We study the critical point in the QCD phase diagram in the Nambu-Jona-Lasino (NJL) model by including a scalar-vector coupled interaction. We find that varying the strength of this interaction, which has no effect on the vacuum properties of QCD, can significantly affect the location of the critical point in the QCD phase diagram, particularly the value of the cirtical temperature. This provides a convenient way to use the NJL-based transport or hydrodynamic model to extract information about the QCD phase diagram from relativistic heavy-ion collisions.
The elastic electromagnetic form factors in the space-like region and valence quark distribution functions for the K+ meson are calculated using the confining Nambu-Jona-Lasinio model with the help of the proper-time regularization scheme, which simulates quark confinement. In this model framework, the dynamics information on the nonperturbative aspects is obtained from quark propagators and bound state amplitudes via Bethe-Salpeter equations. We found that the results on the kaon form factors and valence quark distribution functions are qualitatively in excellent agreement with the existing k…
We discuss inhomogeneous ground states of the Nambu-Jona-Lasino (NJL) and quark-meson (QM) model within mean-field approximation and their possible existence in the respective phase diagrams. For this purpose we focus on lower dimensional modulations and point out that known solutions in the 2+1 and 1+1 dimensional (chiral) Gross-Neveu (GN) model can be lifted to the to the 3+1 dimensional NJL model. This is worked out in detail for one-dimensional modulations and numerical results for the phase diagrams are presented. Focus is put on the critical point and on vanishing temperatures. As an int…
We determine the strength $G_{\rm v}$ of the vector-type four-quark interaction in the entanglement Polyakov-extended Nambu-Jona-Lasinio (EPNJL) model from the results of recent lattice QCD simulations with two-flavor Wilson fermions. The quark-number density is normalized by the Stefan-Boltzmann limit for small baryon chemical potential $μ$ and temperature $T$ higher than the pseudo-critical temperature $T_c$ of the deconfinement transition. The strength determined from the normalized quark-number density is $G_{\rm v}=0.33 G_{\rm s}$ for the strength $G_{\rm s}$ of the scalar-type four-quark…
We investigate the possibility of charged pion condensation in the presence of parallel rotation and magnetic field within the Nambu--Jona-Lasinio model with quarks as the fundamental degrees of freedom. Previous study based on non-interacting Klein-Gordon theory for pions showed that the charged pions will undergo Bose-Einstein condensation under this circumstance [Y. Liu and I. Zahed, Phys. Rev. Lett. ${\bf 120}$, 032001 (2018)]. In this work, we take into account the internal quark structures of charged pions self-consistently through quark polarization loops in an interacting theory, i.e.,…
The breaking of chiral symmetry of light quarks at zero temperature in presence of strong quantizing magnetic field is studied using Nambu-Jona-Lasinio (NJL) model with Thomas-Fermi type semi-classical formalism. It is found that the dynamically generated light quark mass can never become zero if the Landau levels are populated and increases with the increase of magnetic field strength.
We investigate the current-current correlation functions or the so-called response functions of a two-flavor Nambu-Jona-Lasino model at finite temperature and density. We study the linear response by using the functional path integral approach and introducing the conjugated gauge fields as external sources. The response functions can be obtained by expanding the generational functional in powers of the external sources. We derive the response functions parallel to two well-established approximations for the equilibrium thermodynamics: the mean-field theory and a beyond-mean-field theory taking…
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 point out that adding higher dimension operators to the Nambu-Jona-Lasinio model can stabilize chiral symmetry breaking and resolve the issue raised by Kleinert and Van den Bossche that chiral symmetry breaking cannot occur for $N_c \le N_c^{\rm cr}$ due to large quantum fluctuations of the composite fields.
We study the chiral phase transition of the two flavor Nambu-Jona-Lasinio (NJL) model in a sphere with the MIT boundary condition. We find that the MIT boundary condition results in much stronger finite size effects than the antiperiodic boundary condition. Our work may be helpful to study the finite size effects in heavy-ion collision in a more realistic way.
In the frame of flavor SU(2) Nambu--Jona-Lasinio model with $U_A(1)$ breaking term we found that, the structure of two chiral phase transition lines does not exist at low isospin density in real world, and the critical isospin chemical potential for pion superfluidity is exactly the pion mass in the vacuum.
We discuss the 2+1 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 $T-μ_q$ plane.
A possibility of existence of a pseudovector-type quark-antiquark condensate in the quark matter and Nambu-Goldstone modes on that condensate in the Nambu-Jona-Lasinio model
We discuss the lightest scalar resonances, $f_0(600)$, $κ(800)$, $a_0(980)$ and $f_0(980)$ in the extended Nambu Jona-Lasinio model. We find that the model parameters can be tuned, but unnaturally, to accommodate for those scalars except the $f_0(980)$. We also discuss problems encountered in the K Matrix unitarization approximation by using $N_c$ counting technique.
We investigate strong and radiative meson decays in a generalized Nambu--Jona-Lasinio model. The one loop order calculation provides a satisfactory agreement with the data for the mesonic spectrum and for radiative decays. Higher order effects for strong decays of $ρ$ and $K^*$ are estimated to be large. We also discuss the role of the flavour mixing determinantal interaction.
Using the Nambu--Jona-Lasinio (NJL) model we study responses of the pion and kaon masses to changes in the chemical potential, $dm/dμ$, at zero and finite chemical potential. We find that the behavior of $dm/dμ$ for the pion is quite different from that for the kaon. Our results can give a clue for future studies of $dm/dμ$ on the lattice.
We report the first model study of the net charge fluctuations in terms of D-measure within the framework of the Polyakov-Nambu-Jona-Lasinio model. Net charge fluctuation is estimated from the charge susceptibility evaluated using PNJL model. A parameterization of the freeze-out curve has been used to obtain D as a function of sqrt(s). We have discussed our results vis-a-vis recent experimental findings from ALICE collaboration.
Effect of magnetic field on chiral symmetry breaking in a 3-flavor Nambu Jona Lasinio (NJL) model at finite temperature and densities is considered here using an explicit structure of ground state in terms of quark and antiquark condensates. While at zero chemical potential and finite temperature, magnetic field enhances the condensates, at zero temperature, the critical chemical potential decreases with increasing magnetic field.
We investigate pion superfluidity in the frame of two flavor Nambu--Jona-Lasinio model beyond mean field approximation. We calculate the thermodynamics to the next to leading order in an expansion in the inverse number of colors, including both quark and meson contributions at finite temperature and baryon and isospin density. Due to the meson fluctuations, the Sarma phase which exists at mean field level is washed away, and the Bose-Einstein condensation region at low isospin density is highly suppressed.
We present an analysis of two-current correlations for the pion in the Nambu--Jona-Lasinio model, with Pauli--Villars regularization. We provide explicit expressions in momentum space for two-current correlations corresponding to the zeroth component of the vector Dirac bilinear in the quark vertices, which has been evaluated on the lattice. The numerical results show a remarkable qualitative agreement with recent lattice data. The factorization approximation into one-body currents is discussed.
In this review, we summarize recent progress on the possible phases of quantum chromodynamics (QCD) in the presence of a strong magnetic field, mainly from the views of the chiral effective Nambu--Jona-Lasinio model. Four kinds of phase transitions are explored in detail: chiral symmetry breaking and restoration, neutral pseudoscalar superfluidity, charged pion superfluidity and charged rho superconductivity. In particular, we revisit the unsolved problems of inverse magnetic catalysis effect and competition between the chiral density wave and solitonic modulation phases. It is shown that usef…
We calculate the shear $η(T)$ and bulk viscosities $ζ(T)$ as well as the electric conductivity $σ_e(T)$ and heat conductivity $κ(T)$ 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 v…
Given the phenomenological success of the Nambu-Jona-Lasinio model in describing the meson physics in the low energy limit, it is tempting to find the fully relativistically structured nucleon solution in the same model under the similar approximation employed in the mesonic sector. To achieve this goal we need to solve a relativistic Faddeev equation. The factorizability of the two-body T-matrix reduces the three-body Faddeev equation to a tractable two-body Bethe-Salpeter equation. The reduced equation is then solved numerically. Our result indicates that the nucleon consists of three loosel…
Mass spectra and Mott transitions of neutral mesons at finite temperature and magnetic field in frame of three-flavor Polyakov-extended Nambu-Jona-Lasino model
Xi'an University of Posts and Telecommunications（西安邮电大学）；Xi'an Jiaotong University（西安交通大学）
We calculate the shear $η(T)$ and bulk viscosities $ζ(T)$ as well as the electric conductivity $σ_e(T)$ and heat conductivity $κ(T)$ 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 squared $c_s^2(T)$. 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 variabl…
The off--shell electromagnetic vertex function of pions and kaons is studied in a bosonized Nambu--Jona-Lasinio model with a gauge--invariant proper--time cutoff. The slope of the pion form factor with respect to the pion 4--momentum is found to be equal to the on--shell pion charge radius in the chiral limit. The off--shell slope of the $K^0$ form factor is zero, that of the $K^\pm$ about 15\% smaller than that of the pion. We compare our results with those of a recent calculation in chiral perturbation theory.
Using the Nambu-Jona-Lasinio model to describe the nucleon as a quark-diquark state, we discuss the stability of nuclear matter in a hybrid model for the ground state at finite nucleon density. It is shown that a simple extension of the model to simulate the effects of confinement leads to a scalar polarizability of the nucleon. This, in turn, leads to a less attractive effective interaction between the nucleons, helping to achieve saturation of the nuclear matter ground state. It is also pointed out that that the same effect naturally leads to a suppression of ``Z-graph'' contributions with i…
We have investigated shear viscosity of quark matter in presence of a strong uniform magnetic field background where Nambu-Jona-Lasinio model has been considered to describe the magneto-thermodynamical properties of the medium. In presence of magnetic field, shear viscosity coefficient gets split into different components because of anisotropy in tangential stress of the fluid. Four different components can be merged to two components in limit of strong field, where collisional width of quark becomes much lower than its synchrotron frequency. A simplified contact diagram of quark-quark interac…
We have estimated the susceptibilities of conserved charges for 2-flavor strongly interacting matter with varying system sizes, using the Polyakov loop enhanced Nambu Jona-Lasinio model. The susceptibilities for vanishing baryon densities are found to show a scaling with the system volume in the hadronic as well as partonic phase. This scaling breaks down for a temperature range of about 30-50 MeV around the cross-over region. Simultaneous measurements of the various susceptibilities may thus indicate how close to the cross-over region the freeze-out occurs for the fireball created in heavy-io…
In this work we study the electrized quark matter under finite temperature and density conditions in the context of the SU(2) and SU(3) Nambu--Jona-Lasinio models. To this end, we evaluate the effective quark masses and the Schwinger quark-antiquark pair production rate. For the SU(3) NJL model we incorporate in the Lagrangian the 't Hooft determinant and we present a set of analytical expressions more convenient for numerical evaluations. We predict a decrease of the pseudocritical electric field with the increase of the temperature for both models and a more prominent production rate for the…
The real-time formalism at finite temperature and chemical potential for the nonlocal Nambu--Jona-Lasinio model is developed in the presence of a Gaussian covariant regulator. We construct the most general thermal propagator, by means of the spectral function. As a result, the model involves the propagation of massive quasiparticles. The appearance of complex poles is interpreted as a confinement signal, and in this case we have unstable quasiparticles with a finite decay width. An expression for the propagator along the critical line, where complex poles start to appear, is also obtained. A g…
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 …
Chiral phase properties of finite size hadronic systems are investigated within the Nambu--Jona-Lasinio model. Finite size effects are taken into account by making use of the multiple reflection expansion. We find that, for droplets with relatively small baryon numbers, chiral symmetry restoration is enhanced by the finite size effects. However the radius of the stable droplet does not change much, as compared to that without the multiple reflection expansion.
The dual quark condensate $Σ^{(n)}$ proposed recently as a new order parameter of the spontaneous breaking of the ${\mathbb Z}_3$ symmetry are evaluated by the Polyakov-loop extended Nambu--Jona-Lasinio model, where $n$ are winding numbers. The Polyakov-loop extended Nambu--Jona-Lasinio model well reproduces lattice QCD data on $Σ^{(1)}$ measured very lately. The dual quark condensate $Σ^{(n)}$ at higher temperatures is sensitive to the strength of the vector-type four-quark interaction in the Polyakov-loop extended Nambu--Jona-Lasinio model and hence a good quantity to determine the strength.
Recently, it has been shown that the standard Nambu-Jona-Lasinio (NJL) model is not able to reproduce the correct QCD behavior of the gap equation at large density, and therefore a different cutoff procedure at large momenta has ben proposed. We found that, even with this density dependent cutoff procedure, the pure quark phase in neutron stars (NS) interiors is unstable, and we argue that this could be related to the lack of confinement in the original NJL model.
We argue that the spontaneous breakdown of symmetry in the chirally symmetric Nambu--Jona-Lasinio model which was supposed to illustrate the origin of the low mass of pions in hadron physics does not occur due to strong fluctuations in the sigma - pi field space. Although quarks acquire a constituent mass, sigma and pi turn out to have equal heavy masses of the order of the constituent quark mass.
The formalism of Riemannian geometry is applied to study the phase transitions in Nambu -Jona Lasinio (NJL) model. Thermodynamic geometry reliably describes the phase diagram, both in the chiral limit and for finite quark masses. The comparison between the geometrical study of NJL model and of (2+1) Quantum Chromodynamics at high temperature and small baryon density shows a clear connection between chiral symmetry restoration/breaking and deconfinement/confinement regimes.
We present a study of the 1+1 flavor system of strongly interacting matter in terms of the Polyakov$-$Nambu$-$Jona-Lasinio model. We find that though the small isospin symmetry breaking brought in through unequal light quark masses is too small to affect the thermodynamics of the system in general, it may have significant effect in baryon-isospin correlations and have a measurable impact in heavy-ion collision experiments.
The probability P(Delta-Delta) to find the Delta-Delta component inside the deuteron, where Delta stands for the Delta(1232) resonance, is calculated in the Nambu-Jona-Lasinio model of light nuclei. We obtain P(Delta-Delta) = 0.3%. This prediction agrees good with the experimental estimate P(Delta-Delta) < 0.4% at 90% of CL (D. Allasia et al., Phys. Lett. B174 (1986) 450).
Various aspects of the Generalised Nambu-Jona-Lasinio model for QCD in four dimensions are reviewed. The properties of mesonic excitations are discussed in detail, with special attention paid to the chiral pion. The spontaneous chiral symmetry breaking in the vacuum and the effective chiral symmetry restoration in the spectrum of highly excited mesons and baryons are described microscopically.
Elastic electromagnetic form factors for the $ρ^+$ meson are calculated in a Nambu--Jona-Lasinio model which incorporates quark confinement through the use of the proper-time regularization scheme. A comparison is made with recent lattice QCD results and previous quark model calculations for static quantities and the Sachs form factors. The results are qualitatively in good agreement with the lattice QCD calculations, with the exception of the quadrupole moment and corresponding form factor, which may be related to a lack of spherical symmetry on the lattice.
We study a Nambu-Jona-Lasinio (NJL) type model with two-flavor quark matter in $β$-equilibrium. It turns out that the system develops instabilities in the dispersion relations of the diquark fields, i.e., the velocity squared $v^2$ becomes negative in a certain region of the electron chemical potential. The critical point is the same as that of the chromomagnetic instability. The results imply the existence of spatially inhomogeneous diquark condensates in the genuine vacuum. We also discuss gauge equivalent classes between the inhomogeneous diquark condensates and gluon condensates.
The Nambu-Jona-Lasinio model of the deuteron suggested by Nambu and Jona-Lasinio (Phys. Rev. 124 (1961) 246) is formulated from the first principles of QCD. The deuteron appears as a neutron-proton collective excitation, i.e. a Cooper np-pair, induced by a phenomenological local four-nucleon interaction in the nuclear phase of QCD. The model describes the deuteron coupled to itself, nucleons and other particles through one-nucleon loop exchanges providing a minimal transfer of nucleon flavours from initial to final nuclear states and accounting for contributions of nucleon-loop anomalies which…
The D-wave state component of the neutron-proton bound state in the deuteron is calculated in the Nambu-Jona-Lasinio model of light nuclei - the relativistically covariant quantum field theoretic approach to the description of low-energy nuclear forces. The theoretical value of the fraction of the D-wave state relative to the S-wave state is equal to eta_d = 0.0238. This agrees well with the phenomenological value eta_d = 0.0256(4) quoted by Kamionkowski and Bahcall (ApJ. 420, 884 (1994)).
We show how to derive the complete set of electromagnetic corrections to the Nambu-Jona-Lasinio (NJL) model of the nucleon. Our results enable an accurate estimate of the electromagnetic contribution to the neutron-proton mass difference within this model. At the same time, our procedure demonstrates the way to calculate the complete set of meson corrections to the NJL model that maintains chiral symmetry.
We analyze the chiral phase transition of the Nambu--Jona-Lasinio model in the cold and dense region on the lattice developing the Grassmann version of the anisotropic tensor renormalization group algorithm. The model is formulated with the Kogut--Susskind fermion action. We use the chiral condensate as an order parameter to investigate the restoration of the chiral symmetry. The first-order chiral phase transition is clearly observed in the dense region at vanishing temperature with $μ/T\sim O(10^3)$ on a large volume of $V=1024^4$. We also present the results for the equation of state.
The self-energy of quarks is investigated for various models which are inspired by the Nambu--Jona-Lasinio (NJL) model. Including, beyond the Hartree-Fock approximation, terms up to second-order in the quark interaction, the real and imaginary parts of scalar and vector components of the self-energy are discussed. The second-order contributions depend on the energy and momentum of the quark under consideration. This leads to solutions of the Dirac equation which are significantly different from those of a free quark or a quark with constant effective mass, as obtained in the Hartree-Fock appro…
In this work we study the Nambu-Jona-Lasinio model in the SU (2) version with repulsive vector coupling and apply it to quark stellar matter. We discuss the influence of the vector interaction on the equation of state (EoS) and study quark stars that are composed of pure quark matter with two flavors. We show that, increasing the vector coupling, we obtain more massive stars with larger radii for the same central energy density.
We investigate the structure of hybrid stars based on two different constructions: one is based on the Gibbs condition for phase coexistence and considers the existence of a mixed phase (MP), and the other is based on the Maxwell construction and no mixed phase is obtained. The hadron phase is described by the non-linear Walecka model (NLW) and the quark phase by the Nambu-Jona-Lasinio model (NJL). We conclude that the masses and radii obtained are model dependent but not significantly different for both constructions.
We investigate the structure of protoneutron stars (PNS) formed by hadronic and quark matter in $β$-equilibrium described by appropriate equations of state (EOS). For the hadronic matter, we use a finite temperature EOS based on the Brueckner-Bethe-Goldstone many-body theory, with realistic two- and three-body forces. For the quark sector, we employ the Nambu--Jona-Lasinio model. We find that the maximum allowed masses are comprised in a narrow range around 1.8 solar masses, with a slight dependence on the temperature. Metastable hybrid protoneutron stars are not found.
