The chiral phase transition of the strongly interacting matter is investigated at nonzero temperature and baryon chemical potential (${\mu }_B$) within an extended ($2+1$) flavor Polyakov constituent quark-meson model that incorporates the effect of the vector and axial vector mesons. The effect of the fermionic vacuum and thermal fluctuations computed from the grand potential of the model is taken into account in the curvature masses of the scalar and pseudoscalar mesons. The parameters of the model are determined by comparing masses and tree-level decay widths with experimental values in a ${\chi }^2$-minimization procedure that selects between various possible assignments of scalar nonet states to physical particles. We examine the restoration of the chiral symmetry by monitoring the temperature evolution of condensates and the chiral partners’ masses and of the mixing angles for the pseudoscalar $\eta -{\eta }^{\prime }$ and the corresponding scalar complex. We calculate the pressure and various thermodynamical observables derived from it and compare them to the continuum extrapolated lattice results of the Wuppertal-Budapest collaboration. We study the $T-{\mu }_B$ phase diagram of the model and find that a critical endpoint exists for parameters of the model, which give acceptable values of ${\chi }^2$.

The boundary of the first order chiral phase transition region is studied in the $m_{\pi }-m_K-{\mu }_B$ space using the one-loop optimized perturbation theory for the resummation of the perturbative series. Chiral perturbation theory for mesons and baryons is used for the $T=0$ parametrization of the model. The surface of second order transition points bends with increasing ${\mu }_B$ towards the physical point of the $m_{\pi }-m_K$ mass plane allowing for the existence of the critical end point in the ${\mu }_B-T$ plane at the physical point. The location and scaling region of the CEP is explored.

We investigate the influence of the asymmetric quark matter (rho_u\ne rho_d\ne rho_s) on the mass of the quasiparticles and the phase diagram of the chiral quark model parametrized at one-loop level of the renormalized theory, using the optimized perturbation theory for the resummation of the perturbative series. The effect of various chemical potentials introduced in the grand canonical ensemble is investigated with the method of relativistic many-body theory. The temperature dependence of the topological susceptibility is estimated with the help of the Witten-Veneziano mass formula.Comment: RevTeX4, 13 pages, 6 figures, version accepted for publication in Phys. Rev.

The phase diagram of the three-flavor QCD is mapped out in the low mass corner of the ($m_{\pi }-m_K$)-plane with help of the $S{U}_L(3)\times S{U}_R(3)$ linear sigma model ($L\sigma M$). A novel zero temperature parametrization is proposed for the mass dependence of the couplings away from the physical point based on the three-flavor chiral perturbation theory (U(3) ChPT). One-loop thermodynamics is constructed by applying optimized perturbation theory. The unknown dependence of the scalar spectra on the pseudoscalar masses limits the accuracy of the predictions. Results are compared to lattice data and similar investigations with other variants of effective chiral models. The critical value of the pion mass is below 65 MeV for all $m_K$ values $\lesssim 800\mathrm{MeV}$. Along the diagonal $m_{\pi }=m_K$, we estimate $m_{\mathrm{crit}}(\mathrm{diag})=40\pm 20\mathrm{MeV}$.

The chiral phase boundary of strong matter is determined in the T–μ plane from the chiral quark model, applying a non-perturbatively renormalised treatment, involving chains of pion-bubbles and 1-loop fermion contributions. In the absence of explicit symmetry breaking the second order portion of the phase boundary and the location of the tricritical point (TCP) are determined analytically. Sensitivity of the results to the renormalisation scale is carefully investigated. The softening of the σ-pole near the second order transitions is confirmed

We extend our previous investigation of the two-loop $\mathrm{$\Phi${}}$-derivable approximation to the case of a finite chemical potential $$\mu${}$ and discuss Bose-Einstein condensation in the case of a charged scalar field with $O(2)$ symmetry. We show that the approximation is renormalizable by means of counterterms which are independent of both the temperature and the chemical potential. We point out the presence of an additional skew contribution to the propagator as compared to the $$\mu${}=0$ case, which comes with its own gap equation (except at Hartree level). We solve this equation together with the field equation, and the usual longitudinal and transversal gap equations to find that the transition is second order, in agreement with recent lattice results to which we compare. We also discuss a general criterion an approximation should obey for the so-called Silver Blaze property to hold, and we show that any $\mathrm{$\Phi${}}$-derivable approximation at finite temperature and density obeys this criterion if one chooses an UV regularization that does not cut off the Matsubara sums.