The Polyakov−Nambu−Jona-Lasinio model has been quite successful in describing various qualitative features of observables for strongly interacting matter, that are measurable in heavy-ion collision experiments. The question still remains on the quantitative uncertainties in the model results. Such an estimation is possible only by contrasting these results with those obtained from first principles using the lattice QCD framework. Recently a variety of lattice QCD data were reported in the realistic continuum limit. Here we make a first attempt at reparametrizing the model so as to reproduce these lattice data. We find excellent quantitative agreement for the equation of state. Certain discrepancies in the charge and strangeness susceptibilities as well as baryon-charge correlation still remain. We discuss their causes and outline possible directions to remove them.

We present a detailed study of the variation of shear viscosity rj, with temperature and baryon chemical potential within the framework of the Polyakov-Nambu-Jona-Lasinio model, rj is found to depend strongly on the spectral width of the quasiparticles present in the model. The variation of rj across the phase diagram has distinctive features for different kinds of transitions. These variations have been used to study the possible location of the critical end point and are cross-checked with similar studies of variations of specific heat. Finally, using a parametrization of the freeze-out surface in heavy-ion collision experiments, the variation of the shear viscosity to entropy density ratio has also been discussed as a function of the centerof-mass energy of collisions.

Finite size consideration of matter significantly affects transport coefficients like shear viscosity, bulk viscosity, electrical conductivity, which we have investigated here in the framework of the Polyakov-Nambu-Jona-Lasinio model. Owing to the basic quantum mechanics, a non-zero lower momentum cut-off is implemented in momentum integrations, used in the expressions of constituent quark masses and transport coefficients. When the system size decreases, the values of these transport coefficients are enhanced in low temperature range. At high temperature domain, shear viscosity and electrical conductivity become independent of system sizes. Whereas, bulk viscosity, which is associated with scale violating quantities of the system, faces some non-trivial size dependence in this regime. In the phenomenological direction, our microscopic estimations can also be linked with the macroscopic outcome, based on dissipative hydrodynamical simulation.

PACS 25.75.-q -Heavy-ion nuclear reactions relativistic PACS 12.38.Mh -Quark gluon plasma Abstract -We discuss the 2+1 flavor Polyakov loop enhanced Nambu-Jona-Lasinio model in a finite volume. The main objective is to check the volume scaling of thermodynamic observables for various temperatures and chemical potentials. We observe the possible violation of the scaling with system size in a considerable window along the whole transition region in the T − µq plane.Introduction. -The hot and/or dense matter created in ultra-relativistic heavy ion collisions is supposed to possess a rich phase structure. In the intermediate regime of temperature and baryon chemical potential in the range of few hundred MeV, the defining characters of the phases are the color confinement and chiral properties. While for low baryon densities the matter has a smooth crossover from color confined chiral symmetry broken phase to color deconfined chiral symmetry restored phase, at high enough densities, this transition may be of first order. A critical end point seems to naturally occur in such a situation. Establishing this scenario forms an integral part of exploration in the international collaborative experiments at CERN and BNL and the upcoming experiments at GSI.The matter formed in heavy-ion collision experiments has a finite volume, which depends on the size of the colliding nuclei as well as the center of mass energy ( √ s) and

We have gone through a comparative study on two different kind of bulk viscosity expressions by using a common dynamical model. The Polyakov-Nambu-Jona-Lasinio (PNJL) model in the realm of mean-field approximation, including up to eight quark interactions for 2+1 flavor quark matter, is treated for this common dynamics. We have probed the numerical equivalence as well as discrepancy of two different expressions for bulk viscosity at vanishing quark chemical potential. Our estimation of bulk viscosity to entropy density ratio follows a decreasing trend with temperature, which is observed in most of the earlier investigations. We have also extended our estimation for finite values of quark chemical potential.