesonic observables in a hot medium is analyzed as a tool to investigate the restoration of chiral and axial symmetries in the context of the Polyakov-loop extended Nambu-JonaLasinio model. The results of the extended model lead to the conclusion that the effects of the Polyakov loop are fundamental for reproducing lattice findings. In particular, the partial restoration of the chiral symmetry is faster in the Polyakov-Nambu-Jona-Lasinio model than in the Nambu-Jona-Lasinio one, and it is responsible for several effects: the meson-quark coupling constants show a remarkable difference in both models, there is a faster tendency to recover the Okubo-Zweig-Iizuka rule, and finally the topological susceptibility nicely reproduces the lattice results around T=T c % 1:0.

We investigate the phase diagram of the so-called Polyakov-Nambu-Jona-Lasinio model at finite temperature and non-zero chemical potential with three quark flavors. Chiral and deconfinement phase transitions are discussed and the relevant order-like parameters are analyzed. The results are compared with simple thermodynamic expectations and lattice data. We present the phase diagram in the (T, µ B ) plane, paying special attention to the critical end point: as the strength of the flavor-mixing interaction becomes weaker, the critical end point moves to low temperatures and can even disappear.

The effects of a type of regularization for finite temperatures on the restoration of chiral and axial symmetries are investigated within the SU(3) Nambu-Jona-Lasinio model. The regularization consists in using an infinite cutoff in the integrals that are convergent at finite temperature, a procedure that allows one to take into account the effects of high momentum quarks at high temperatures. It is found that the critical temperature for the phase transition is closer to lattice results than the one obtained with the conventional regularization, and the restoration of chiral and axial symmetries, signaled by the behavior of several observables, occurs simultaneously and at a higher temperature. The restoration of the axial symmetry appears as a natural consequence of the full recovering of the chiral symmetry that was dynamically broken. By using an additional ansatz that simulates instanton suppression effects, by means of a convenient temperature dependence of the anomaly coefficient, we found that the restoration of U(2) symmetry is shifted to lower values, but the dominant effect at high temperatures comes from the new regularization that enhances the decrease of quark condensates, especially in the strange sector.

The behavior of neutral pseudoscalar mesons π 0 , η and η ′ in hot and dense matter is investigated, in the framework of the three flavor Nambu-Jona-Lasinio model. Three different scenarios are considered: zero density and finite temperature, zero temperature and finite density in a flavor asymmetric medium with and without strange valence quarks, and finite temperature and density. The behavior of mesons is analyzed in connection with possible signatures of restoration of symmetries. In the high density region and at zero temperature it is found that the mass of the η ′ increases, the deviation from the mass of the η being more pronounced in matter without strange valence quarks.