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.Comment: Prepared for Strangeness in Quark Matter 2011, Sept. 18--24, Cracow, Polan

Exploring the role of model parameters and regularization procedures in the thermodynamics of the PNJL model

The equation of state and the critical behavior around the critical end point are studied in the context of the Polyakov--Nambu--Jona--Lasinio model. We prove that a convenient choice of the model parameters is crucial to get the correct description of isentropic trajectories. The physical relevance of the effects of the regularization procedure is insured by the agreement with general thermodynamic requirements. The results are compared with simple thermodynamic expectations and lattice data.Comment: Talk given at XIII International Conference on Hadron Spectroscopy (Hadron 2009), Tallahassee, Florida, USA, 29 Nov - 4 Dec, 200

How parameters and regularization affect the PNJL model phase diagram and thermodynamic quantities

We explore the phase diagram and the critical behavior of QCD thermodynamic quantities in the context of the so-called Polyakov--Nambu--Jona-Lasinio model. We show that this improved field theoretical model is a successful candidate for studying the equation of state and the critical behavior around the critical end point. We argue that a convenient choice of the model parameters is crucial to get the correct description of isentropic trajectories. The effects of the regularization procedure in several thermodynamic quantities is also analyzed. The results are compared with simple thermodynamic expectations and lattice data.Comment: 27 pages, 7 figures, 4 tables; PRD versio

Restoration of UA_A(1) symmetry and meson spectrum in hot or dense matter

We explore the effects of breaking and restoration of chiral and axial symmetries using an extended three-flavor Nambu-Jona-Lasinio model that incorporates explicitly the axial anomaly through the 't Hooft interaction. We implement a temperature (density) dependence of the anomaly coefficient motivated by lattice results for the topological susceptibility. The spectrum of scalar and pseudoscalar mesons is analyzed bearing in mind the identification of chiral partners and the study of its convergence. We also concentrate on the behavior of the mixing angles that give us relevant information on the issue under discussion. The results suggest that the axial part of the symmetry is restored before the possible restoration of the full U(3)$\otimes$U(3) chiral symmetry might occur.Comment: 9 pages, 5 figures. Talk given at Joint Meeting Heidelberg-Liege-Paris-Rostock (HLPR 2004), Spa, Belgium, 16-18 Dec 200

Effects of the restoration of UA_A(1) symmetry on pseudoscalar meson observables

We investigate the restoration of chiral SU$(3)\otimes$SU$(3)$ and axial U$_A$(1) symmetries, at finite temperature and density, in the framework of the three flavor Nambu-Jona-Lasinio model with anomaly. We implement a temperature (density) dependence of the anomaly coefficient motivated by lattice results for the topological susceptibility and we discuss the restoration of symmetries by analyzing the behavior of the mesonic chiral partners and of the mixing angles. The results indicate that the axial part of the symmetry is restored before the possible restoration of the full U(3)$\otimes$U(3) chiral symmetry can occur.Comment: 4 pages, 1 figure. Contribution to Proc. Int. Europhysics Conf. on High Energy Physics (HEP2005), 21-27.7.2005, Lisboa, Portuga

Interplay between chiral and axial symmetries in a SU(2) Nambu--Jona-Lasinio Model with the Polyakov loop

We consider a two flavor Polyakov--Nambu--Jona-Lasinio (PNJL) model where the Lagrangian includes an interaction term that explicitly breaks the U$_A(1)$ anomaly. At finite temperature, the restoration of chiral and axial symmetries, signaled by the behavior of several observables, is investigated. We compare the effects of two regularizations at finite temperature, one of them, that allows high momentum quarks states, leading to the full recovery of chiral symmetry. From the analysis of the behavior of the topological susceptibility and of the mesonic masses of the axial partners, it is found in the SU(2) model that, unlike the SU(3) results, the recovery of the axial symmetry is not a consequence of the full recovery of the chiral symmetry. Thus, one needs to use an additional idea, by means of a temperature dependence of the anomaly coefficient, that simulates instanton suppression effects.Comment: 21 pages, 5 figures; PRD versio

Vertebrate somite development and neural patterning

The segmentation of the axial skeleton and peripheral nervous system involves a complex integration of multiple patterning molecules. For the latter, axon-repelling molecules in the posterior half-sclerotome are particularly important. This study built on a previously performed mouse microarray screen for novel candidate genes in the posterior half-sclerotome. Multiple candidates were selected for whole-mount in situ hybridization in chick. Two were expressed in the posterior half-sclerotome: thrombin receptor (F2R) and fibronectin leucine rich transmembrane protein-2 (Flrt2). Flrt2 was selected for siRNA-mediated knockdown and a new in ovo transfection technique for somites successfully developed. Scrambled siRNA-transfection did not affect morphogenesis, somite patterning or axon guidance. However, Flrt2 siRNA-transfection resulted in defects in notochord, dermomyotome and neural tube morphogenesis, and in the de-fasciculation and mis-targeting of spinal axons into the posterior half-sclerotome and dermomyotome. Hence, Flrt2 may be a chemorepellent for spinal axons. An unidentified peanut agglutinin (PNA)-binding glycoprotein in the posterior half-sclerotome was previously shown to repel spinal axons. In this project, the expression of a family of mucin-type O-glycosylation enzymes (which could glycosylate the PNA-binding protein) was investigated by whole-mount in situ hybridization in chick, but none was differentially expressed in the posterior half-sclerotome. One candidate for the PNA-binding glycoprotein, Presenilin1, was investigated because of previously published loss of spinal nerve segmentation in Presenilin1 mutants. However, analysis of Presenilin1-hypomorphic mutant mouse embryos showed this was not the PNA-binding molecule. Live-immunostaining for a second candidate, prolyl 4-hydroxylase, beta polypeptide (P4HB), showed its expression coincided with PNA-binding at the surface of posterior half-sclerotome cells. P4HB siRNA-transfection into somites reduced PNA binding and disrupted spinal axon segmentation and expression of a posterior sclerotome marker, Uncx4.1. Overall, these results suggest that P4HB is a strong candidate to be the key PNA-binding glycoprotein in the posterior half-sclerotome that repels spinal axons