H. Hansen

The QCD critical end point in the PNJL model

We investigate the role played by the Polyakov loop in the dynamics of the chiral phase transition in the framework of the so-called Polyakov-Nambu-Jona-Lasinio (PNJL) model in the SU(2) sector. We present the phase diagram where the inclusion of the Polyakov loop moves the critical points to higher temperatures, compared with the Nambu-Jona-Lasinio model results. The critical properties of physical observables, such as the baryon number susceptibility and the specific heat, are analyzed in the vicinity of the critical end point, with special focus on their critical exponents. The results with the PNJL model are closer to lattice results and we also recover the universal behavior of the critical exponents of both the baryon susceptibility and the specific heat.

Phase diagram and critical properties within an effective model of QCD: the Nambu-Jona-Lasinio model coupled to the Polyakov loop

We investigate the phase diagram of the so-called Polyakov–Nambu–Jona-Lasinio model at finite temperature and non-zero chemical potential with three quark flavors. Chiral and deconfinement phase transitions are discussed and the relevant order-like parameters are analyzed. The results are compared with simple thermodynamic expectations and lattice data. We present the phase diagram in the (T, μB) plane, paying special attention to the critical end point: as the strength of the flavor-mixing interaction becomes weaker, the critical end point moves to low temperatures and can even disappear.

Scalar-pseudoscalar meson behavior and restoration of symmetries in SU(3) PNJL model

The modification of mesonic observables in a hot medium is analyzed as a tool to investigate the restoration of chiral and axial symmetries in the context of the Polyakov-loop extended Nambu-Jona-Lasinio model. The results of the extended model lead to the conclusion that the effects of the Polyakov loop are fundamental for reproducing lattice findings. In particular, the partial restoration of the chiral symmetry is faster in the Polyakov-Nambu-Jona-Lasinio model than in the Nambu-Jona-Lasinio one, and it is responsible for several effects: the meson-quark coupling constants show a remarkable difference in both models, there is a faster tendency to recover the Okubo-Zweig-Iizuka rule, and finally the topological susceptibility nicely reproduces the lattice results around T/T{sub c}{approx_equal}1.0.

Phase transition and critical end point driven by an external magnetic field in asymmetric quark matter

The location of the critical end point (CEP) in the QCD phase diagram is determined under different scenarios. The effect of strangeness, isospin/charge asymmetry and an external magnetic field is investigated. The discussion is performed within the 2+1 flavor Nambu–Jona-Lasinio model with Polyakov loop. It is shown that isospin asymmetry shifts the CEP to larger baryonic chemical potentials and smaller temperatures. At large asymmetries the CEP disappears. However, a strong enough magnetic field drives the system into a first order phase transition.

Some properties of two Nambu-Jona-Lasinio -type models with inputs from lattice QCD

IPNL, Universit´e de Lyon/Universit´e Lyon 1, CNRS/IN2P3, 4 rue E.Fermi,F-69622 Villeurbanne Cedex, FranceWe investigate the phase diagram of the so-called Polyakov–Nambu–Jona-Lasinio (PNJL) model at finite temperature and nonzero chemicalpotential. The calculations are performed in the light and strange quarksectors (u, d, s), which includes the ’t Hooft instanton induced interactionterm that breaks the axial symmetry, and the quarks are coupled to the(spatially constant) temporal background gauge field. On one hand, a spe-cial attention is payed to the critical end point (CEP). The strength of theflavor-mixing interaction alters the CEP location, since when it becomesweaker the CEP moves to low temperatures and can even disappear. Onthe other hand, we also explore the connection between QCD, a nonlocalNambu–Jona-Lasinio type model and the Landau gauge gluon propaga-tor. Possible links between the quenched gluon propagator and low energyhadronic phenomenology are investigated.PACS numbers: 11.10.Wx, 11.30.Rd, 12.40.-y

The QCD Critical End Point in the Context of the Polyakov--Nambu--Jona-Lasinio Model

We investigate the phase diagram of the so-called Polyakov--Nambu--Jona-Lasinio model at finite temperature and nonzero chemical potential with three quark flavors. Chiral and deconfinement phase transitions are discussed, and the relevant order-like parameters are analyzed. A special attention is payed to the critical end point (CEP): the influence of the strangeness on the location of the CEP is studied; also the strength of the flavor-mixing interaction alters the CEP location, once when it becomes weaker the CEP moves to low temperatures and can even disappear.

Sensitivity of predictions in an effective model: Application to the chiral critical end point position in the Nambu-Jona-Lasinio model

The measurement of the position of the chiral critical end point (CEP) in the QCD phase diagram is under debate. While it is possible to predict its position by using effective models specifically built to reproduce some of the features of the underlying theory (QCD), the quality of the predictions (e.g., the CEP position) obtained by such effective models, depends on whether solving the model equations constitute a well- or ill-posed inverse problem. Considering these predictions as being inverse problems provides tools to evaluate if the problem is ill-conditioned, meaning that infinitesimal variations of the inputs of the model can cause comparatively large variations of the predictions. If it is ill-conditioned, it has major consequences because of finite variations that could come from experimental and/or theoretical errors. In the following, we shall apply such a reasoning on the predictions of a particular Nambu-Jona-Lasinio model within the mean field + ring approximations, with special attention to the prediction of the chiral CEP position in the (T-μ) plane. We find that the problem is ill-conditioned (i.e. very sensitive to input variations) for the T-coordinate of the CEP, whereas, it is well-posed for the μ-coordinate of the CEP. As a consequence, when the chiral condensate varies in a 10MeV range, μCEP varies far less. As an illustration to understand how problematic this could be, we show that the main consequence when taking into account finite variation of the inputs, is that the existence of the CEP itself cannot be predicted anymore: for a deviation as low as 0.6% with respect to vacuum phenomenology (well within the estimation of the first correction to the ring approximation) the CEP may or may not exist.

The QCD critical end point driven by an external magnetic field in asymmetric quark matter

The effect of the isospin/charge asymmetry and an external magnetic field in the location of the critical end point (CEP) in the QCD phase diagram is investigated. By using the 2+1 flavor Nambu--Jona-Lasinio model with Polyakov loop (PNJL), it is shown that the isospin asymmetry shifts the CEP to larger baryonic chemical potentials and smaller temperatures, and in the presence of a large enough isospin asymmetry the CEP disappears. Nevertheless, a sufficiently high external magnetic field can drive the system into a first order phase transition again.

Phase diagram and critical properties in the Polyakov–Nambu–Jona‐Lasinio model

We investigate the phase diagram of the so‐called Polyakov–Nambu–Jona‐Lasinio model at finite temperature and nonzero chemical potential with three quark flavours. Chiral and deconfinement phase transitions are discussed, and the relevant order‐like parameters are analyzed. The results are compared with simple thermodynamic expectations and lattice data. A special attention is payed to the critical end point: as the strength of the flavour‐mixing interaction becomes weaker, the critical end point moves to low temperatures and can even disappear.