Polyakov Nambu Jona-Lasinio Model Research Articles

Kaon superfluidity in the early Universe

Previously, it was found that pion superfluidity could be realized in the quantum chromodynamics (QCD) epoch of the early Universe, when lepton flavor asymmetry |le+lμ| is large enough to generate a charge chemical potential |μQ| larger than vacuum pion mass. By following the same logic, kaon superfluidity might also be possible when |le+lμ| is so large that |μQ| becomes larger than vacuum kaon mass. Such a possibility is checked by adopting Ginzburg-Landau approximation within the three-flavor Polyakov–Nambu–Jona-Lasinio model. Consider the case with full chemical balance, though kaon superfluidity could be stable compared to the chiral phases with only σ condensations, it would get killed by the more favored homogeneous pion superfluidity. If we introduce mismatch between s and d quarks, kaon superfluidity would require so large s quark density that such a state is impossible in the early Universe. Published by the American Physical Society 2024

Nonextensive effects on QCD chiral phase diagram and baryon-number fluctuations within Polyakov-Nambu-Jona-Lasinio model* *Supported by the National Natural Science Foundation of China (12005192) and the Project funded by China Postdoctoral Science Foundation (2020M672255, 2020TQ0287)

In this paper, a version of the Polyakov-Nambu-Jona-Lasinio (PNJL) model based on nonextensive statistical mechanics is presented. This new statistics summarizes all possible factors that violate the assumptions of the Boltzmann-Gibbs (BG) statistics to a dimensionless nonextensivity parameter q. Thus, when q tends to 1, it returns to the BG case. Within the nonextensive PNJL model, we found that as q increases, the location of the critical end point (CEP) exhibits non-monotonic behavior. That is, for , CEP moves in the direction of lower temperature and larger quark chemical potential. However, for , CEP turns to move in the direction of lower temperature and lower quark chemical potential. In addition, we studied the moments of the net-baryon number distribution, that is, variance (), skewness (S), and kurtosis (κ). Our results are generally consistent with the latest experimental data reported, especially for , when q is set to .

Repulsive character induced by optimized perturbation techniques on the Polyakov-loop-extended Nambu—Jona-Lasinio model.

The determination of the critical point on the QCD phase diagram depends experimentally on thermodynamic quantities related to the cumulants of the pressure. These quantities appear as coefficients in the Taylor expansion of the pressure and, specifically for the second order cumulant c 2, QCD results on the lattice (LQCD) show that it raises with the temperature towards the Stefan-Boltzmann limit. On the other hand, when one evaluates c 2 within quark effective models considering a repulsion on the vector channel parametrized by GV , this observable reaches a maximum just after Tc , deviating itself from LQCD predictions. Here we apply the Optimized Perturbation Theory (OPT) method to the two flavor Polyakov–Nambu–Jona-Lasinio model (at GV = 0) to confront our results with those furnished by LQCD simulations. We show that c 2 behaves satisfactorily at low-T and close to Tc , but, with GV ≠ 0, it develops a maximum at high-T. Our conclusions indicate that it would be possible that the correct high temperature behavior of c 2 beyond LN limit could be properly achieved by effective quark models if they also mimic the so-called asymptotic freedom phenomenon.

Thermodynamical properties of hot and magnetized quark matter within the SU(2) Polyakov-Nambu-Jona-Lasinio model: vacuum magnetic regularization scheme

In this work we implement the recent proposed vacuum magnetic regularization (VMR) scheme to the two flavor Polyakov–Nambu–Jona-Lasinio model in order to describe some basic thermodynamic properties such as the pressure, entropy and energy density. We show that this procedure allows the evaluation of the renormalized magnetization, which agrees with LQCD data. Potential physical differences are also explored when other three possible regularization schemes are adopted to describe the chiral condensate.

Isospin asymmetric matter in a nonlocal chiral quark model

We analyze the features of strongly interacting matter in the presence of nonzero isospin chemical potential $\mu_I$, within a nonlocal two-flavor Polyakov-Nambu-Jona-Lasinio (PNJL) model. For a system at finite temperature $T$, we describe the behavior of various thermodynamic quantities and study the phase diagram in the $\mu_I - T$ plane. In particular, it is found that for values of $\mu_I$ larger than the pion mass and temperatures lower than a critical value of about 170 MeV the system lies in an isospin symmetry broken phase signaled by the presence of a nonzero pion condensate. Our results for the phase diagram are found to be in better agreement with those arising from lattice QCD calculations, as compared to the predictions from other theoretical approaches like the local PNJL model.

Phase diagram for strongly interacting matter in the presence of a magnetic field using the Polyakov–Nambu–Jona-Lasinio model with magnetic field dependent coupling strengths

We study the phase diagram for strongly interacting matter using the 't Hooft determinant extended Nambu--Jona-Lasinio model with a Polyakov loop in the light and strange quark sectors (\emph{up}, \emph{down} and \emph{strange}) focusing on the effect of a magnetic field dependence of the coupling strengths of these interactions. This dependence was obtained so as to reproduce recent lattice QCD results for the magnetic field dependence of the quarks dynamical masses. A finite magnetic field is known to induce several additional first-order phase transition lines with the respective Critical End Points (CEP) in the temperature-quark chemical potential phase diagram when compared to the zero magnetic field case. A study of the magnetic field dependence in the range $eB=0-0.6~\mathrm{GeV}^2$ of the location of these CEPs reveals that the initial one as well as several of the new ones only survive up to a critical magnetic field. Only two remain in the upper limit of the studied magnetic field strength. A comparison of the results obtained with versions of the model with and without Polyakov loop is also done. We also found that the inclusion of the magnetic field dependence on the coupling strengths, while not changing the qualitative features of the phase diagram, affects the location of these CEPs. The comparison of results with and without a regularization cutoff in the medium part of the integrals does not show a significant change.

On the critical endpoint and the first‐order phase transition in the extended Polyakov Nambu Jona‐Lasinio Lagrangian

AbstractThe (Polyakov) Nambu‐ Jona‐Lasinio (PNJL) approach is an effective theory for low energies which shares with Quantumchromodynamics (QCD) the global symmetries. This approach is easy to handle and allows for analytical results for many of the observables which are of interest for the studies of ultrarelativistic heavy‐ion collisions but also for the merger and collisions of neutron stars. It allows in particular to study the density and temperature dependence of quark masses and of the masses of mesons and baryons as well as the chiral phase transition. In recent times, this transition came in the focus of interest because it is expected that the upcoming experiments at the Fair (Germany) and NICA (Russia) facilities will observe a Quark‐Gluon‐Plasma (QGP) at finite baryon chemical potential. In this contribution, we show that the extended PNJL model is able to describe the properties of symmetric matter at vanishing chemical potential, as determined by lQCD calculations.

Finite temperature properties of a modified Polyakov–Nambu–Jona-Lasinio model

Thermodynamic properties of strongly interacting matter are investigated using the Polyakov loop enhanced Nambu$-$Jona-Lasinio model along with some modifications to include the hadrons. Various observables are shown to have a close agreement with the numerical data of QCD on lattice. The advantage of the present scheme over a similar study using a switching function is that here no extra parameters are to be fitted. As a result the present scheme can be easily extended for finite chemical potentials.

Magnetized hot and dense quark matter in the Polyakov Nambu–Jona–Lasinio model

In a strong magnetic field, the hot dense quark matter is investigated in the Polyakov Nambu–Jona–Lasinio model. The value of a traced Polyakov loop is found as a nonmonotonous function of the chemical potential at lower magnetic fields and as a monotonous increasing function at high magnetic fields. The decreasing pseudocritical temperatures for the chiral restoration and the deconfinement crossover are reproduced by a temperature-and-magnetic-field-dependent coupling constant to reflect the inverse magnetic catalysis. Furthermore, the deconfined but chiral broken phase can be observed in the split region of the Tχ and Tϕ.

Equation of state of PNJL model under the influence of thermal mass and magnetic field

We present analytical results of the equation of state (EOS) described by a model of thermal quark mass and magnetic potential term introduced in Polyakov–Nambu–Jona–Lasinio (PNJL) model for two-flavour quarks. Under the influence of thermal quark mass and magnetic field term in the potential, the calculated results of EOS using the model are enhanced in a good pattern up to the temperature $$T=2.2T_{c} $$ MeV and can follow result similar to the unmagnetised field when the temperature is increased beyond $$T=2.2T_{c}$$ MeV. The result shows that the thermodynamic behaviour agrees well with the standard properties of quantum chromodynamics (QCD) thermodynamics and enhance the result up to $$2.2T_{c}$$ from the earlier predicted results and show the same behaviour beyond $$2.2T_{c}~$$ MeV.

Thermodynamic properties and transport coefficients of QCD matter within the nonextensive Polyakov–Nambu–Jona-Lasinio model

We present a non-extensive version of the Polyakov-Nambu-Jona-Lasinio model which is based on the non-extentive statistical mechanics. This new statistics is characterized by a dimensionless non-extensivity parameter $q$ that accounts for all possible effects violating the assumptions of the Boltzmann-Gibbs statistics (when $q\rightarrow1$, it returns to the Boltzmann-Gibbs case). Using this q-Polyakov-Nambu-Jona-Lasinio model and including two different Polyakov-loop potentials, we discussed the influence of the parameter $q$ on chiral and deconfinement phase transition, various thermodynamic quantities and transport coefficients at finite temperature and zero quark chemical potential. We found that the Stefan-Boltzmann limit is actually related to the choice of statistics. For example, in the Tsallis statistics, the thermodynamic quantities $\frac{\epsilon}{T^{4}}$, $\frac{p}{T^{4}}$ and $\frac{s}{T^{3}}$ all increase with $q$, exceed their usual Stefan-Boltzmann limits and tend to a new $q$-related Tsallis limit at temperature high enough. Interestingly, however, due to a surprising cancellation, the high temperature limit of $c_{s}^{2}$ is still its SB limit $1/3$. In addition, we found some similarities between the non-extensive effect and the finite-size effect. For example, as $q$ increases (size decreases), the criticality of $\frac{c_{v}}{T^{3}}$ and $c_{s}^{2}$ gradually disappears. Besides, in order to better study the non-extensive effect, we defined a new susceptibility and calculated the response of thermodynamic quantities and transport coefficients to $q$. And found that their response patterns are different.

Fluctuations, criticality and nonequilibrium effect of the QCD matter

The multiplicity distributions of net-baryon number fluctuation in the first-order chiral phase transition associated with the nonequlibrium effect are investigated within the improved Polyakov–Nambu–Jona–Lasinio model. Compared with the idealized first-order transition in equilibrium, the calculation indicates that the density fluctuations in the metastable and unstable regions are more violent, which possibly affects the statistical distributions of density fluctuation in later stage of an expanding system. Signals induced by the first-order phase transition and those from the nonequilibrium effect are discussed in detail, which could be exploited to identify the first-order phase transition. Besides, the critical exponents of the thermodynamic quantities at both the critical end point and spinodal boundary are investigated.

Phases of Hadron-Quark Matter in (Proto) Neutron Stars

In the first part of this paper, we investigate the possible existence of a structured hadron-quark mixed phase in the cores of neutron stars. This phase, referred to as the hadron-quark pasta phase, consists of spherical blob, rod, and slab rare phase geometries. Particular emphasis is given to modeling the size of this phase in rotating neutron stars. We use the relativistic mean-field theory to model hadronic matter and the non-local three-flavor Nambu–Jona-Lasinio model to describe quark matter. Based on these models, the hadron-quark pasta phase exists only in very massive neutron stars, whose rotational frequencies are less than around 300 Hz. All other stars are not dense enough to trigger quark deconfinement in their cores. Part two of the paper deals with the quark-hadron composition of hot (proto) neutron star matter. To this end we use a local three-flavor Polyakov–Nambu–Jona-Lasinio model which includes the ’t Hooft (quark flavor mixing) term. It is found that this term leads to non-negligible changes in the particle composition of (proto) neutron stars made of hadron-quark matter.

Confinement effects from a PNJL model at zero temperature regime

The Polyakov-Nambu-Jona-Lasinio (PNJL) model is a model that incorporates confinement effects in the Nambu-Jona-Lasinio (NJL) model through the addition of the Polyakov loop (Φ). These effects are studied at finite temperature regime. However, at zero temperature its modified Fermi-Dirac distributions become step functions and Φ disappears from the equations of state (EOS), as well as the Polyakov potential, leading the model to the conventional form of the NJL model. In this work we propose a variation of the PNJL model where all the couplings depend on Φ with the constraint that the interactions vanish at the deconfinement phase where Φ reaches its maximum value and the quarks behave as free particles. In this approach, coupling constants of original PNJL model become now dependent on Φ. As a consequence, all equations of state present a dependence even at zero temperature regime. The thermodynamics of this new model is discussed.

Strange matter and kaon to pion ratio in the SU(3) Polyakov–Nambu–Jona-Lasinio model

The behavior of strange matter in the frame of the SU(3) Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model including the ${U}_{A}(1)$ anomaly is considered. We discuss the appearance of a peak in the ratio of the number of strange mesons to nonstrange mesons known as the ``horn.'' The PNJL model gives a schematic description of the chiral phase transition and meson properties at finite temperature and density. By using the model, we can show that the splitting of kaon and antikaon masses appears as a result of the introduction of density. This may explain the difference in the ${K}^{+}/{\ensuremath{\pi}}^{+}$ ratio and the ${K}^{\ensuremath{-}}/{\ensuremath{\pi}}^{\ensuremath{-}}$ ratio at low $\sqrt{{s}_{NN}}$ and their tendency to the same value at high $\sqrt{{s}_{NN}}$. We also show that the rise in the ratio ${K}^{+}/{\ensuremath{\pi}}^{+}$ appears near the critical endpoint when we build the ${K}^{+}/{\ensuremath{\pi}}^{+}$ ratio along the phase-transition diagram and it can be considered as a critical region signal.

Finite volume effects on the chiral phase transition from Dyson–Schwinger equations of QCD

Within the framework of Dyson–Schwinger equations of QCD, we study the finite volume effects on the chiral phase transition, especially the influence on the position of the possible pseudo-critical end point (pCEP). The results show that in the chiral limit case (the current quark mass m=0), the absolute value of quark condensate decreases for smaller volumes, and more interestingly, so does the pseudo-critical temperature Tc(μ=0), which is in agreement with the Polyakov Nambu–Jona-Lasinio model result and opposite to the Polyakov linear sigma model prediction. These conclusions hold for m>0 case in our calculations. Moreover, the results of pCEP as a function of different volumes show that T of pCEP also decreases for smaller volumes, but μ of pCEP will increase, which are qualitatively more close to Polyakov linear sigma model results. For our model setup, results for systems with a size larger than (5 fm)3 closely approximate those from infinite volume, but if the volume is smaller, the corrections are non-negligible, even significantly affect signatures of the results from an infinite system. There also exists some possibility that, if the system size is too small, the whole phase transition would be crossover, which means no pCEP exists at all. It is no doubt that, finite volume effects deserve further researches.

Transport coefficients in a finite volume Polyakov–Nambu–Jona-Lasinio model

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 trans- port coefficients are enhanced in low temperature range. At high temperature domain, shear viscos- ity 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.

Equation of state of a quark-meson mixture in the improved Polyakov–Nambu–Jona-Lasinio model at finite chemical potential

We study the equation of state of QCD using an improved version of the three-flavor Polyakov-Nambu-Jona-Lasinio model beyond the mean-field approximation. It incorporates the effects of unquenched quarks into the Polyakov-loop effective potential, as well as mesonic contributions to the grand-canonical potential. We study in full detail the calculation of the thermodynamical potential in this approach and compare the resulting pressure and entropy density with the most-recent lattice-QCD calculations at zero baryochemical potential. Finally, we present some exploratory results at finite chemical potential which include the phase diagram of the model, the quark and meson masses, and finally, the thermodynamical pressure.

A comparative study on two different approaches of bulk viscosity in the Polyakov–Nambu–Jona-Lasinio model

We have gone through a comparative study on two different kinds 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.

Polyakov–Nambu–Jona-Lasinio model in finite volumes

We discuss the 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 plane.