We have calculated the shear viscosity coefficient η of the strongly interacting matter in the relaxation time approximation, where a quasiparticle description of quarks with their dynamical masses is considered from the Nambu-Jona-Lasinio model. Due to the thermodynamic scattering of quarks with pseudoscalar-type condensate (i.e., pion), a nonzero Landau damping will be acquired by the propagating quarks. This Landau damping may be obtained from the Landau cut contribution of the in-medium self-energy of a quark-pion loop, which is evaluated in the framework of real-time thermal field theory. From the basic idea of the QCD asymptotic freedom at high temperatures and densities, a weakly interacting quark gluon plasma (QGP) is naturally expected to be produced in heavy ion collision (HIC) experiments. However, the experimental data from the BNL Relativistic Heavy Ion Collider (RHIC), especially the measured elliptic flow, indicate that nuclear matter is a strongly interacting liquid instead of a weakly interacting gas. The recent hydrodynamical calculations [1,2] as well as some calculations of kinetic transport theory [3,4] conclude that the matter produced in a HIC must have very small shear viscosity. The shear viscosity of the fluid is generally quantified by the the coefficient η and it physically interprets the ability to transfer momentum over a distance of the mean free path. Hence the lower values of η means the constituents of the matter interact strongly to transfer the momentum easily. Whereas a weakly interacting system must have large η because in this case the momentum transfer between the constituents becomes strenuous.Several theoretical attempts have been taken to calculate the η of the strongly interacting matter at very high [5], intermediate [6,7], and low [8][9][10][11][12][13][14][15][16] temperatures, where some special attention was drawn to the smallness of its original value with respect to its lower bound (η =s 4π, where s is the entropy density), commonly known as the KSS bound [26]. A most interesting fact, which has been added with the recent theoretical understanding of η for strongly interacting matter, is that the η/s may reach a minimum in the vicinity of a phase transition [19][20][21][22][23] (see also [27]) like the liquid-gas phase transition of certain materials, e.g., nitrogen, helium, or water. These investigations demand a better understanding to zoom in on the temperature T dependence of η of the strongly interacting matter near the phase transition. Inspired by this motivation, in this Brief Report we have addressed the η(T ) due to forward and backward scattering of the quark-pion interaction.In the relaxation time approximation, the η of the quark [23] and pion [15,16] medium (for μ = 0) can be expressed aswhereand n π = 1 e βωπ −1 are, respectively, the Fermi-Dirac distribution of the quark and the Bose-Einstein distribution of the pion withπ . The Q and π are Landau damping of the quark and pion, respectively. Following the quasiparticle description of the Nambu-J...

The properties of the vector meson current-current correlation function and its spectral representation are investigated in details with and without isoscalar-vector interaction within the framework of effective QCD approach, namely Nambu-Jona-Lasinio (NJL) model and its Polyakov Loop extended version (PNJL), at finite temperature and finite density. The influence of the isoscalar-vector interaction on the vector meson correlator is obtained using the ring resummation known as the Random Phase Approximation (RPA). The spectral as well as the correlation function in PNJL model show that the vector meson retains its bound property up to a moderate value of temperature above the phase transition. Using the vector meson spectral function we, for the first time, obtained the dilepton production rate from a hot and dense medium within the framework of PNJL model that takes into account the nonperturbative effect through the Polyakov Loop fields. The dilepton production rate in PNJL model is enhanced compared to NJL and Born rate in the deconfined phase due to the suppression of color degrees of freedom at moderate temperature. The presence of isoscalar-vector interaction further enhances the dileption rate over the Born rate in the low mass region. Further, we also have computed the Euclidean correlation function in vector channel and the conserved density fluctuation associated with temporal correlation function appropriate for a hot and dense medium. The dilepton rate and the Euclidean correlator are also compared with available lattice data and those quantities in PNJL model are found to agree well in certain domain.

Fluctuations of conserved quantum numbers are associated with the corresponding susceptibilities because of the symmetry of the system. The underlying fact is that these fluctuations as defined through the static correlators become identical to the direct calculation of these susceptibilities defined through the thermodynamic derivatives, due to the fluctuation-dissipation theorem. Through a rigorous exercise we explicitly show that a diagrammatic calculation of the static correlators associated with the conserved quark number fluctuations and the corresponding susceptibilities are possible in the case of mean field theories, if the implicit dependence of the mean fields on the quark chemical potential are taken into account appropriately. As an aside we also give an analytical prescription for obtaining the implicit dependence of the mean fields on the quark chemical potential.

We report a first case study of the phase diagram of 2+1 flavor strongly interacting matter in β−equilibrium, using the Polyakov−Nambu−Jona-Lasinio model. Physical characteristics of relevant thermodynamic observables have been discussed. A comparative analysis with the corresponding observables in the Nambu-Jona-Lasinio model is presented. We find distinct differences between the models in terms of a number of thermodynamic quantities like the speed of sound, specific heat, various number densities as well as entropy. The present study is expected to give us a better insight into the role that the superdense matter created in heavy ion collision experiments play in our understanding of the properties of matter inside the core of supermassive stars in the Universe.

We present a study of the 1+1 flavor system of strongly interacting matter in terms of the Polyakov−Nambu−Jona-Lasinio model. We find that though the small isospin symmetry breaking brought in through unequal light quark masses is too small to affect the thermodynamics of the system in general, it may have significant effect in baryon-isospin correlations and have a measurable impact in heavy-ion collision experiments. PACS numbers: 12.38.Aw, 12.38.Mh, I. INTRODUCTIONSignatures of phases of matter with deconfined color charges is under critical investigation for last few decades, both theoretically and experimentally. Quantum Chromodynamics (QCD) is the formulation for first principle studies of strongly interacting matter. Along with the local color symmetry, the quark sector has few global symmetries also. In the chiral limit for two light flavors u and d, we have global vector and axial vector symmetry SU V (2) ⊗ SU A (2). For non-zero quark masses, the axial symmetry SU A (2) is explicitly broken, while for non-zero quark mass difference vector (isospin) symmetry SU V (2) is explicitly broken. At low energies the isospin symmetry breaking (ISB) has relevance in many aspects of hadronic observables [1]. Apart from the quark mass difference, ISB effects may be brought in by electromagnetic contributions as well. Low energy π − K scattering has been studied considering the inclusion of electromagnetic correction into the effective Lagrangian [2]. In the chiral quark model, ISB of valence and sea quark distributions in protons and neutrons has been studied in [3,4] and thermodynamics has been discussed in [5]. ISB may also have significant effect in the context of existence of CP violating phase [6]. Some Lattice QCD investigation of the effect of unequal quark masses was done in Ref. [7] and recently the effect of ISB on different hadronic observables were studied in Ref. [8,9]. Within the framework of chiral perturbation theory the isospin breaking effect in quark condensates has been studied considering m u = m d and electromagnetic corrections as well, where the authors have given an analysis of scalar susceptibilities [10,11]. Both of the above-mentioned effects have been incorporated also in Nambu−Jona-Lasinio (NJL) model [12] to study the influence of the isospin symmetry breaking on the orientation of chiral symmetry breaking.In the context of high energy heavy ion collisions where strongly interacting matter is supposed to exist in a state of thermal and chemical equilibrium, the ISB effects have not been explored much. Fluctuations and correlations of conserved charges are important and sensitive probes for heavy ion physics. Most of the theoretical studies in this respect are in isospin symmetric limit (see e.g. [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]). Here we present our first case study of ISB effect on fluctuations and correlations of strongly interacting matter within the framework of the Polyakov loop enhanced Nambu−Jona-Lasinio (PNJL) model. We discuss the possible ...

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A detailed general relativistic (GR) calculation of the neutrino path for a general metric describing a rotating star is studied. We have calculated the neutrino path along a plane, with the consideration that the neutrino does not at any time leave the plane. The expression for the minimum photosphere radius (MPR) is obtained and matched with the Schwarzschild limit. The MPR is calculated for the stars with two different equations of state (EOS) each rotating with two different velocities. The results shows that the MPR for the hadronic star is much greater than the quark star and the MPR increases as the rotational velocity of the star decreases. The MPR along the polar plane is larger than that along the equatorial plane.

In this work we have re-explored our earlier study on the vector meson spectral function and its spectral property in the form of dilepton rate in a two-flavour Polyakov loop extended Nambu-JonaLasinio (PNJL) model in presence of a strong entanglement between the chiral and Polyakov loop dynamics. The entanglement considered here is generated through the four-quark scalar type interaction in which the coupling strength depends on the Polyakov loop and runs with temperature and chemical potential. The entanglement effect is also considered for the four-quark vector type interaction in the same manner. We observe that the entanglement effect relatively enhances the color degrees of freedom due to the running of the both scalar and vector couplings. This modifies the vector meson spectral function and thus the spectral property such as the dilepton production rate in low invariant mass also gets modified.