Chiral symmetry restoration at nonzero temperature and quark densities are investigated in the framework of a linear sigma model with $N_f=3$ light quark flavors. After the derivation of the grand potential in mean-field approximation, the nonstrange and strange condensates, the in-medium masses of the scalar and pseudoscalar nonets are analyzed in hot and dense medium. The influence of the axial anomaly on the nonet masses and the isoscalar mixings on the pseudoscalar $\eta \mathrm{\text{−}}{\eta }^{\prime }$ and scalar $\sigma (600)\mathrm{\text{−}}{f}_0(1370)$ complex are examined. The sensitivity of the chiral phase transition as well as the existence and location of a critical end point in the phase diagram on the value of the sigma mass are explored. The chiral critical surface with and without the influence of the axial $U(1{)}_A$ anomaly is elaborated as a function of the pion and kaon masses for several values of the sigma mass.

• Received 11 August 2008

DOI:https://doi.org/10.1103/PhysRevD.79.014018