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 transition gets weakened and eventually turns into a second-order transition or a cross-over, the domain of inhomogeneous phases is less affected. In particular the location of the Lifshitz point in terms of temperature and density is not modified. Consequently, the critical point disappears from the phase diagram and only a Lifshitz point (showing a different critical behavior) remains. As a result, susceptibilities remain finite.
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.
Chiral quark models with Polyakov loop at finite temperature have been often used to describe the phase transition. We show how the transition to a hadron resonance gas is realized based on the quantum and local nature of the Polyakov loop.
We study the spatial inhomogeneity of the Polyakov loop induced by inhomogeneous chiral condensates. We formulate an effective model of gluons on the background fields of chiral condensates, and perform its lattice simulation. On the background of inhomogeneous chiral condensates, the Polyakov loop exhibits an in-phase spatial oscillation with the chiral condensates. We also analyze the heavy quark potential and show that the inhomogeneous Polyakov loop indicates the inhomogeneous confinement of heavy quarks.
In the Nambu--Jona-Lasinio model with Polyakov loops, we explore the relation between the deconfinement and chiral phase transitions within the mean-field approximation. We focus on the phase structure of the model and study the susceptibilities associated with corresponding order parameters.
We study the thermodynamics of the Nambu--Jona-Lasinio model with Polyakov loops, where spontaneous chiral symmetry breaking and confinement are taken into account. We focus on the phase structure of the model and explore the susceptibilities associated with corresponding order parameters under the mean-field approximation.
Unquenching of the Polyakov-loop potential showed to be an important improvement for the description of the phase structure and thermodynamics of strongly-interacting matter at zero quark chemical potentials with Polyakov-loop extended chiral models. This work constitutes the first application of the quark backreaction on the Polyakov-loop potential at nonzero density. The observation is that it links the chiral and deconfinement phase transition also at small temperatures and large quark chemical potentials. The build up of the surface tension in the Polyakov-loop extended Quark-Meson model i…
In an extension of the Nambu-Jona-Lasinio model where the quarks interact with the temporal gluon field, represented by the Polyakov loop, we explore the relation between the deconfinement and chiral phase transitions. The effect of Polyakov loop dynamics on thermodynamic quantities, on the phase structure at finite temperature and baryon density and on various susceptibilities is presented. Particular emphasis is put on the behavior and properties of the fluctuations of the (approximate) order parameters and their dependence on temperature and net--quark number density. We also discuss how th…
We analyze the chiral restoration and deconfinement transitions in the framework of a non-local chiral quark model which includes terms leading to the quark wave function renormalization, and takes care of the effect of gauge interactions by coupling the quarks with the Polyakov loop. Non-local interactions are described by considering both a set of exponential form factors, and a set of form factors obtained from a fit to the mass and renormalization functions obtained in lattice calculations.
We investigate the chiral condensate and the dressed Polyakov loop or dual chiral condensate at finite temperature and density in two-flavor Nambu--Jona-Lasinio model. The dressed Polyakov loop is regarded as an equivalent order parameter of deconfinement phase transition in a confining theory. We find the behavior of dressed Polyakov loop in absence of any confinement mechanism is quite interesting, with only quark degrees of freedom present, it still shows an order parameter like behavior. It is found that in the chiral limit, the critical temperature for chiral phase transition coincides wi…
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-Jona-Lasinio (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…
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.
In the heavy, static quark mass regime of QCD, the Polyakov loop is well known to be an order parameter of the deconfinement phase transition; however, the sensitivity of the Polyakov loop to the deconfinement of light, dynamical quarks is less clear. On the other hand, from the perspective of an effective Lagrangian written in the vicinity of the chiral transition, the Polyakov loop is an energy-like operator and should hence scale as any energy-like operator would. We show here that the Polyakov loop and heavy-quark free energy are sensitive to the chiral transition, i.e. their scaling is co…
Nambu--Jona-Lasinio-type models have been used extensively to study the dynamics of the theory of the strong interaction at finite temperature and quark chemical potential on a phenomenological level. In addition to these studies, which are often performed under the assumption that the ground state of the theory is homogeneous, searches for the existence of crystalline phases associated with inhomogeneous ground states have attracted a lot of interest in recent years. In this work, we study the Polyakov-loop extended Nambu--Jona-Lasinio model and find that the existence of a crystalline phase …
We address a possible relation between the expectation value of the Polyakov loop in pure gluodynamics and full QCD based on Polyakov Chiral Quark Models where constituent quarks and the Polyakov loop are coupled in a minimal way. To this end we use a center symmetry breaking Gaussian model for the Polyakov loop distribution which accurately reproduces gluodynamics data above the phase transition in terms of dimension 2 gluon condensate. The role played by the quantum and local nature of the Polyakov loop is emphasized.
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 chiral and deconfinement transitions in the framework of the strong coupling lattice QCD for color SU(3) with one species of unrooted staggered fermion at finite temperature and quark chemical potential. We take account of the leading order Polyakov loop terms as well as the next-to-next-to-leading order (1/g^4) fermionic terms of the strong coupling expansion in the effective action. We investigate the Polyakov loop effects by comparing two approximation schemes, a Haar measure method (no fluctuation from the mean field) and a Weiss mean-field method (with fluctuations). The ef…
We discuss the relation between the Polyakov loop and the chiral order parameter at finite temperature. For that purpose we analyse an effective model proposed by Gocksch and Ogilvie, which is constructed by the double expansion of strong coupling and large dimensionality. We make improvements in dealing with the model and then obtain plausible results for the behaviours of both the Polyakov loop and the chiral scalar condensate. The pseudo-critical temperature read from the Polyakov loop turns out to coincide exactly with that read from the chiral scalar condensate. Within the model study bas…
We use the Polyakov loop coupled quark-meson model to approximate low energy QCD and present results for the chiral and deconfinement transitions in the presence of a constant magnetic background $B$ at finite temperature $T$ and baryon chemical potential $μ_B$. We investigate effects of various gluoni potentials on the deconfinement transition with and without a fermionic backreaction at finite $B$. Additionally we investigate the effect of the Polyakov loop on the chiral phase transition, finding that magnetic catalysis at low $μ_B$ is present, but weakened by the Polyakov loop.
We discuss how the simultaneous crossovers of deconfinement and chiral restoration can be realized. We propose a dynamical mechanism assuming that the effective potential gives a finite value of the chiral condensate if the Polyakov loop vanishes. Using a simple model, we demonstrate that our idea works well for small quark mass, though there should be further constraints to reach the perfect locking of two phenomena.
We analyze the role played by the Polyakov loop in the description of the chiral phase transition within the framework of nonlocal SU(3) chiral models with flavor mixing. We show that its presence provides a substantial enhancement of the predicted critical temperature, bringing it to a better agreement with the most recent results of lattice calculations.
Heat kernel expansions at finite temperature of massless QCD and chiral quark models generate effective actions relevant for both low and high temperature QCD. The key relevance of the Polyakov Loop to maintain the large and non-perturbative gauge invariance at finite temperature is stressed.
We analyze the consequences of the inclusion of the gluonic Polyakov loop in chiral quark models at finite temperature. Specifically, the low-energy effective chiral Lagrangian from two such quark models is computed. The tree level vacuum energy density, quark condensate, pion decay constant and Gasser-Leutwyler coefficients are found to acquire a temperature dependence. This dependence is, however, exponentially small for temperatures below the mass gap in the full unquenched calculation. The introduction of the Polyakov loop and its quantum fluctuations is essential to achieve this result an…
We describe how the inclusion of the gluonic Polyakov loop incorporates large gauge invariance and drastically modifies finite temperature calculations in chiral quark models after color neutral states are singled out. This generates an effective theory of quarks and Polyakov loops as basic degrees of freedom. We find a strong suppression of finite temperature effects in hadronic observables triggered by approximate triality conservation (Polyakov cooling), so that while the center symmetry breaking is exponentially small with the constituent quark mass, chiral symmetry restoration is exponent…
We describe results for the confinement-deconfinement phase transition as predicted by the Nambu--Jona-Lasinio model where the local and quantum Polyakov loop is coupled to the constituent quarks in a minimal way (PNJL). We observe that the leading correlation of two Polyakov loops describes the chiral transition accurately. The effects of the current quark mass on the transition are also analysed.
While the Polyakov loop is an order parameter of the deconfinement transition in the heavy quark mass regime of QCD, its sensitivity to the deconfinement of light, dynamical quarks in QCD is not apparent. On the other hand, the quark mass dependence of the Polyakov loop is sensitive to the appearance of a chiral phase transition. Using lattice QCD calculations in the staggered fermion discretization scheme at finite values of the lattice spacing, $aT = 1/8$, we show here, for the first time, that the Polyakov loop expectation value, and the heavy quark free energy extracted from it, behave lik…
A quark-meson-diquark plasma is considered within the PNJL model for dynamical chiral symmetry breaking and restoration in quark matter. Based on a generalized Beth-Uhlenbeck approach to mesons and diquarks we present the thermodynamics of this system including the Mott dissociation of mesons and diquarks at finite temperature. A striking result is the suppression of the diquark abundance below the chiral restoration temperature by the coupling to the Polyakov loop, because of their color degree of freedom. This is understood in close analogy to the suppression of quark distributions by the sa…
We investigate chiral and deconfinement transitions in the strong coupling lattice QCD for color SU(3). We combine the leading order Polyakov loop effective action of the strong coupling expansion and the next-to-next-to-leading order (1/g^4) fermionic effective action with one species of unrooted staggered fermion. Two approximation schemes are adopted to evaluate the Polyakov loop effects; a Haar measure method (no fluctuation from the mean field) and a Weiss mean-field method (with fluctuations). The Polyakov loop is found to suppress the chiral condensate and to reduce the chiral transitio…
Thermodynamical properties of asymmetric strange quark matter using the Polyakov Chiral $\text{SU(3)}$ quark mean field (PCQMF) model at finite temperature and chemical potential have been investigated. Within the PCQMF model, the properties of quark matter are calculated through the scalar fields $σ$, $ζ$, $δ$ and $χ$, the vector fields $ω$, $ρ$ and $ϕ$ and the Polyakov loop fields $Φ$ and $\barΦ$. The isospin splitting of constituent quark masses is observed at large isospin asymmetry. The effect of temperature and strangeness fraction on energy per baryon and equation of state is found to b…
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 behavior of the quark condensates at zero chemical potential and finite temperature subject to an external magnetic field is studied within the three flavor Nambu--Jona-Lasinio model with Polyakov loop (PNJL) and its extension, the so-called entangled PNJL model (EPNJL). A comparison with recent lattice QCD data is performed and it is shown that at $T=0$ MeV the light quark condensates are in quantitative agreement. At finite temperature, although there is an overall reasonable agreement with several lattice results, it is shown that in the lattice calculations the effect due to the electr…
We consider the pseudocritical temperatures for the chiral and deconfinement transitions within a Polyakov-loop Dyson-Schwinger equation approach which employs a nonlocal rank-2 separable model for the effective gluon propagator. These pseudocritical temperatures differ by a factor of two when the quark and gluon sectors are considered separately, but get synchronized and become coincident when their coupling is switched on. The coupling of the Polyakov-loop to the chiral quark dynamics narrows the temperature region of the QCD transition in which chiral symmetry and deconfinement is establish…
At finite temperature, chiral quark models do not incorporate large gauge invariance which implies genuinely non-perturbative finite temperature gluonic degrees of freedom. Motivated by this observation, we describe how the coupling of the Polyakov loop as an independent degree of freedom to quarks not only accounts for large gauge invariance, but also allows to establish in a dynamical way the interaction between composite hadronic states such as Goldstone bosons to finite temperature non-perturbative gluons in a medium which can undergo a confinement-deconfinement phase transition.
We investigate theta-vacuum effects on the QCD phase diagram for the realistic 2+1 flavor system, using the three-flavor Polyakov-extended Nambu-Jona-Lasinio (PNJL) model and the entanglement PNJL model as an extension of the PNJL model. The theta-vacuum effects make the chiral transition sharper. For large theta-vacuum angle the chiral transition becomes first order even if the quark number chemical potential is zero, when the entanglement coupling between the chiral condensate and the Polyakov loop is taken into account. We finally propose a way of circumventing the sign problem on lattice Q…
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.
We discuss the relation between the Polyakov loop and the chiral order parameter at finite temperature by using the Gocksch-Ogilvie model with fundamental or adjoint quarks. The model is based on the double expansion of strong coupling and large dimensionality on the lattice. In an analytic way with the mean field approximation employed, we show that the confined phase must be accompanied by the spontaneous breaking of the chiral symmetry for both fundamental and adjoint quarks. Then we proceed to numerical analysis to look into the coupled dynamics of the Polyakov loop and the chiral order pa…
The Polyakov loop is included in the SU(2)_L x SU(2)_R chiral quark-meson model by considering the propagation of the constituent quarks, coupled to the (sigma,pi) meson multiplet, on the homogeneous background of a temporal gauge field, diagonal in color space. The model is solved at finite temperature and quark baryon chemical potential both in the chiral limit and for the physical value of the pion mass by using an expansion in the number of flavors N_f. Keeping the fermion propagator at its tree-level, a resummation on the pion propagator is constructed which resums infinitely many orders …
The aim of this work is to shed light on some lesser known aspects of Polyakov-loop--extended chiral models (namely the Polyakov-loop extended Nambu--Jona-Lasinio and Quark-Meson models), especially on the correlation of the quark sector with the Polyakov loop. We show that the ordering of chiral and Polyakov-loop transitions and their difference in temperature as seen in lattice QCD calculations could be realized with a critical scale of the Polyakov-loop potential that is larger than the one in pure gauge theory. The comparison of the results for the Polyakov-loop susceptibility obtained usi…
Within the framework of Polyakov-Nambu-Jona-Lasinio model and by means of Multiple Reflection Expansion, we study the finite volume effects on chiral phase transition, especially its influence on the location of the possible critical end point (CEP) and masses of mesons. Our result shows that as the radius of spherical volume decreases, the location of CEP shifts toward smaller temperature while changes little in chemical potential. As for the finite volume effects on the masses of mesons, the masses of $π$ and $K$ increase with decreasing volume, while for $σ$, $η$ and $η'$ the situation is t…
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…
Chiral phase transition is investigated in an $SU(3)_L \times SU(3)_R$ symmetric vector meson extended linear sigma model with additional constituent quarks and Polyakov loops (extended Polyakov quark meson model). The parameterization of the Lagrangian is done at zero temperature in a hybrid approach, where the mesons are treated at tree-level, while the constituent quarks at 1-loop level. The temperature and baryochemical potential dependence of the two assumed scalar condensates are calculated from the hybrid 1-loop level equations of states. The order of the phase transition along the $T=0…
The relation between the deconfinement and chiral phase transition is explored in the framework of an Polyakov-loop-extended two-flavor quark-meson (PQM) model. In this model the Polyakov loop dynamics is represented by a background temporal gauge field which also couples to the quarks. As a novelty an explicit quark chemical potential and N_f-dependence in the Polyakov loop potential is proposed by using renormalization group arguments. The behavior of the Polyakov loop as well as the chiral condensate as function of temperature and quark chemical potential is obtained by minimizing the grand…
We study the phase diagram of the three flavor Polyakov-Nambu-Jona Lasinio (PNJL) model and in particular the interplay between chiral symmetry restoration and deconfinement crossover. We compute chiral condensates, quark densities and the Polyakov loop at several values of temperature and chemical potential. Moreover we investigate on the role of the Polyakov loop dynamics in the transition from nuclear matter to quark matter.
The derivative of the grand potential in mean field approximation, non-strange and strange condensates and deconfinement phase-transition in thermal and dense hadronic medium are verified in extended SU(3) linear sigma-model (eLSM). In determining the chiral phase-transition, the chiral condensates sigma_x and sigma_y are analysed. The chiral mesonic phase-structures in temperature- and density-dependence are taken as free parameters to be fitted. These parameters are classified corresponding to scalar meson nonets; (pseudo)-scalar and (axial)-vector. For deconfinement phase-transition, effect…
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 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…
The phase diagram at finite temperature and density is investigated in the framework of the Polyakov linear sigma model (PLSM) with three light quark flavors in the mean field approximation. It is found that in the PLSM, the three phase transitions, i.e, the chiral restoration of $u,d$ quarks, the chiral restoration of $s$ quark, and the deconfinement phase transition are independent. There exists two-flavor quarkyonic phase at low density and three-flavor quarkyonic phase at high density. The critical end point (CEP) which separating the crossover from the first-order line in the PLSM model i…
A recent Monte Carlo study of {\em quenched} QCD showed that the chiral condensate is non-vanishing above $T_c$ in the phase where the average of the Polyakov loop $P$ is complex. We show how this is related to the dependence of the spectrum of the Dirac operator on the boundary conditions in Euclidean time. We use a random matrix model to calculate the density of small eigenvalues and the chiral condensate as a function of $\arg P$. The chiral symmetry is restored in the $\arg P=2π/3$ phase at a higher $T$ than in the $\arg P=0$ phase. In the phase $\arg P = π$ of the $SU(2)$ gauge theory the…
We study the thermodynamics and phase diagrams of two-flavor quantum chromodynamics using the Polyakov-loop extended quark-meson (PQM) model and the Pisarski-Skokov chiral matrix ($χM$) model. At temperatures up to $T\approx2T_c$ and baryon chemical potentials up to $μ_B=400\ \rm{MeV}$, both models show reasonable agreement with the pressure, energy density, and interaction measure as calculated on the lattice. The Polyakov loop is found to rise significantly faster with temperature in models than on the lattice. In the low-temperature and high baryon density regime, the two models predict dif…
The effects of the Polyakov loop and of a regularization procedure that allows the presence of high momentum quark states at finite temperature is investigated within the Polyakov-loop extended Nambu--Jona-Lasinio model. The characteristic temperatures, as well as the behavior of observables that signal deconfinement and restoration of chiral and axial symmetries, are analyzed, paying special attention to the behavior of strangeness degrees of freedom. We observe that the cumulative effects of the Polyakov loop and of the regularization procedure contribute to a better description of the therm…
We study the finite temperature behavior of light scalar and pseudoscalar meson properties in the context of a three-flavor nonlocal chiral quark model. The model includes mixing with active strangeness degrees of freedom, and takes care of the effect of gauge interactions by coupling the quarks with the Polyakov loop. We analyze the chiral restoration and deconfinement transitions, as well as the temperature dependence of meson masses, mixing angles and decay constants. The critical temperature is found to be T_c = 202 MeV, in better agreement with lattice results than the value recently obta…
We determine the quark condensate and the dressed Polyakov loop from the finite temperature Landau gauge quark propagator evaluated with U(1)-valued boundary conditions in an approximation to quenched QCD. These gauge invariant quantities allow for an investigation of the chiral and deconfinement transition. We compare results from Dyson-Schwinger equations on a lattice with infinite volume continuum results and study the temperature and quark mass dependence of both quantities. In particular we investigate the chiral condensate and the dressed Polyakov loop in the chiral limit. We also consid…
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 discuss the relation between the Polyakov loop and the chiral order parameter at finite temperature by using an effective model. We clarify why and how the pseudo-critical temperature associated with the Polyakov loop should coincide with that of the chiral condensate.
In order to characterize the higher order moments of the particle multiplicity, we implement the linear-sigma model with Polyakov-loop correction. We first studied the critical phenomena and estimated some thermodynamic quantities. Then, we compared all these results with the first--principle lattice QCD calculations. Then, the extensive study of non-normalized four moments is followed by investigating their thermal and density dependence. We repeat this for moments normalized to temperature and chemical potential. The fluctuations of the second order moment is used to estimate the chiral phas…
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…
