Narrow Results

We investigate color superconductivity and chiral symmetry restoration at finite temperature and baryon density in the frame of standard two flavor Nambu–Jona-Lasinio model. We derive the diquark mass in RPA, discuss its constraint on the coupling constant in the diquark channel, and find a strong competition between the two phase transitions when the coupling constant is large enough.

We investigate the isospin chemical potential effect in the frame of SU(2) Nambu-Jona-Lasinio model. When the isospin chemical potential is less than the vacuum pion mass, the phase structure with two chiral phase transition lines does not happen due to U_A(1) breaking of QCD. When the isospin chemical potential is larger than the vacuum pion mass, the ground state of the system is a Bose-Einstein condensate of charged pions.

The possibility that the Pauli interaction could influence the critical temperature of chiral transition is investigated. We work within the Nambu-Jona–Lasinio model at the mean field level, with quark anomalous magnetic moment as a parameter.

In this paper, the coupling strength G of the Nambu–Jona-Lasinio (NJL) model is modified by incorporating quark’s feedback into the gluon propagator. The modified two-flavor NJL model with the quark-dependent coupling strength is explored. The quark condensate in this framework has a conspicuous agreement with the lattice quantum chromodynamics (QCD) results at finite temperature. Then, it is compared with the original NJL model in both zero (chiral limit) and nonzero current quark mass. The QCD phase diagram and susceptibilities are investigated in the temperature–chemical potential $(T-\mu )$ plane. Therefore, the pseudo-critical temperature $T_{\mathrm{\text{c}}}$ and the critical end point (CEP) are worked out and compared with original NJL model or lattice QCD results. In addition, the pion mass and decay constant are studied at finite temperature.

Based on the two flavor Nambu–Jona-Lasinio (NJL) model with a proper time regularization, we used stationary wave condition (SWC) for the first time to study the influence of the finite volume effects on the chiral phase transition of quark matter at finite temperature. It is found that when the cubic volume size $L$ is larger than $L_{max}^{\mathrm{\text{SWC}}}=500$ fm, the chiral quark condensate is indistinguishable from that at $L=\infty$. Here, it should be noted that 500 fm is far greater than the size of QGP produced at laboratory and the lattice QCD simulation space size. It is also much larger than the previous limit size $L_{max}^{\mathrm{\text{APBC}}}=5$ fm estimated by the commonly used anti-periodic boundary condition (APBC). We also found that when the space size $L$ is less than $L_{min}^{\mathrm{\text{SWC}}}=0.25$ fm, the spontaneous symmetry breaking concept is no longer valid. In addition, we first introduce the spatial susceptibility, and through the study of the spatial susceptibility, it was revealed for the first time that the chiral phase transition caused by the finite volume effects in the non-chiral limit is a crossover.

At zero temperature and finite chemical potential, the gap equation of cold dense quark matter under external magnetic field is studied with NJL model in the mean-field approximation. By introducing new methods, it is found that the Nambu phase has sophisticated structures which have not been studied before. As a consequence, the phase diagram is expanded and divided into five areas, in each area the condensate has unique behaviors with chemical potential varying. Furthermore, the expanded phase diagram is used to predict the order of phase transition between the Nambu phase and the Wigner phase, it can also be used to explain the relations of dynamical mass and chemical potential. Meanwhile, the metastable states and cascade effect of dynamical mass are studied in this paper.

Following our recently proposed self-consistent mean field approximation approach, we have done some researches on the chiral phase transition of strong interaction matter within the framework of Nambu-Jona-Lasinio (NJL) model. The chiral susceptibility and equation of state (EOS) are computed in this work for both two-flavor and three-flavor quark matter for contrast. The Pauli–Villars scheme, which can preserve gauge invariance, is used in this paper. Moreover, whether the three-flavor quark matter is more stable than the two-flavor quark matter or not in quark stars is discussed in this work. In our model, when the bag constant are the same, the two-flavor quark matter has a higher pressure than the three-flavor quark matter, which is different from what Witten proposed in his pioneering work.

The pion and kaon properties in a nuclear medium at nonvanishing temperature as well as the quantum chromodynamics (QCD) chiral condensate in the presence of a magnetic field for various baryon densities are studied in the Nambu–Jona–Lasinio (NJL) model with the help of the proper-time regularization (PTR) scheme, simulating a QCD confinement. The density dependence of the quark mass in symmetric nuclear matter is obtained from the quark-meson coupling (QMC) model, which shares the same covariant feature with the NJL model, at quark level. We then analyze the QCD chiral condensates and dynamical masses for various baryon densities at finite temperature and magnetic field as well as the pion and kaon masses, pion and kaon weak-decay constants, pion- and kaon-quark coupling constants, and wave function renormalization factors for various baryon densities at finite temperature. We find that the QCD chiral condensates suppress with increasing temperature and baryon density and enhance under the presence of a magnetic field, which are consistent with other model predictions. Interestingly, the wave function renormalization factors for the pion and kaon increase with respect to temperature and reduce as the baryon density increases are found.

We calculate the low energy π π scattering lengths and , the coupling of the ρ to the pion g_{ρ π π}, the total width of the ρ, the low q² behavior of the pion electromagnetic form factor, and the pion scalar form factor within a chiral SU(2)_f NJL-type Lagrangian where the spin 1 ρ meson is generated from a four-quark tensor interaction. Such a simple model avoids the mathematical complication related to π - a₁ mixing. Two types of regularization are discussed, mainly affecting the values of and . We find rather good agreement with data. The ρ meson described in this way does not account for the meson vector dominance model: it does not contribute to the scattering lengths, and the charge radius of the pion is mainly ascribed to the bare photon quark coupling. Even if the shape of the electromagnetic form factor is well reproduced, the strong increase near the ρ pole does not account for the ρ→ππ decay but only reflects the structure of the ρ.

This work is a follow up of recent investigations where the implications of a generalized heat kernel expansion is studied, constructed to incorporate non-perturbatively the effects of a non-commutative quark mass matrix in a fully covariant way at each order of the expansion. As underlying Lagrangian we use the Nambu – Jona-Lasinio (NJL) model of QCD, with SU_f(3) and U_A(1) breaking, the latter generated by the 't Hooft flavor determinant interaction. The associated bosonized Lagrangian is derived in leading stationary phase approximation (SPA) and up to second order in the generalized heat kernel expansion. Its symmetry breaking pattern is shown to have a complex structure, involving all powers of the mesonic fields allowed by symmetry. The considered Lagrangian yields a reliable playground for the study of the implications of symmetry and vacuum structure on the mesonic spectra, which we evaluate for the scalar and pseudoscalar meson nonets and compare with other approaches and experiment.

The properties of two-flavored massless Nambu–Jona-Lasinio (NJL) model in (1+1)-dimensional R¹ × S¹ space–time with compactified space coordinate are investigated in the presence of isospin and quark number chemical potentials μ_I, μ. The consideration is performed in the large N_c limit, where N_c is the number of colored quarks. It is shown that at L = ∞ (L is the length of the circumference S¹) the charged pion condensation (PC) phase with zero quark number density is realized at arbitrary nonzero μ_I and for rather small values of μ. However, at arbitrary finite values of L the phase portrait of the model contains the charged PC phase with nonzero quark number density (in the case of periodic boundary conditions for quark fields). Hence, finite sizes of the system can serve as a factor promoting the appearance of the charged PC phase in quark matter with nonzero baryon densities. In contrast, the phase with chiral symmetry breaking may exist only at rather large values of L.

The temperature behavior of the pion width in the hadronic phase is investigated in the framework of the Nambu–Jona–Lasinio (NJL) model. The contribution to the width from the pion–pion collision is considered with a scalar sigma-meson as an intermediate state. It is shown that the pion width significantly broadens at $T>0.1$GeV. Using the two-step iteration method, suggested by Kadanoff and Baym, the pion spectral function in a hot pion gas is calculated at different temperatures.

In this paper, we study the influence of different regularization schemes on the critical endpoint (CEP) of chiral phase transition within a cubic box with volume $V\sim L^3$. A two-flavor Nambu–Jona-Lasinio model at finite temperature $T$ and chemical potential $\mu$ is adopted as the effective model of the strong interacting matter. Due to the finite volume of the box, the momentum integral in gap equation is replaced by discrete summation, and an anti-periodic boundary condition for quark field is applied. We employ the Schwinger’s proper time and the Pauli–Villars regularization (PVR) schemes, respectively. It is found that the first-order phase transition line displays an intriguing “staircase” behavior, and eventually disappears as $T$ increases. In particular, there is no existence of the CEP for both regularization schemes in infinite volume limit $V\to \infty$. However, for the finite volume, the locations of the CEPs with proper time and PVR are determined, respectively.

We have applied the resonating (Res-) mean-field approximation (MFA) to fermion systems with large quantum fluctuations over the usual MFA to a naive Nambu-Jona-Lasinio (NJL) model involving no current quark mass term. In our approach, as part of the model the normalization volume is kept finite, which plays an important role. This attempt has been quite successful in explaining the pion and sigma-meson masses, but the values of the order parameter for quark condensate and the pion decay constant are too small. This fact suggests us that the Res-MFA including no isospin causes such a problem. To avoid the serious drawback, if we naturally extend the NJL model to include two-flavor degrees of freedom and make an SU(2)_f resonating Hartree-Fock (Res-HF) approximation, it is expected that the magnitudes of the order parameter and the pion decay constant are much improved. Using this extended NJL model, they are calculated again and both the numerical values and f_π reach good agreements with their experimental ones.

Quark matter at finite temperature and subject to strong magnetic fields is possibly present in the early stages of heavy ion collisions and in the interior of protoneutron stars. We use the mean field approximation to investigate this type of quark matter described by the Nambu–Jona-Lasinio model. The effect of the magnetic field on the effective quark masses and chemical potentials is only felt for quite strong magnetic fields, above 5 × 10¹⁸G, with larger effects for the lower densities. Spin polarizations are more sensitive to weaker magnetic fields and are larger for lower temperatures and lower densities.

For quark matter at finite baryon chemical potential, its density develops large fluctuations when it undergoes a first-order phase transition. Based on the Nambu–Jona–Lasinio (NJL) model, we have used the linear response theory to study the growth rate of density fluctuations and its dependence on the wavelength of unstable modes. Using the transport equation derived from the NJL model, we have also studied the time evolution of the unstable modes and the density fluctuations in a baryon-rich quark matter that is confined in a finite volume. Allowing the expansion of the quark matter, we have further studied the survivability of the density fluctuations as the density and temperature of the quark matter decrease. Possible experimental signatures of the density fluctuations have been suggested.

In this paper, we use the two-flavor Nambu–Jona-Lasinio model together with the proper time regularization that has both ultraviolet and infrared cutoffs to study the chiral phase transition at finite temperature and zero chemical potential. The involved model parameters in our calculation are determined in the traditional way. Our calculations show that the dependence of the results on the choice of the parameters are really small, which can then be regarded as an advantage besides such a regularization scheme is Lorentz invariant.

We study the QCD phase diagram in the framework of a nonlocal three-flavor quark model. We determine the model parameters from vacuum meson phenomenology, considering lattice QCD-inspired nonlocal form factors. Then we analyze the features of the deconfinement and chiral restoration transitions for systems at nonzero temperature and chemical potential.

For quark matter at finite baryon chemical potential, its density develops large fluctuations when it undergoes a first-order phase transition. Based on the Nambu–Jona–Lasinio (NJL) model, we have used the linear response theory to study the growth rate of density fluctuations and its dependence on the wavelength of unstable modes. Using the transport equation derived from the NJL model, we have also studied the time evolution of the unstable modes and the density fluctuations in a baryon-rich quark matter that is confined in a finite volume. Allowing the expansion of the quark matter, we have further studied the survivability of the density fluctuations as the density and temperature of the quark matter decrease. Possible experimental signatures of the density fluctuations have been suggested.