Polyakov–Nambu–Jona-Lasinio Models and QCD Phase Diagram

Strongly interacting matter under extreme conditions is a topic of continuing interest, both from the point of view of ultrarelativistic heavy-ion collisions and lattice QCD. In our work we use approaches based on the timehonored Nambu–Jona-Lasinio model in order to investigate the nature of the different phases of QCD matter at finite temperatures and densities. From hadron spectroscopy it is well-known that the chiral symmetry of the QCD Lagrangian is spontaneously broken, manifested in mass gaps between, e. g., the vector and pseudovector mesons. When dealing with two light upand down quarks (mu ≈ md ∼ O(10MeV) plus one heavy strange quark (ms ∼ O(100MeV) one has to additionally include the anomalous breaking of the axial U(1) symmetry. This last point is particularly important in order to describe the mass splitting between the etaand the eta-prime meson. The NJL model and a nonlocal version of it, both used in our work, can account for this symmetry breaking pattern. The thermodynamical description of NJL type models does not inlcude the important feature of confinement. This can be introduced by implementing the Polyakov loop 〈Φ〉 as the proper order parameter for the confinementdeconfinement transition. The resulting models are of the Polyakov-loop extendend NJL (PNJL) type [1, 2, 3]. Finite temperature and finite density phenomena are described by standard means of thermal field theory. The nonlocal approach leads the phase diagram shown in Fig. 1. It shows the low-density behavior expected from lattice QCD calculations: namely a crossover region that terminates at a critical point located at TCEP ≈ 170MeV and μCEP ≈ 180MeV which marks the endpoint of the following first order transition line. From our investigations of the phase diagram we conclude that the location of the critical point is sensitive to the strength of the axialU(1) breaking. A better understanding of the mechanism at the origin of these transitions requires the investigation of fluctuations beyond mean field in the PNJL model. By performing numerical simulations of the thermodynamics using standard Monte-Carlo techniques we can perform this improvement [4]. The relevance of fluctuations on the thermodynamics is particularly evident looking at the flavor non-diagonal second derivative of the thermodynamic grand canonical partition function with respect to quark chemical potentials. The PNJL mean field calculation predicts a vanishing coefficient, whereas fluctuations (primarily of pionic origin) are at the origin of a non-zero value of this flavor off-diagonal susceptibility, χud. In Fig. 2 the good agreement between ∗Work supported in part by GSI, BMBF, and by the DFG Excellence Cluster “Origin and Structure of the Universe”. lattice data and the Monte-Carlo calculation (MC-PNJL) clearly shows the role of such fluctuations in the model.