The present work generalizes a nonlocal version of the Polyakov-loop-extended Nambu and Jona-Lasinio (PNJL) model to the case of three active quark flavors, with inclusion of the axial U(1) anomaly. Gluon dynamics is incorporated through a gluonic background field, expressed in terms of the Polyakov loop. The thermodynamics of the nonlocal PNJL model accounts for both chiral and deconfinement transitions. Our results obtained in mean-field approximation are compared to lattice QCD results for $N_f=2+1$ quark flavors. Additional pionic and kaonic contributions to the pressure are calculated in random phase approximation. Finally, this nonlocal three-flavor PNJL model is applied to the finite density region of the QCD phase diagram. It is confirmed that the existence and location of a critical point in this phase diagram depend sensitively on the strength of the axial U(1) breaking interaction.

• Received 18 November 2009

DOI:https://doi.org/10.1103/PhysRevD.81.074034