The Polyakov loop extended Nambu--Jona-Lasinio (PNJL) model with imaginary chemical potential is studied. The model possesses the extended ${\mathbb Z}_{3}$ symmetry that QCD does. Quantities invariant under the extended ${\mathbb Z}_{3}$ symmetry, such as the partition function, the chiral condensate and the modified Polyakov loop, have the Roberge-Weiss (RW) periodicity. The phase diagram of confinement/deconfinement transition derived with the PNJL model is consistent with the RW prediction on it and the results of lattice QCD. The phase diagram of chiral transition is also presented by the PNJL model.
We consider how does the introduction of a Polyakov loop affects the spatially inhomogeneous quark condensate. The primary result of our work is that the existence of the spatially non-uniform chiral phase is confirmed within the Polyakov NJL model in a chiral limit. These findings are obtained both in a 3d-cutoff and in a Schwinger (proper time) regularization schemes.
The phase diagram at finite temperature and chemical potential for the Polyakov-NJL model with eight quark interactions is reviewed for the SU(3) flavor case.
The critical endpoint (CEP) and the phase structure are studied in the Polyakov-loop extended Nambu--Jona-Lasinio model in which the scalar type eight-quark (σ^4) interaction and the vector type four-quark interaction are newly added. The σ^4 interaction largely shifts the CEP toward higher temperature and lower chemical potential, while the vector type interaction does oppositely. At zero chemical potential, the σ^4 interaction moves the pseudo-critical temperature of the chiral phase transition to the vicinity of that of the deconfinement phase transition.
We elucidate how the color neutrality is harmed in the Polyakov Nambu-Jona Lasinio (PNJL) model at finite density within the adopted mean field approximation. Also we point out how usual assumption about the diagonal form of the Wilson loop may fail in the presence of the diquark condensate on several grounds.
The Nambu Jona-Lasinio model with a Polyakov loop is extended to finite isospin chemical potential case, which is characterized by simultaneous coupling of pion condensate, chiral condensate and Polyakov loop. The pion condensate, chiral condensate and the Polyakov loop as functions of temperature and isospin chemical potential are investigated by minimizing the thermodynamic potential of the system. The resulting $(T,μ_I)$ phase diagram is studied with emphasis on the critical point and Polyakov loop dynamics. The tricritical point for the pion superfluidity phase transition is confirmed and …
We investigate the rapid rise of the dressed Polyakov loop in the Nambu--Jona-Lasinio (NJL) model as a function of temperature. In QCD such a behaviour is interpreted as a confinement- deconfinement phase transition. However, we demonstrate that in the NJL model this is simply a remnant of the chiral transition.
It is believed that there exists a rich phase structure of quantum chromodynamics (QCD) at finite temperature and baryon density, namely, the deconfinement process from hadron gas to quark-gluon plasma, the transition from chiral symmetry breaking phase to the symmetry restoration phase, and the color superconductivity at low temperature and high baryon density. In the present work we study the hadron-quark phase transition by investigating the binodal surface and extending it to finite temperature in order to mimic the QCD phase diagram. In order to obtain these conditions we use different mo…
To study the high energy nuclear physics and the associated phenomenon, as the QGP/hadronic matter phase transition, the Nambu and Jona-Lasinio model (NJL) appears as an interesting alternative to the Quantum Chromodynamics, which is not solvable at the considered energies. Indeed, the NJL model allows describing the quarks physics, at finite temperatures and finite densities. Furthermore, in order to try to correct a limitation of the NJL model, i.e. the absence of confinement, it was proposed to couple the quarks/antiquarks to a Polyakov loop: it forms the PNJL model. The objective of this t…
We explore the thermodynamics and phase structure of the Polyakov loop-extended two flavor chiral quark--meson (PQM) model beyond the mean-field approximation at imaginary chemical potential. Our approach is based on the functional renormalization group (FRG) method. At finite temperature and imaginary chemical potential, we solve the renormalization group flow equation for a scale-dependent thermodynamic potential in the presence of the gluonic background field. We determine behavior of order parameters of the PQM model in the FRG approach and compute the phase diagram. We compare our FRG res…
We study how the charge neutrality affects the phase structure of three-flavor PNJL model. We point out that, within the conventional PNJL model at finite density the color neutrality is missing because the Wilson line serves as an external ``colored'' field coupled to dynamical quarks. In this paper we heuristically assume that the model may still be applicable. To get color neutrality one has then to allow non vanishing color chemical potentials. We study how the quark matter phase diagram in $(T,m_s^2/μ)$-plane is affected by imposing neutrality and by including the Polyakov loop dynamics. …
The phase structure of the two-flavor Polyakov-loop extended Nambu-Jona-Lashinio model is explored at finite temperature and imaginary chemical potential with a particular emphasis on the confinement-deconfinement transition. We point out that the confined phase is characterized by a $\cos3μ_I/T$ dependence of the chiral condensate on the imaginary chemical potential while in the deconfined phase this dependence is given by $\cosμ_I/T$ and accompanied by a cusp structure induced by the Z(3) transition. We demonstrate that the phase structure of the model strongly depends on the choice of the P…
The phase structure of Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model is explored at imaginary chemical potential, with particular emphasis on the deconfinement transition. We point out that the statistical confinement nature of the model naturally leads to characteristic dependence of the chiral condensate $<\bar{q}q>$ on $θ=μ_I/T$. We introduce a dual parameter for the deconfinement transition by making use of this dependence. By changing a four-fermion coupling constant, we tune the location of the critical endpoint of the deconfinement transition.
We investigate the role of the isoscalar vector interaction and the dynamics of the Polyakov loop on inhomogeneous phases in the phase diagram of the two-flavor Nambu-Jona--Lasinio (NJL) model. Thereby we concentrate on phases with a one-dimensional modulation, explicitly domain-wall solitons and, for comparison, the chiral spiral. While the inclusion of the Polyakov loop merely leads to quantitative changes compared to the original NJL model, the presence of a repulsive vector-channel interaction has significant qualitative effects: Whereas for homogeneous phases the first-order phase transit…
Using the Polyakov extended Nambu-Jona-Lasinio (PNJL) model with imaginary chemical potential, the relation between the Roberge-Weiss (RW) phase transition and the extended Z3 symmetry is studied. At low temperature, there is approximate continuous symmetry under the phase transformation of the Polyakov loop with the shift of the imaginary chemical potential. Due to this continuous symmetry, the Polyakov loop can oscillate smoothly as the imaginary chemical potential increases. At high temperature, this continuous symmetry is broken to an exact discrete symmetry, the extended Z3 symmetry, and …
We analyze the thermodynamical properties of a system of strongly interacting particles at vanishing quark chemical potential in the framework of a recently developed extension of the Polyakov-Nambu-Jona-Lasinio Model. In addition to eight quark interactions terms, non-canonical terms which explicitly break chiral symmetry up to the same order in a $1/N_c$ expansion ($N_c$ number of colors) are included. A recently proposed Polyakov potential is considered and the results are compared to lattice QCD data resulting in a favorable scenario for the recent model variants.
We explore the NJL model with Polyakov loops for a system of three colors and two flavors within the mean-field approximation, where both chiral symmetry and confinement are taken into account. We focus on the phase structure of the model and study the chiral and Polyakov loop susceptibilities.
In this article we study a nonlocal Nambu--Jona-Lasinio (nNJL) model with a Gaussian regulator in presence of a uniform magnetic field. We take a mixed approach to the incorporation of temperature in the model, and consider aspects of both real and imaginary time formalisms. We include confinement in the model through the quasiparticle interpretation of the poles of the propagator. The effect of the magnetic field in the deconfinement phase transition is then studied. It is found that, like with chiral symmetry restoration, magnetic catalysis occurs for the deconfinement phase transition. It i…
The QCD phase diagram at zero chemical potential and finite temperature subject to an external magnetic field is studied within the three flavor Nambu--Jona-Lasinio (NJL) model and the NJL model with the Polyakov loop (PNJL). A scalar coupling parameter dependent on the magnetic field intensity is considered. The scalar coupling has been fitted so that the lattice QCD pseudocritical chiral transition temperatures are reproduced and in the limit of large magnetic field decreases with the inverse of the magnetic field intensity. This dependence of the coupling allows to reproduce the lattice QCD…
Here we studied the possible diffusion speed for relativistic fluid in different effective quantum chromodynamics models: Nambu-Jona-Lasinio (NJL), Polyakov loop extended NJL, entangled PNJL (EPNJL) model.
To obtain deeper understanding of QCD properties at finite temperature, we consider the Fourier decomposition of the grand-canonical partition function based on the canonical ensemble method via the imaginary chemical potential. Expectation values are, then, represented by summation over each canonical sector. We point out that the modified Polyakov-loop can play an important role in the canonical ensemble; for example, the Polyakov-loop paradox which is known in the canonical ensemble method can be evaded by considering the quantity. In addition, based on the periodicity issue of the modified…
We investigate the properties of scalar and pseudo-scalar mesons at finite temperature and quark chemical potential in the framework of the Nambu-Jona-Lasinio (NJL) model coupled to the Polyakov loop (PNJL model) with the aim of taking into account features of both chiral symmetry breaking and deconfinement. The mesonic correlators are obtained by solving the Schwinger-Dyson equation in the RPA approximation with the Hartree (mean field) quark propagator at finite temperature and density. In the phase of broken chiral symmetry a narrower width for the sigma meson is obtained with respect to th…
We draw the three-flavor phase diagram as a function of light- and strange-quark masses for both zero and imaginary quark-number chemical potential, using the Polyakov-loop extended Nambu-Jona-Lasinio model with an effective four-quark vertex depending on the Polyakov loop. The model prediction is qualitatively consistent with 2+1 flavor lattice QCD prediction at zero chemical potential and with degenerate three-flavor lattice QCD prediction at imaginary chemical potential.
Phase transitions in the imaginary chemical potential region are studied by the Polyakov loop extended Nambu-Jona-Lasinio (PNJL) model that possesses the extended Z3 symmetry. The extended Z3 invariant quantities such as the partition function, the chiral condensate and the modifed Polyakov loop have the Roberge-Weiss (RW) periodicity. There appear four types of phase transitions; deconfinement, chiral, Polykov-loop RW and chiral RW transitions. The orders of the chiral and deconfinement transitions depend on the presence or absence of current quark mass, but those of the Polykov-loop RW and c…
The nonanalyticity and the sign problem in the Z3-symmetric heavy quark model at low temperature are studied phenomenologically. For the free heavy quarks, the nonanalyticity is analyzed in the relation to the zeros of the grand canonical partition function. The Z3-symmetric effective Polyakov-line model (EPLM) in strong coupling limit is also considered as an phenomenological model of Z3-symmetric QCD with large quark mass at low temperature. We examine how the Z3-symmetric EPLM approaches to the original one in the zero-temperature limit. The effects of the Z3-symmetry affect the structure o…
We study two-color QCD in an external magnetic backround at finite temperature using the Polyakov-loop extended two-flavor two-color NJL model. At T=0, the chiral condensate is calculated and it is found to increase as a function of the magnetic field $B$. In the chiral limit the deconfinement transition lies below the chiral transition for nonzero magnetic fields $B$. At the physical point, the two transitions seem to coincide for field strengths up to $|qB|\approx 5m_π^2$ whereafter they split. The splitting between the two increases as a function of $B$ in both the chiral limit and at the p…
We extend the Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model by introducing an effective four-quark vertex depending on Polyakov loop. The effective vertex generates entanglement interactions between Polyakov loop and chiral condensate. The new model is consistent with lattice QCD data at imaginary quark-number chemical potential and real and imaginary isospin chemical potentials, particularly on strong correlation between the chiral and deconfinement transitions and also on the quark-mass dependence of the order of the Roberge-Weiss endpoint predicted by lattice QCD very lately. We in…
We present initial results of a numerical investigation of the chiral symmetry restoring transition in the (3+1)-dimensional Nambu -- Jona-Lasinio model with both non-zero baryon chemical potential (mu_B) and isospin chemical potential (mu_I). With non-zero isospin chemical potential, the model suffers from a sign problem. We proceed in two ways: (i) We perform ``partially quenched'' simulations in which mu_I is made non-zero only during the measurement of chiral observables; (ii) We perform full simulations with imaginary isospin chemical potential with the aim to analytically continue result…
Firstly we qualitatively analyze the formation of the dip and peak structures of the kurtosis $κσ^2$ of net baryon number fluctuation along imagined freeze-out lines and discuss the signature of the existence of the QCD critical end point (CEP) in the Nambu--Jona-Lasinio (NJL) model, Polyakov-NJL (PNJL) model as well as $μ$-dependent PNJL($μ$ PNJL) model with different parameter sets, and then we apply a realistic PNJL model with parameters fixed by lattice data at zero chemical potential, and quantitatively investigate its $κσ^2$ along the real freeze-out line extracted from experiments. The …
At finite imaginary values of the chemical potential, QCD is free of the sign problem. Moreover, at high temperatures the partition function exhibits a new symmetry (the Roberge-Weiss symmetry) connecting phases with different orientations of the Polyakov loop, and the corresponding phase transitions between these. In this contribution we investigate the perturbative one-loop effective potential for the Polyakov loop in the presence of imaginary isospin as well as baryon chemical potentials. This leads to a novel phase diagram, which reveals an interesting insight about the rich phase structur…
We explore the phase diagram of two-flavor QCD at imaginary values of baryon and isospin chemical potentials analyzing the thermodynamic potential of QCD analytically and that of the Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model numerically. QCD has no pion condensation at imaginary baryon and isospin chemical potentials, and therefore has discrete symmetries that are not present at real baryon and isospin chemical potentials. The PNJL model possesses all the discrete symmetries. The PNJL model can reproduce qualitatively lattice QCD data presented very lately.
With the aim of setting constraints for the modeling of the QCD phase diagram, the phase structure of the two-flavor Polyakov-loop extended Nambu and Jona-Lasinio (PNJL) model is investigated in the range of imaginary chemical potentials ($μ_\mathrm{I}$) and compared with available $N_f=2$ lattice QCD results. The calculations are performed using the advanced nonlocal version of the PNJL model with the inclusion of vector-type quasiparticle interactions between quarks, and with wave-function-renormalization corrections. It is demonstrated that the nonlocal PNJL model reproduces important featu…
We determine the baryon spectrum of 1 + 1 + 1-flavor QCD in the presence of strong background magnetic fields using lattice simulations at physical quark masses for the first time. Our results show a splitting within multiplets according to the electric charge of the baryons and reveal, in particular, a reduction of the nucleon masses for strong magnetic fields. This first-principles input is used to define constituent quark masses and is employed to set the free parameters of the Polyakov loop-extended Nambu-Jona-Lasinio (PNJL) model in a magnetic field-dependent manner. The so constructed mo…
The chiral condensate and dressed Polyakov loop at finite temperature and density have been investigated in the framework of Nf = 2+1 Nambu-Jona-Lasinio (NJL) model with two degenerate u, d quarks and one strange quark. In the case of explicit chiral symmetry breaking with physical quark masses, it is found that the phase transitions for light u, d quarks and s quark are sequentially happened, and the separation between the transition lines for different flavors becomes wider and wider with the increase of baryon density. For each flavor, the pseudo-critical temperatures for chiral condensate …
We clarify regions where the canonical approach works well at the finite temperature and density in the Nambu-Jona-Lasinio (NJL) and Polyakov-NJL (PNJL) models. The canonical approach is a useful method for avoiding the sign problem in lattice QCD simulations at finite density, but it involves some parameters. We find that number densities computed from the canonical approach are consistent with exact values in most of the confinement phase within the parameters, which are applicable in lattice QCD.
We evaluate the finite temperature scalar sunset diagram with imaginary square masses, that appears in the Gribov-Zwanziger approach to Yang-Mills (YM) theory beyond one-loop order. Since YM theory at finite temperature is governed by center-symmetry and the Polyakov loop, we also include the possibility of a constant temporal background gauge field in the form of color-dependent imaginary chemical potentials.
We test the reliability of the the Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model, comparing the model result with the lattice data at nonzero imaginary chemical potential. The PNJL model with the vector-type four-quark and scalar-type eight-quark interactions reproduces the lattice data on the pseudocritical temperatures of the deconfinement and chiral phase transitions. The QCD phase diagram in the real chemical potential region is predicted by the PNJL model. The critical endpoint survives, even if the vector-type four-quark interaction is taken into account.
Temperature dependence of pion and sigma-meson screening masses is evaluated by the Polyakov-loop extended Nambu--Jona-Lasinio model with the entanglement vertex (EPNJL model). We propose a practical way of calculating meson screening masses in the NJL-type effective models. The method based on the Pauli-Villars regularization solves the well-known difficulty that the evaluation of screening masses is not easy in the NJL-type effective models. The method is applied to analyze temperature dependence of pion screening masses calculated with state-of-the-art lattice simulations with success in re…
Dynamical Symmetry breaking and meson masses are studied in the Nambu-Jona-Lasinio (NJL) model at finite temperature and chemical potential using the dimensional regularization. Since the model is not renormalizable in four space-time dimensions, physical results and parameters depend on the regularization method. Following the imaginary time formalism, we introduce the temperature, $T$ and the chemical potential, $μ$. The parameters in the model are fixed by calculating the pion mass and decay constant in the dimensional regularization at $T=μ=0$.
We discuss the behavior of two point functions for Polyakov loops in a SU(3) gauge theory about the critical temperature, T_c. From a Z(3) model, in mean field theory we obtain a prediction for the ratio of masses at T_c, extracted from correlation functions for the imaginary and real parts of the Polyakov loop. This ratio is m_i/m_r = 3 if the potential only includes terms up to quartic order in the Polyakov loop; its value changes as pentic and hexatic interactions become important. The Polyakov Loop Model then predicts how m_i/m_r changes above T_c.
We discuss a three-flavor Nambu--Jona-Lasinio (NJL) type quantum field theoretical approach to the quark matter equation of state (EoS) with scalar diquark condensate, isoscalar vector mean field and Kobayashi-Maskawa-'t Hooft (KMT) determinant interaction. While often the diquark and vector meson couplings are considered as free parameters, we will fix them here to their values according to the Fierz transformation of a one-gluon exchange interaction. In order to estimate the effect of a possible change in the vacuum pressure of the gluon sector at finite baryon density we exploit a recent mo…
The chemical-potential dependence of pi and sigma meson masses is analyzed at both real and imaginary chemical potentials, $μ_\mathrm{R}$ and $μ_\mathrm{I}$, by using the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model that possesses both the extended ${\mathbb Z}_3$ symmetry and the chiral symmetry. In the $μ_\mathrm{I}$ region, the meson masses have the Roberge-Weiss periodicity. Assuming that the meson masses will be measured at finite $μ_\mathrm{I}$ by lattice QCD in future, we simulate how meson masses at finite $μ_\mathrm{R}$ are extracted from those at finite $μ_\mathrm{I}$, and…
In this chapter, we discuss several aspects of the theory of strong interactions in presence of a strong magnetic background. In particular, we summarize our results on the effect of the magnetic background on chiral symmetry restoration and deconfinement at finite temperature. Moreover, we compute the magnetic susceptibility of the chiral condensate and the quark polarization at zero temperature. Our theoretical framework is given by chiral models: the Nambu-Jona-Lasinio (NJL), the Polyakov improved NJL (or PNJL) and the Quark-Meson (QM) models. We also compare our results with the ones obtai…
NJL-type effective models represent a low-energy realization of QCD and incorporate pertinent aspects such as chiral symmetry and its spontaneous breaking, the center symmetry in the heavy-quark limit as well as the axial anomaly. One such model, the Polyakov-quark-meson model for three light quark flavors, is introduced in order to study the phase structure of strongly-interacting matter. With recent high-statistics lattice QCD simulations of the finite-temperature equation of state, a detailed comparison with model results becomes accessible. Such comparisons allow to estimate volume and tru…
We study the implications of the spontaneous and explicit Z(3) center symmetry breaking for the Polyakov loop susceptibilities. To this end, ratios of the susceptibilities of the real and imaginary parts, as well as of the modulus of the Polyakov loop are computed within an effective model using a color group integration scheme. We show that the essential features of the lattice QCD results of these ratios can be successfully captured by the effective approach. Furthermore we discuss a novel scaling relation in one of these ratios involving the explicit breaking field, volume, and temperature.
The susceptibilities of the real and imaginary parts, as well as of the modulus of the Polyakov loop, are computed in SU(3) lattice gauge theory. We show that the ratios of these susceptibilities are excellent probes of the deconfinement transition, independent of the renormalization of the Polyakov loop and only weakly dependent on the system size. The ratios are almost temperature independent above and below the transition and exhibit a discontinuity at the transition temperature. This characteristic behavior can be understood in terms of the global Z(3) symmetry of the Yang-Mills Lagrangian…
The color superconductivity was studied with an adaptation of the Nambu and Jona-Lasinio model (NJL). This one was coupled to a Polyakov loop, to form the PNJL model. A $μ$-dependent Polyakov loop potential was considered. An objective of the presented works was to describe the analytical calculations required to establish the equations to be solved, in all of the treated cases. They concerned the normal quark phase, the 2-flavor color-superconducting and the color-flavor-locked phases, in an SU(3)f X SU(3)c description. The calculations were performed according to the temperature T, the chemi…
We estimate the axion properties i.e. its mass, topological susceptibility and the self-coupling within the framework of Polyakov loop enhanced Nambu-Jona-Lasinio (PNJL) model at finite temperature and quark chemical potential. PNJL model, where quarks couple simultaneously to the chiral condensate and to a background temporal quantum chromodynamics (QCD) gauge field, includes two important features of QCD phase transition, i.e. deconfinement and chiral symmetry restoration. The Polyakov loop in PNJL model plays an important role near the critical temperature. We have shown significant differe…
We study the large-N_c behavior of the critical temperature T_c for chiral symmetry restoration in the framework of the Nambu-Jona-Lasinio (NJL) model and the linear σ-model. While in the NJL case T_c scales as N_c^0 and is, as expected, of the same order as Λ_QCD (just as the deconfinement phase transition), in the σ-model the scaling behavior reads T_c \propto N_c^1/2. We investigate the origin of the different scaling behavior and present two improvements of the σ-model: (i) a simple, phenomenologically motivated temperature dependence of the parameters and (ii) the coupling to the Polyakov…
We investigate chemical-potential ($μ$) and temperature ($T$) dependence of scalar and pseudo-scalar meson masses for both real and imaginary $μ$, using the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model with three-flavor quarks. A three-flavor phase diagram is drawn in $μ^2$-$T$ plane where positive (negative) $μ^2$ corresponds to positive (imaginary) $μ$. A critical surface is plotted as a function of light- and strange-quark current mass and $μ^2$. We show that $μ$-dependence of the six-quark Kobayashi-Maskawa-'t Hooft (KMT) determinant interaction originated in $U_\mathrm{A}(1)$ a…
We give a theoretical framework to obtain a low-energy effective theory of quantum chromodynamics (QCD) towards a first-principle derivation of confinement/deconfinement and chiral-symmetry breaking/restoration crossover transitions. In fact, we demonstrate that an effective theory obtained using simple but non-trivial approximations within this framework enables us to treat both transitions simultaneously on equal footing. A resulting effective theory is regarded as a modified and improved version of nonlocal Polyakov-loop extended Nambu-Jona-Lasinio (nonlocal PNJL) models proposed recently b…
By using the dressed Polyakov loop or dual chiral condensate as an equivalent order parameter of the deconfinement phase transition, we investigate the relation between the chiral and deconfinement phase transitions at finite temperature and density in the framework of three-flavor Nambu--Jona-Lasinio (NJL) model. It is found that in the chiral limit, the critical temperature for chiral phase transition coincides with that of the dressed Polyakov loop in the whole $(T,μ)$ plane. In the case of explicit chiral symmetry breaking, it is found that the phase transitions are flavor dependent. For e…
We first extend our formulation for the calculation of $π$- and $σ$-meson screening masses to the case of finite chemical potential $μ$. We then consider the imaginary-$μ$ approach, which is an extrapolation method from imaginary chemical potential ($μ=i μ_{\rm I}$) to real one ($μ=μ_{\rm R}$). The feasibility of the method is discussed based on the entanglement Polyakov-loop extended Nambu--Jona-Lasinio (EPNJL) model in 2-flavor system. As an example, we investigate how reliable the imaginary-$μ$ approach is for $π$- and $σ$-meson screening masses, comparing "screening masses at $μ_{\rm R}$ i…
We have studied the vector meson spectral function (VMSF) in a hot and dense medium within an effective QCD model namely the Nambu-Jona-Lasinio (NJL) and its Polyakov Loop extended version (PNJL) with and without the effect of isoscalar vector interaction (IVI). The effect of the IVI has been taken into account using the ring approximation. We obtained the dilepton production rate (DPR) using the VMSF and observed that at moderate temperature it is enhanced in the PNJL model as compared to the NJL and Born rate due to the suppression of color degrees of freedom.
We obtain the in-medium effective potential of the three-flavor Polyakov-Quark-Meson model as a real function of real variables in the Polyakov loop variable, to allow for the study of all possible minima of the model. At finite quark chemical potential, the real and imaginary parts of the effective potential, in terms of the Polyakov loop variables, are made apparent, showing explicitly the fermion sign problem of the theory. The phase diagram and other equilibrium observables, obtained from the real part of the effective potential, are calculated in the mean-field approximation. The obtained…
