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 ...

Updated constraints from neutron star masses and radii impose stronger restrictions on the equation of state for baryonic matter at high densities and low temperatures. The existence of two-solar-mass neutron stars rules out many soft equations of state with prominent "exotic" compositions. The present work reviews the conditions required for the pressure as a function of baryon density in order to satisfy these constraints. Several scenarios for sufficiently stiff equations of state are evaluated. The common starting point is a realistic description of both nuclear and neutron matter based on a chiral effective field theory approach to the nuclear many-body problem. Possible forms of hybrid matter featuring a quark core in the center of the star are discussed using a threeflavor Polyakov-Nambu-Jona-Lasinio (PNJL) model. It is found that a conventional equation of state based on nuclear chiral dynamics meets the astrophysical constraints. Hybrid matter generally turns out to be too soft unless additional strongly repulsive correlations, e.g. through vector current interactions between quarks, are introduced. The extent to which strangeness can accumulate in the equation of state is also discussed.

Studies of the QCD phase diagram must properly include nucleonic degrees of freedom and their thermodynamics in the range of baryon chemical potentials characteristic of nuclear matter. A useful framework for incorporating relevant nuclear physics constraints in this context is a chiral nucleon-meson effective Lagrangian. In the present paper, such a chiral nucleon-meson model is extended with systematic inclusion of mesonic fluctuations using the functional renormalization group approach. The resulting description of the nuclear liquid-gas phase transition shows a remarkable agreement with three-loop calculations based on in-medium chiral effective field theory. No signs of a chiral first-order phase transition and its critical endpoint are found in the region of applicability of the model, i.e. up to twice the density of normal nuclear matter and at temperatures T 100 MeV. Fluctuations close to the critical point of the first-order liquid-gas transition are also examined with a detailed study of chiral and baryon number susceptibilities.