QCD thermodynamics is investigated by means of the Polyakov-loop-extended Nambu Jona-Lasinio (PNJL) model, in which quarks couple simultaneously to the chiral condensate and to a background temporal gauge field representing Polyakov loop dynamics. The behaviour of the Polyakov loop as a function of temperature is obtained by minimizing the thermodynamic potential of the system. A Taylor series expansion of the pressure is performed. Pressure difference and quark number density are then evaluated up to sixth order in quark chemical potential, and compared to the corresponding lattice data. The validity of the Taylor expansion is discussed within our model, through a comparison between the full results and the truncated ones.

An updated version of the PNJL model is used to study the thermodynamics of N f 2 quark flavors interacting through chiral four-point couplings and propagating in a homogeneous Polyakov loop background. Previous PNJL calculations are extended by introducing explicit diquark degrees of freedom and an improved effective potential for the Polyakov loop field. The mean field equations are treated under the aspect of accommodating group theoretical constraints and issues arising from the fermion sign problem. The input is fixed exclusively by selected pure-gauge lattice QCD results and by pion properties in vacuum. The resulting T; phase diagram is studied with special emphasis on the critical point, its dependence on the quark mass and on Polyakov loop dynamics. We present successful comparisons with lattice QCD thermodynamics expanded to finite chemical potential .

A nonlocal covariant extension of the two-flavor Nambu and Jona-Lasinio (NJL) model is constructed, with built-in constraints from the running coupling of QCD at high-momentum and instanton physics at low-momentum scales. Chiral low-energy theorems and basic current algebra relations involving pion properties are shown to be reproduced. The momentumdependent dynamical quark mass derived from this approach is in agreement with results from Dyson-Schwinger equations and lattice QCD. At finite temperature, inclusion of the Polyakov loop and its gauge invariant coupling to quarks reproduces the dynamical entanglement of the chiral and deconfinement crossover transitions as in the (local) PNJL model, but now without the requirement of introducing an artificial momentum cutoff. Steps beyond the mean-field approximation are made including mesonic correlations through quark-antiquark ring summations. Various quantities of interest (pressure, energy density, speed of sound etc.) are calculated and discussed in comparison with lattice QCD thermodynamics at zero chemical potential. The extension to finite quark chemical potential and the phase diagram in the (T, µ)-plane are also discussed.

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 meanfield 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 3-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. * Work supported in part by BMBF, GSI, the DFG Excellence Cluster "Origin and Structure of the Universe" and by the Elitenetzwerk Bayern.Polyakov-loop dynamics. The resulting Polyakov-Nambu-Jona-Lasinio PNJL model [7-12, 27-29, 48] has been remarkably successful in describing the two-flavor thermodynamics of QCD. However, this earlier version of the PNJL approach still worked with an artificial momentum space cutoff, Λ NJL ≈ (0.6-0.7) GeV, which prohibits establishing connections with well-known properties of QCD at higher momentum scales such as the running coupling and momentumdependent quark mass function. Furthermore, thermodynamically consistent results at high temperatures and densities cannot be achieved using the original (local) PNJL model. In particular, a meaningful extrapolation to the high-density region with its variety of color-superconducting phases cannot be performed once the quark Fermi momentum becomes comparable to the NJL cutoff. The nonlocal PNJL model does not have such a priori limitations.In fact the nonlocal two-flavor PNJL model [2] solves this problem by introducing momentumdependent quark interactions that permit realizing the high-momentum interface with QCD and Dyson-Schwinger calculations at the level of the quark quasiparticle propagators. The present work takes a next major step by extending this nonlocal PNJL model to N f = 3 flavors, now incorporating the strange quark. This step involves a detailed study of the axial U(1) anomaly, its role in separating the flavor singlet component of the pseudoscalar meson nonet from the Nambu-Goldstone boson sector, and its thermodynamical implications. It will turn out, that the nonlocal PNJL model does not suffer from the pathologies mentioned above, and hence it does not have any a priori limitations. Therefore, it is well-suited to investigate the high-density and high-temperature region of strongly interacting matter.From hadron spectroscopy it is well-known that only eight of the nine lightest pseudoscalar mesons (the pions, the kaons, and the eta meson) have pseudo-Goldstone boson character. The eta-prime meson, on the other hand, has a mass of m ...

Quark number susceptibilities at finite quark chemical potential are investigated in the framework of the Polyakov-loop-extended Nambu Jona-Lasinio (PNJL) model. A detailed comparison is performed between the available lattice data, extrapolated using a Taylor expansion around vanishing chemical potential, and PNJL results consistently obtained from a Taylor series truncated at the same order. The validity of the Taylor expansion is then examined through a comparison between the full and truncated PNJL model calculations. * Work supported in part by BMBF, GSI and INFN