On the critical end point of the QCD and the NJL model phase diagrams

The relation between the NJL model and QCD with condensed gluons

We try to find the relation between the three-flavor Nambu-Jona-Lasinio model and QCD based on the hypothesis that the gluon momenta are sharply condensed around the QCD scale, μ_g. We find that the effective four- and six-fermion interactions, G_4 and G_6, should be scaled by G_4 proportional to μ_g^(-2) and G_6 proportional to μ_g^(-5) being consistent with the mass dimension counting in the obtained effective Lagrangian. We then study the μ_g dependence on the phase diagram of the chiral phase transition at finite temperature and chemical potential and the location of the critical point. We…

An innovative approach for sketching the QCD phase diagram within the NJL model using Lagrange Multipliers

We develop a new approach for sketching the quantum chromodynamics phase-diagram within the Nambu--Jona-Lasinio model for arbitrarily large values of the coupling constant, temperature and chemical potential based upon the strategy of Lagrange multipliers that constrains the corresponding gap equation and its mass gradient. Our approach distinguishes continuous from discountinuous phase transitions and thus is capable of locating the position of the Critical End Point from the thermodynamical parameters of the model alone, without direct reference to the chiral susceptibility or any other obse…

The $T-μ$ phase diagram of the NJL model in the presence of explicit symmetry-breaking interactions

It is shown that the strange quark mass undergoes a first order transition in a generalized 3 flavor Nambu--Jona-Lasinio (NJL) Lagrangian which includes a complete set of explicit chiral symmetry breaking interactions. This transition occurs in a moderate chemical potential region $μ\sim 400$ MeV, in addition to the usual chiral transition associated with the light quark sector. This favors the formation of stable strange quark matter at chemical potentials which are considerably lower than the ones discussed in the literature. The reason for this behavior is discussed.

Critical behaviors near the (tri-)critical end point of QCD within the NJL model

We investigate the dynamical chiral symmetry breaking and its restoration at finite density and temperature within the two-flavor Nambu-Jona-Lasinio model, and mainly focus on the critical behaviors near the critical end point (CEP) and tricritical point (TCP) of quantum chromodynamics. The multi-solution region of the Nambu and Wigner ones is determined in the phase diagram for the massive and massless current quark, respectively. We use the various susceptibilities to locate the CEP/TCP and then extract the critical exponents near them. Our calculations reveal that the various susceptibiliti…

Inhomogeneous phases near the chiral critical point in NJL-type models

In this talk we discuss the role of inhomogeneous phases in the phase diagram of the Nambu-Jona-Lasinio (NJL) and the quark meson (QM) model. By means of a generalized Ginzburg-Landau (GL) expansion it is concluded that the critical point in the mean-field phase diagram of the NJL model is in fact a Lifshitz point where homogeneous spontaneously broken, inhomogeneous and restored phases meet. This picture is confirmed by a mean-field calculation for inhomogeneous phases with a one-dimensional modulation. For the latter it is shown that recent results within lower dimensional models can be exte…

Thermodynamics of the 3-flavor NJL model : chiral symmetry breaking and color superconductivity

Employing an extended three flavor version of the NJL model we discuss in detail the phase diagram of quark matter. The presence of quark as well as of diquark condensates gives raise to a rich structure of the phase diagram. We study in detail the chiral phase transition and the color superconductivity as well as color flavor locking as a function of the temperature and chemical potentials of the system.

NJL model derived from QCD

We apply Bogolubov approach to QCD with two light quarks to demonstrate a spontaneous generation of an effective interaction, leading to the Nambu -- Jona-Lasinio model. The resulting theory contains two parameters: average low-energy value of $α_s$ and current light quark mass $m_0$. All other low-energy parameters: the pion decay constant, mass of the $π$-meson, mass of the $σ$-meson and its width, the constituent quark mass, the quark condensate are expressed in terms of the two input parameters in satisfactory correspondence to experimental data and chiral phenomenology. {\it E.g.} in the …

Search of QCD phase transition points in the canonical approach of the NJL model

We study the Lee-Yang zeros in the canonical approach to search phase transition points at finite temperature and density in the Nambu-Jona-Lasinio (NJL) model as an effective model of QCD. The canonical approach is a promising method to avoid the sign problem in lattice QCD at finite density. We find that a set of Lee-Yang zeros computed with finite degrees of freedom can be extrapolated to those with infinite degrees of freedom, providing the correct phase transition point. We propose the present method as a useful method for actual lattice simulations for QCD.

具有手征不平衡和强磁场的QCD相结构的非广延NJL模型研究

Non-extensive NJL model study of QCD phase structure with chiral imbalance and strong magnetic fields

基于Tsallis非广延统计的两味NJL模型，研究强磁场和手征不平衡下的QCD相结构与热力学性质，发现非平衡效应降低临界温度并导致磁催化到逆磁催化的转变。

Thermal Phase Transition in the NJL Model of QCD

We present results from numerical studies of the NJL model with two massless quarks at nonzero temperature. We show that the model undergoes a second order chiral phase transition which belongs to the 3d O(4) spin model universality class.

$τ^{-} \to π^{-} π^{0} ν_τ$ decay in the extended NJL model

The width of the decay $τ^{-} \to π^{-} π^{0} ν_τ$ was calculated in the extended NJL model. Contact interaction of $W$ boson with pion pair as well as the contribution of the $ρ$ mesons in ground and first radial-exited states are taken into account. The sum of the contact diagram and diagram with intermediate $ρ$ meson in the ground state leads to the result which coincides with the result of the vector-dominance model. Our results are in satisfactory agreement with experimental data.

Polyakov-NJL model with eight quark interactions

The phase diagram at finite temperature and chemical potential for the Polyakov-NJL model with eight quark interactions is reviewed for the SU(3) flavor case.

BEC-BCS crossover driven by the axial anomaly in the NJL model

We study the QCD phase structure in the three-flavor Nambu--Jona-Lasinio model, incorporating the chiral-diquark interplay due to the axial anomaly. We demonstrate that for a certain range of model parameters, the low temperature critical point predicted by a Ginzburg-Landau analysis appears in the phase diagram. In addition, we show that the axial anomaly presents a new scenario for a possible BEC-BCS crossover in the color-flavor locked phase of QCD.

通过机器学习确定磁化QCD物质中的NJL耦合和AMM

Determining the NJL Coupling and AMM in Magnetized QCD Matter via Machine Learning

本文利用机器学习框架，通过格点QCD数据确定NJL模型中的运行耦合常数和夸克异常磁矩比，揭示强磁场下QCD真空的响应。

The decay $τ\to K^{*0}(892) K^- ν_τ$ in the extended NJL model

In the extended Nambu -- Jona-Lasinio model, the decay width of $τ\to K^{*0}(892) K^- ν_τ$ is calculated. The contributions from the contact diagram and diagrams with intermediate axial-vector, vector and pseudoscalar mesons in the ground and first radially excited states are taken into account. It is shown that axial-vector and vector channel with a contact diagram give a dominant contribution to the decay width. The obtained results for the decay width $τ\to K^{*0}(892) K^- ν_τ$ are in satisfactory agreement with experimental data. A prediction for differential distribution over the invarian…

Model analysis on thermal UV-cutoff effects on the critical boundary in hot QCD

We study the critical boundary on the quark-mass plane associated with the chiral phase transition in QCD at finite temperature. We point out that the critical boundaries obtained from the Lattice QCD simulation and the chiral effective model are significantly different; in the (Polyakov-loop coupled) Nambu--Jona-Lasinio (NJL) model we find that the critical mass is about one order of magnitude smaller than the value reported in the Lattice QCD case. It is known in the Lattice QCD study that the critical mass goes smaller in the continuum limit along the temporal direction. To investigate the …

强磁场下非广延NJL模型中的QCD相变

QCD phase transition with non-extensive NJL model in the strong magnetic field

本研究基于非广延NJL模型探究强磁场下三味夸克物质的QCD相变，发现系统始终为交叉过渡且赝临界温度随非广延参数增大而降低，同时揭示了磁场与非广延参数对系统热力学、磁学性质及迹反常、声速的影响。

Quark matter under strong magnetic fields in SU(2) NJL-type models: parameter dependence of the cold dense matter phase diagram

The phase structure of magnetized cold quark matter is analyzed in the framework of the two-flavor Nambu-Jona-Lasinio models paying special attention to its dependence on the model parameters as different values within the phenomenological allowed range are considered. We first discuss the simpler chiral limit case, and then the more realistic situation of finite current masses. We show that in spite of the difference in the nature of some transitions, both cases are alike and exhibit a rather rich phase structure for a significant range of acceptable parameters. A simplification of the phase …

A NJL-based study of the QCD critical line

We employ a 3 flavor NJL model to stress some general remarks about the QCD critical line. The dependence of the critical curve on $μ_q=(μ_u+μ_d)/2$ and $μ_I=(μ_u-μ_d)/2$ is discussed. The quark masses are varied to confirm that, in agreement with universality arguments, the order of transition depends on the number of active flavors $N_f$. The slope of the critical curve vs. chemical potential is studied as a function of $N_f$. We compare our results with those recently obtained in lattice simulations to establish a comparison among different models.

Aspects of the phase diagram in (P)NJL-like models

We discuss three applications of NJL- and PNJL-like models to assess aspects of the QCD phase diagram: First, we study the effect of mesonic correlations on the pressure below and above the finite temperature phase transition within a nonlocal PNJL model beyond the mean-field approximation. Second, we reconstruct the phase boundary of an NJL model from a Taylor expansion of the chiral susceptibility about $μ= 0$ and compare the result with the exact phase boundary. Finally, we demonstrate the realization of the "non-standard scenario" for the critical surface in a three-flavor PNJL model with …

稠密三色与二色QCD及部分类QCD的NJL模型的对偶对称性

Dual symmetries of dense three and two-color QCD and some QCD-like NJL models

本文在无质量NJL和QCD模型框架下，研究了稠密两色与三色夸克物质相图在对偶变换下的对称性质，揭示了CSB、带电PC及重子超流相之间的对偶对称性。

The deconfinement phase transition, hadronization and the NJL model

One of the confident predictions of QCD is that at sufficiently high temperature and/or density, hadronic matter should undergo a thermodynamic phase transition to a colour deconfined state of matter - popularly called the Quark-Gluon Plasma (QGP). In low energy effective theories of Quantum Chromodynamics (QCD), one usually talks of the chiral transition for which a well defined order parameter exists. We investigate the dissociation of pions and kaons in a medium of hot quark matter decsribed by the Nambu - Jona Lasinio (NJL) model. The decay widths of pion and kaon are found to be large but…

The phase diagram and bulk thermodynamical quantities in the NJL model at finite temperature and density

We reexamine the recent instanton motivated studies of Alford, Rajagopal and Wilczek, and Berges and Rajagopal in the framework of the standard SU(2) Nambu-Jona-Lasinio model. The chiral phase diagram is calculated in the temperature--density plane, and the pressure is evaluated as the function of the density. Obtaining simple approximate relations describing the $T$-$μ$ and $T$-$p_F$ phase transition lines we find that the results of the instanton based model and that of the NJL model are identical. The diquark transition line is also given.

QCD-inspired determination of NJL model parameters

The QCD phase diagram at finite temperature and density has attracted considerable interest over many decades now, not least because of its relevance for a better understanding of heavy-ion collision experiments. Models provide some insight into the QCD phase structure but usually rely on various parameters. Based on renormalization group arguments, we discuss how the parameters of QCD low-energy models can be determined from the fundamental theory of the strong interaction. We particularly focus on a determination of the temperature dependence of these parameters in this work and comment on t…

Scalar density fluctuation at critical end point in NJL model

Soft mode near the critical end point in the phase diagram of two-flavor Nambu--Jona-Lasinio (NJL) model is investigated within the leading 1/N_c approximation with N_c being the number of the colors. It is explicitly shown by studying the spectral function of the scalar channel that the relevant soft mode is the scalar density fluctuation, which is coupled with the quark number density, while the sigma meson mode stays massive.

Causal aspects of effective QCD models

Here we studied the possible diffusion speed for relativistic fluid in different effective quantum chromodynamics models: Nambu-Jona-Lasinio (NJL), Polyakov loop extended NJL, entangled PNJL (EPNJL) model.

3-dimensional QCD phase diagram with pion condensate in the NJL model

With the isovector coupling constants adjusted to reproduce the physical pion mass and lattice QCD results in baryon-free quark matter, we have carried out rigourous calculations for the pion condensate in the 3-flavor Nambu-Jona-Lasinio model, and studied the 3-dimensional QCD phase diagram. With the increasing isospin chemical potential $μ_I$, we have observed two nonzero solutions of the pion condensate at finite baryon chemical potentials $μ_B$, representing respectively the pion superfluid phase and the Sarma phase, and their appearance and disappearance correspond to a second-order (firs…

Nambu-Jona-Lasinio模型中的重子手征孤子

Baryons as Chiral Solitons in the Nambu--Jona-Lasinio Model

评述了Nambu-Jona-Lasinio（NJL）模型中重子作为手征孤子的描述.大$N_C$ QCD为重子的孤子描述提供了一个动力。讨论了QCD中手征对称性自发破缺的严格结果。然后认为，NJL模型提供了一个公平的描述低能强子物理。因此，NJL模型被用来模拟QCD的低能手征味动力学。该模型是玻色化的泛函积分技术和新兴的有效介子理论的物理内容进行了讨论。特别是，它与Skyrme模型的关系。求出了玻色化NJL模型的静态孤子解，讨论了它们的性质，并研究了各种介子场的影响。这些考虑为威滕的猜想提供了强有力的支持，即重子可以理解为有效介子理论的孤子解。然后将NJL模型的手征孤子量子化，研究了核子的各种静态性质。研究了半经典量子化孤子的主要$1/N_C$修正。研究了手征孤子的介子随时间的涨落，并利用它估计了孤子质量的量子修正。最后，超子被描述为手征孤子的NJL模型。这是在这两个，集体旋转的方法Yabu和安藤以及在束缚态的方法卡兰和Klebanov。

Magnetized QCD phase diagram

Using the 2+1 flavor Nambu--Jona-Lasinio (NJL) model with the Polyakov loop, we determine the structure of the QCD phase diagram in an external magnetic field. Beyond the usual NJL model with constant couplings, we also consider a variant with a magnetic field dependent scalar coupling, which reproduces the Inverse Magnetic Catalysis (IMC) at zero chemical potential. We conclude that the IMC affects the location of the Critical End Point, and found indications that, for high enough magnetic fields, the chiral phase transition at zero chemical potential might change from an analytic to a first-…

Determination of Scalar Meson Masses in QCD-inspired Quark Models

We compare two QCD-inspired quark models with four-fermion interaction, without and with the remnant coupling to low-energy gluons, in the regime of dynamical chiral symmetry breaking (DCSB). The first one, the Nambu-Jona-Lasinio (NJL) model ensures the factorization of scalar and pseudoscalar meson poles in correlators, the well-known Nambu relation between the scalar meson mass and the dynamical quark mass, $m_σ = 2 m_{dyn}$, and the residual chiral symmetry in coupling constants characteristic for the linear $σ$-model. The second one, the Gauged NJL model, happens to be qualitatively differ…

QCD phase diagram with chiral imbalance in NJL model: duality and lattice QCD results

In addition to temperature and baryon chemical potential there are other parameters that matter in the real quark matter. One of them is isospin asymmetry which does exist in nature, for example, in the compact stars and in heavy ion collisions. The chiral imbalance, the difference between left- and right-handed quarks, is another phenomenon that could occur in quark matter. We have shown that lattice QCD results support the existence of the approximate duality in real QCD. The rise of pseudo-critical temperature with increase of chiral chemical potential $μ_{5}$ (the much debated effect recen…

Inverse Magnetic Catalysis in the three-flavor NJL model with axial-vector interaction

In this paper we explore the chiral phase transition in QCD within the three-flavor Nambu-Jona-Lasinio (NJL) model with a negative coupling constant in the isoscalar axial-vector channel, which is associated with a polarized instanton--anti-instanton molecule background. The QCD phase diagram described in this scenario shows a new first order phase transition around the transition temperature $T_c$ toward a phase without chiral condensates, but with nontrivial dynamic chiral chemical potentials for the light quarks, spontaneously giving rise to local $\mathcal {CP}$ violation and local chirali…

Color superconductivity vs. pseudoscalar condensation in a three-flavor NJL model

We calculate numerically the phase diagram of the three-flavor Nambu-Jona-Lasinio model at zero and finite temperature as a function of the up, down, and strange quark chemical potentials. We focus on the competition between pseudoscalar condensation and color superconductivity. We find that the two types of phases are separated by first-order transitions.

Phase diagram of chiral and diquark condensates at finite temperature and density in the 2-dimensional Gross Neveu model

We construct the phase diagram of the chiral and diquark condensates at finite temperature and density in the 1+1 dimensional (2D) two flavor massless Gross Neveu model. The resultant phase diagram shows (I) the chiral condensed phase at low temperature and density, (II) the diquark condensed phase at low temperature and high density, and (III) the chiral and diquark coexisting phase at low temperature and intermediate density. This phase structure is also seen in the 3D Gross Neveu model and the 4D Nambu Jona-Lasinio (NJL) model. Thus the phase diagrams of the chiral and diquark condensates i…

Critical end point in a thermo-magnetic nonlocal NJL model

In this article we explore the critical end point in the $T-μ$ phase diagram of a thermomagnetic nonlocal Nambu--Jona-Lasinio model in the weak field limit. We work with the Gaussian regulator, and find that a crossover takes place at $μ, B=0$. The crossover turns to a first order phase transition as the chemical potential or the magnetic field increase. The critical end point of the phase diagram occurs at a higher temperature and lower chemical potential as the magnetic field increases. This result is in accordance to similar findings in other effective models. We also find there is a critic…

磁化非广延QCD介质的NJL模型分析

An NJL model analysis of a magnetised nonextensive QCD medium

本研究在2+1味NJL模型中分析磁场对非广延QCD介质的影响，发现常数耦合下磁催化效应减弱，而高非广延参数q可消除逆磁催化现象。

Gauged Nambu-Jona-Lasinio model and axionic QCD string

We propose an axionic QCD string scenario based on the original flux-tube model by Kogut and Susskind, and then incorporate it into a gauged Nambu-Jona-Lasinio (NJL) model. Axial anomaly is studied by a new topological coupling from the string side, and by the 't Hooft vortex from the NJL side, respectively. The nontrivial phase distribution of the quark condensate plays an important role in this scenario.

Chiral phase transition in an extended NJL model with higher-order multi-quark interactions

The chiral phase transition is studied in an extended Nambu--Jona-Lasinio model with eight-quark interactions. Equations for scalar and vector quark densities, derived in the mean field approximation, are nonlinear and mutually coupled. The scalar-type nonlinear term hastens the restoration of chiral symmetry, while the scalar-vector mixing term makes the transition sharper. The scalar-type nonlinear term shifts the critical endpoint toward the values predicted by lattice QCD simulations and the QCD-like theory.

Is a generalized NJL model the effective action of massless QCD?

A local and gauge invariant alternative version of QCD for massive fermions introduced in previous works, is considered here to just propose a theory which includes Nambu-Jona-Lasinio (NJL) terms in its defining action in a renormalizable form. The Lagrangian includes a special kind of new vertices which at first sight, look as breaking power counting renormalizability. However, these terms also modify the quark propagators, to become more decreasing that the Dirac propagator at large momenta, indicating that the theory is renormalizable. Therefore, it follows the surprising conclusion that th…

A renormalizable extension of the NJL-model

The Nambu-Jona-Lasinio model is supplemented by the quark interaction generated by the one-gluon exchange. The employed gluon propagator exhibits the correct large momentum behavior of QCD, whereas the Landau-pole at low energies is screened. The emerging constituent quark model is one-loop renormalizable and interpolates between the phenomenologically successful Nambu-Jona-Lasinio model at low energies and perturbative QCD at high momenta. Consequently, the momentum dependence of the quark self-energy at high energy coincides with the prediction from perturbative QCD. The chiral phase transit…

Chiral imbalanced hot and dense quark matter: NJL analysis at the physical point and comparison with lattice QCD

Hot and dense quark matter with isospin and chiral imbalances is investigated in the framework of the (3+1)-dimensional Nambu--Jona-Lasinio model (NJL) in the large-$N_c$ limit ($N_c$ is the number of quark colors). Its phase structure is considered in terms of baryon -- $μ_B$, isospin -- $μ_I$ and chiral isospin -- $μ_{I5}$ chemical potentials. It is shown in the paper that (i) in the chiral limit there is a duality between chiral symmetry breaking (CSB) and charged pion condensation (PC) phenomena. (ii) At the physical point, i.e. at nonzero bare quark mass $m_0$, and temperature this dualit…

Critical chiral hypersurface of the magnetized NJL model

In pursuit of the sketching the effective magnetized QCD phase diagram, we found conditions on the critical coupling for chiral symmetry breaking in the Nambu-Jona-Lasinio model in a nontrivial thermo-magnetic environment. Critical values for the plasma parameters, namely, temperature and magnetic field strength for this to happen are hence found in the mean field limit. The magnetized phase diagram is drawn from the criticality condition for different models of the effective coupling describing the inverse magnetic catalysis effect.

Quarkyonic Chiral Spirals in the Nambu-Jona-Lasinio Approach

We explore the inhomogeneous QCD phases at finite density and temperature using a (3+1)-dimensional Nambu-Jona-Lasinio (NJL) model in the large Nc limit with an additional attractive tensor-tensor interaction channel. For single modulated solutions, the problem reduces to solving the gap equation of a Chiral Gross-Neveu (NJL2) theory, whose minimum solution is a periodic array of chirally twisted kinks. At zero temperature, the minimum solution reduces to the quarkyonic chiral spiral found in quarkyonic matter. The connection between the quarkyonic matter and our (3+1)-dimensional NJL model is…

Light Scalar Mesons in the Improved Ladder Approximation of QCD with Strong $U_A(1)$ Breaking

The spectrum and the mixing angle of the light scalar nonet mesons are studied using the extended Nambu-Jona-Lasinio (NJL) model as well as the improved ladder approximation (ILA) of QCD with U_A(1) symmetry breaking interaction. The U_A(1) breaking is represented by the Kobayashi-Maskawa-'t Hooft (KMT) interaction. The strength of the KMT interaction in the NJL model is determined so as to reproduce the electromagnetic decays of the ηmeson. That in the ILA approach is determined so as to reproduce the pseudoscalar meson spectrum. In the extended NJL model, we study the qualitative features of…

Kaon Condensation in a Nambu--Jona-Lasinio (NJL) Model at High Density

We demonstrate a fully self-consistent microscopic realization of a kaon-condensed colour-flavour locked state (CFLK0) within the context of a mean-field NJL model at high density. The properties of this state are shown to be consistent with the QCD low-energy effective theory once the proper gauge neutrality conditions are satisfied, and a simple matching procedure is used to compute the pion decay constant, which agrees with the perturbative QCD result. The NJL model is used to compare the energies of the CFLK0 state to the parity even CFL state, and to determine locations of the metal/insul…

Magnetic field induced corrections to the NJL model coupling constant from vacuum polarization

Magnetic field dependent corrections for the coupling constant of the Nambu-Jona-Lasinio model are calculated by considering the one-loop background field method. These coupling constants turn out to break chiral and flavor symmetries and they lead to a slight improvement of the numerical values of the up and down quark condensates when compared to results from lattice QCD. The corresponding magnetic field dependencies of the neutral pion and kaon masses are also presented and compared with available lattice QCD calculations. The resulting magnetic field correction to the $η-η'$ mixing angle i…

Phase diagram of the three-dimensional NJL model

With the exception of confinement the three-dimensional Nambu-Jona-Lasinio (NJL_3) model incorporates many of the essential properties of QCD. We discuss the critical properties of the model at nonzero temperature T and/or nonzero chemical potential $μ$. We show that the universality class of the thermal transition is that of the d=2 classical spin model with the same symmetry. We provide evidence for the existence of a tricritical point in the ($μ$,temperature) plane. We also discuss numerical results by Hands et al. which showed that the system is critical for $μ>μ_c$ and the diquark condens…

The use of the canonical approach in effective models of QCD

We clarify regions where the canonical approach works well at the finite temperature and density in the Nambu-Jona-Lasinio (NJL) and Polyakov-NJL (PNJL) models. The canonical approach is a useful method for avoiding the sign problem in lattice QCD simulations at finite density, but it involves some parameters. We find that number densities computed from the canonical approach are consistent with exact values in most of the confinement phase within the parameters, which are applicable in lattice QCD.

The QCD critical point from the Nambu-Jona-Lasino model with a scalar-vector interaction

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.

Magnetized color superconducting quark matter under compact star conditions: Phase structure within the SU(2)f NJL model

The properties of magnetized color superconducting cold dense quark matter under compact star conditions are investigated using a $SU(2)_f$ Nambu Jona-Lasinio (NJL)-type model in which the divergences are treated using a magnetic field independent regularization scheme in order to avoid unphysical oscillations. We study the phase diagram for several model parametrizations. The features of each phase are analyzed through the behavior of the chiral and superconducting condensates together with the different particle densities for increasing chemical potential or magnetic field. While confirming …

Coupling of pion condensate, chiral condensate and Polyakov loop in an extended NJL model

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 …

重子束缚态在非本地NJL模型中的研究

Baryonic Bound States in the Non-Local NJL Model

本文基于非本地NJL模型探讨重子束缚态，利用相对论Faddeev方法将三体问题简化为有效夸克-双夸克问题，并通过求解Bethe-Salpeter方程确定重子质量。

The three flavor LOFF phase of QCD

We explore the Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase of QCD with three flavors, using a Ginzburg-Landau expansion of the free energy, and a NJL point-like four-fermion interaction, with the quantum numbers of single-gluon exchange.

从分形NJL模型获得T×μ相图

$T \times μ$ phase diagram from a fractal NJL model

本文基于分形NJL模型，通过引入μ依赖耦合，构建了与实验数据和格点QCD计算一致的T×μ相图，考虑了广义统计并有效描述STAR数据。