Polyakov-Nambu-Jona-Lasinio Research Articles

Publisher’s Note: Deconfinement and chiral restoration within the SU(3) Polyakov–Nambu–Jona-Lasinio and entangled Polyakov–Nambu–Jona-Lasinio models in an external magnetic field [Phys. Rev. D89, 016002 (2014)

Publisher’s Note: Deconfinement and chiral restoration within the SU(3) Polyakov–Nambu–Jona-Lasinio and entangled Polyakov–Nambu–Jona-Lasinio models in an external magnetic field [Phys. Rev. D<b>89</b>, 016002 (2014)

Deconfinement and chiral restoration within the SU(3) Polyakov–Nambu–Jona-Lasinio and entangled Polyakov–Nambu–Jona-Lasinio models in an external magnetic field

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 electric charge quark difference is stronger and the restoration of the $u$ quark chiral symmetry starts at lower temperatures. When considering the EPNJL model with a Polyakov loop scale parameter that depends on the magnetic field, it is possible to obtain an earlier rise of the Polyakov loop with the increase of the magnetic field and due to the entanglement, the inverse magnetic catalysis is found as in the lattice QCD calculations.

Polyakov–Nambu–Jona-Lasinio phase diagrams and quarkyonic phase from order parameters

We show that the magnitude of the order parameters in the Polyakov--Nambu--Jona-Lasinio (PNJL) model given by the quark condensate and the Polyakov loop can be used as a criterion to clearly identify, without ambiguities, phases and boundaries of the strongly interacting matter, namely, the broken/restored chiral symmetry and confinement/deconfinement regions. This structure is represented by the projection of the order parameters in the temperature-chemical potential plane, which allows a clear identification of pattern changes in the phase diagram. Such a criterion also enables the emergence of a quarkyonic phase even in the two-flavor system. We still show that this new phase diminishes due to the influence of an additional vector-type interaction in the PNJL phase diagrams and is quite sensitive to the effect of the change of the ${T}_{0}$ parameter in the Polyakov potential. Finally, we show that the phases and boundaries constructed by our method indicate that the order parameters should be more strongly correlated, as in the case of the entanglement PNJL model. This result suggests a novel way to pursue further investigation of new interactions between the order parameters in order to improve the PNJL model.

Transport coefficients from the Nambu–Jona-Lasinio model for SU(3)f

We calculate the shear $\eta(T)$ and bulk viscosities $\zeta(T)$ as well as the electric conductivity $\sigma_e(T)$ and heat conductivity $\kappa(T)$ within the Nambu-Jona-Lasinio model for 3 flavors as a function of temperature as well as the entropy density $s(T)$, pressure $P(T)$ and speed of sound $c_s^2(T)$. We compare the results with other models such as the Polyakov-Nambu-Jona-Lasinio (PNJL) model and the dynamical quasiparticle model (DQPM) and confront these results with lattice QCD data whenever available. We find the NJL model to have a limited predictive power for the thermodynamic variables and various transport coefficients above the critical temperature whereas the PNJL model and DQPM show acceptable results for the quantities of interest.

Role of vector interaction and axial anomaly in the PNJL modeling of the QCD phase diagram

Effects of a flavor singlet vector interaction in the Polyakov–Nambu–Jona-Lasinio (PNJL) Model are studied in combination with the axial U(1) breaking Kobayashi–Maskawa–ʼt Hooft interaction, using an improved, consistent cutoff scheme. We confirm that the first-order chiral phase transition at moderate baryon chemical potentials and its critical point, a generic feature of NJL-type models without vector coupling, disappear for sufficiently large vector coupling strength gv. New results are presented concerning the curvature of the crossover boundary in the T–μ plane close to μ=0 and its dependence on gv.

Restoration of Axial Symmetry and Its Possible Relation with Restoration of Chiral Symmetry and Deconfinement at Finite Temperature

The phase transitions characterized by deconfinement and restoration of chiral symmetry as well as the restoration of axial symmetry, at finite temperature, are investigated in the framework of SU(2) Polyakov-Nambu-Jona-Lasinio (PNJL) models with the U$_A$(1) anomaly. The thermodynamics of the phase transitions, the topological susceptibility, the meson spectrum, and, in particular, the convergence of axial and chiral partners are analyzed, in the framework of the ordinary PNJL model and in its extension, the entangled Polyakov-Nambu-Jona-Lasinio (EPNJL) model. The latter incorporates entanglement between restoration of chiral symmetry and deconfinement.

Cross sections in the Polyakov–Nambu–Jona-Lasinio model: study of reactions involving quarks, antiquarks, mesons, diquarks and baryons

We estimated some cross sections associated with reactions between quarks, antiquarks, diquarks and baryons. It concerns elastic scatterings with quarks and antiquarks, mesonization and baryonization processes of a quark/antiquark gas. The data were calculated according to the center of mass energy , the temperature and the baryonic density. To perform this task, we employed the Polyakov–Nambu–Jona-Lasinio (PNJL) model. We proposed to compare some of these results with the ones obtained in a pure NJL description.

Vector interaction strength in Polyakov–Nambu–Jona-Lasinio models from hadron-quark phase diagrams

We estimate the vector interaction strength of the Polyakov-Nambu-Jona-Lasinio (PNJL) parametrizations, assuming that its transition curves should be as close as possible of the recently studied RMF-PNJL hadron-quark phase diagrams. Such diagrams are obtained matching relativistic mean-field hadronic models, and the PNJL quark ones. By using this method we found for the magnitude of the vector interaction, often treated as a free parameter, a range of 7.66 GeV$^{-2}\lesssim G_V \lesssim 16.13$ GeV$^{-2}$, or equivalently, $1.52 \lesssim G_V/G_s \lesssim 3.2$, with $G_s$ being the scalar coupling constant of the model. These values are compatible but restricts the range of 4 GeV$^{-2}\lesssim G_V \lesssim 19$ GeV$^{-2}$, recently obtained from lattice QCD data through a different mean-field model approach.

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.

Some properties of two Nambu-Jona-Lasinio -type models with inputs from lattice QCD

We investigate the phase diagram of the so-called Polyakov--Nambu--Jona-Lasinio (PNJL) model at finite temperature and nonzero chemical potential. The calculations are performed in the light and strange quark sectors ($u$, $d$, $s$), which includes the 't Hooft instanton induced interaction term that breaks the axial symmetry, and the quarks are coupled to the (spatially constant) temporal background gauge field. On one hand, a special attention is payed to the critical end point (CEP). The strength of the flavor-mixing interaction alters the CEP location, since when it becomes weaker the CEP moves to low temperatures and can even disappear. On the other hand, we also explore the connection between QCD, a nonlocal Nambu--Jona-Lasinio type model and the Landau gauge gluon propagator. Possible links between the quenched gluon propagator and low energy hadronic phenomenology are investigated.

PNJL model for adjoint fermions

Recent work on QCD-like theories has shown that the addition of adjoint fermions obeying periodic boundary conditions to gauge theories on R3× S1can lead to a restoration of center symmetry and confinement for sufficiently small circumference L of S1. At small L, perturbation theory may be used reliably to compute the effective potential for the Polyakov loop P in the compact direction. Periodic adjoint fermions act in opposition to the gauge fields, which by themselves would lead to a deconfined phase at small L. In order for the fermionic effects to dominate gauge field effects in the effective potential, the fermion mass must be sufficiently small. This indicates that chiral symmetry breaking effects are potentially important. We develop a Polyakov-Nambu-Jona Lasinio (PNJL) model which combines the known perturbative behavior of adjoint QCD models at small L with chiral symmetry breaking effects to produce an effective potential for the Polyakov loop P and the chiral order parameter ψ̄ψ A rich phase structure emerges from the effective potential. Our results [1] are consistent with the recent lattice simulations of Cossu and D'Elia [2], which found no evidence for a direct connection between the small-L and large-L confining regions. Nevertheless, the two confined regions are connected indirectly if an extended field theory model with an irrelevant four-fermion interaction is considered. Thus the small-L and large-L regions are part of a single confined phase.

Chiral Symmetry in Strongly Interacting Matter

This is a brief summary of topics that were presented as lectures within the programme "New Frontiers in QCD 2010" at the Yukawa Institute of Theoretical Physics in Kyoto. The basic subject is phases and symmetry breaking patterns as they emerge from the approximate chiral symmetry of QCD. Part I focuses on the QCD interface with nuclear physics via chiral effective field theory. This includes nuclear thermodynamics and, in particular, constraints for compressed and hot baryonic matter provided by the density and temperature dependence of the chiral condensate. Part II explores aspects of the QCD phase diagram using a non-local improved version of the Polyakov - Nambu - Jona-Lasinio (PNJL) model. A prominent feature of such an approach is the occurence of a dynamical entanglement between chiral and deconfinement crossover transitions. Comparisons with available results from lattice QCD thermodynamics will be made.

Investigation of the phase diagram and bulk thermodynamic properties using the Polyakov–Nambu–Jona-Lasinio model with eight-quark interactions

We present the bulk thermodynamic properties and phase diagram of strongly interacting matter in an extension of the 3-flavor Nambu--Jona-Lasinio (NJL) and Polyakov--Nambu--Jona-Lasinio (PNJL) models of QCD. Using a three-momentum cutoff scheme, we have extended the multiquark interaction terms up to eight order so that the stability of the vacuum is ensured in these models. We explore the effects of various combinations of the two eight-quark couplings ${g}_{1}$ and ${g}_{2}$ and present a comparative study between the NJL and PNJL models as well as lattice QCD data. The main effect of the eight-quark interaction term is to shift the critical end point in the $T\ensuremath{-}\ensuremath{\mu}$ phase diagram to a lower value of $\ensuremath{\mu}$ and a higher value of $T$, thus bringing them closer to lattice QCD results.

Polyakov–Nambu–Jona-Lasinio model for adjoint fermions with periodic boundary conditions

Recent work on QCD-like theories has shown that the addition of adjoint fermions obeying periodic boundary conditions to gauge theories on ${R}^{3}\ifmmode\times\else\texttimes\fi{}{S}^{1}$ can lead to a restoration of center symmetry and confinement for sufficiently small circumference $L$ of ${S}^{1}$. At small $L$, perturbation theory may be used reliably to compute the effective potential for the Polyakov loop $P$ in the compact direction. Periodic adjoint fermions act in opposition to the gauge fields, which by themselves would lead to a deconfined phase at small $L$. In order for the fermionic effects to dominate gauge field effects in the effective potential, the fermion mass must be sufficiently small. This indicates that chiral symmetry breaking effects are potentially important. We develop a Polyakov--Nambu--Jona-Lasinio (PNJL) model which combines the known perturbative behavior of adjoint QCD models at small $L$ with chiral symmetry breaking effects to produce an effective potential for the Polyakov loop $P$ and the chiral order parameter $\overline{\ensuremath{\psi}}\ensuremath{\psi}$. A rich phase structure emerges from the effective potential. Our results are consistent with the recent lattice simulations of Cossu and D'Elia, which found no evidence for a direct connection between the small-$L$ and large-$L$ confining regions. Nevertheless, the two confined regions are connected indirectly if an extended field theory model with an irrelevant four-fermion interaction is considered. Thus the small-$L$ and large-$L$ regions are part of a single confined phase.

Scalar-pseudoscalar meson behavior and restoration of symmetries in SU(3) Polyakov–Nambu–Jona-Lasinio model

The modification of mesonic observables in a hot medium is analyzed as a tool to investigate the restoration of chiral and axial symmetries in the context of the Polyakov-loop extended Nambu--Jona-Lasinio model. The results of the extended model lead to the conclusion that the effects of the Polyakov loop are fundamental for reproducing lattice findings. In particular, the partial restoration of the chiral symmetry is faster in the Polyakov--Nambu--Jona-Lasinio model than in the Nambu--Jona-Lasinio one, and it is responsible for several effects: the meson-quark coupling constants show a remarkable difference in both models, there is a faster tendency to recover the Okubo-Zweig-Iizuka rule, and finally the topological susceptibility nicely reproduces the lattice results around $T/{T}_{c}\ensuremath{\approx}1.0$.

Mesonic excitations andπ−πscattering lengths at finite temperature in the two-flavor Polyakov–Nambu–Jona-Lasinio model

The mesonic excitations and $s$-wave $\ensuremath{\pi}\mathrm{\text{\ensuremath{-}}}\ensuremath{\pi}$ scattering lengths at finite temperature are studied in the two-flavor Polyakov--Nambu--Jona-Lasinio (PNJL) model. The masses of the $\ensuremath{\pi}$ and $\ensuremath{\sigma}$ mesons, pion-decay constant, the pion-quark coupling strength, and the scattering lengths ${a}_{0}$ and ${a}_{2}$ at finite temperature are calculated in the PNJL model with two forms of Polyakov-loop effective potential. The obtained results are almost independent of the choice of the effective potentials. The calculated results in the PNJL model are also compared with those in the conventional Nambu--Jona-Lasinio model and indicate that the effect of color confinement screens the effect of temperature below the critical one in the PNJL model. Furthermore, the Goldberger-Treiman relation and the Gell-Mann--Oakes--Renner relation are extended to the case at finite temperature in the PNJL model.

Neutrality issue in the Polyakov-loop Nambu–Jona-Lasinio model

We elucidate how the color neutrality is harmed in the Polyakov Nambu-Jona Lasinio 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.

Three flavor Nambu–Jona-Lasinio model with Polyakov loop and competition with nuclear matter

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.

Thermodynamics of the Polyakov-Nambu-Jona-Lasinio model with nonzero baryon and isospin chemical potentials

We have extended the Polyakov-Nambu-Jona-Lasinio (PNJL) model for two degenerate flavors to include the isospin chemical potential (${\ensuremath{\mu}}_{I}$). All the diagonal and mixed derivatives of pressure with respect to the quark number (proportional to baryon number) chemical potential (${\ensuremath{\mu}}_{0}$) and isospin chemical potential up to sixth order have been extracted at ${\ensuremath{\mu}}_{0}={\ensuremath{\mu}}_{I}=0$. These derivatives give the generalized susceptibilities with respect to quark and isospin numbers. Similar estimates for the flavor diagonal and off-diagonal susceptibilities are also presented. Comparison to lattice QCD (LQCD) data of some of these susceptibilities for which LQCD data are available show similar temperature dependence, though there are some quantitative deviations above the crossover temperature. We have also looked at the effects of instanton induced flavor mixing coming from the ${U}_{A}(1)$ chiral symmetry breaking 't Hooft determinantlike term in the NJL part of the model. The diagonal quark number and isospin susceptibilities are completely unaffected. The off-diagonal susceptibilities show significant dependence near the crossover. Finally we present the chemical potential dependence of specific heat and speed of sound within the limits of chemical potentials where neither diquarks nor pions can condense.

Susceptibilities and speed of sound from the Polyakov-Nambu-Jona-Lasinio model

We present the Taylor expansion coefficients of the pressure in quark number chemical potential ${\ensuremath{\mu}}_{0}={\ensuremath{\mu}}_{B}/3={\ensuremath{\mu}}_{u}={\ensuremath{\mu}}_{d}$, for the strongly interacting matter as described by the Polyakov-Nambu-Jona-Lasinio (PNJL) model for two light degenerate flavors of quarks $u$ and $d$. The expansion has been done up to eighth order in ${\ensuremath{\mu}}_{0}$, and the results are consistent with recent estimates from Lattice. We have further obtained the specific heat ${C}_{V}$, squared speed of sound ${v}_{s}^{2}$, and the conformal measure $\mathcal{C}$.