M. Ferreira, P. Costa, C. Providência, O. Lourenço, T. Frederico
Apart from Magnetic Catalysis at low temperatures, recent LQCD studies have shown the opposite effect at temperatures near the transition region: instead of enhancing, the magnetic field suppresses the quark condensates (Inverse Magnetic Catalysis). In this paper, two approaches are discussed within NJL-type models with Polyakov Loop that reproduce both effects.
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Chromomagnetic Catalysis of Color Superconductivity in a (2+1)-dimensional NJL Model
本文研究了恒定均匀色磁场$H$对色超导形成的影响。在（2+1）维Nambu-Jona-Lasinio模型的框架下，考虑了两种不同的四费米子结构的$<\bar qq>$和双夸克$<qq>$凝聚.特别是，它表明，存在一个临界值$H_c$的外部色磁场，使在$H>H_c$的非零双夸克凝聚动态创建（所谓的色磁催化效应的颜色超导性）。此外，在某些情况下，外部色磁场可能会增强色超导的双夸克凝聚。
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…
Inverse magnetic catalysis in field theory and gauge-gravity duality
本文采用场论Nambu-Jona-Lasinio（NJL）模型和全息Sakai-Sugimoto模型，在温度、重子化学势和磁场的三维参数空间中研究了手征相变的表面.后者是一个自上而下的方法，以重力对偶的QCD与渐近大量的颜色，并成为，在一定的限制，对偶的NJL类模型。我们的主要观察结果是，在非零化学势下，磁场可以恢复手征对称性，这与磁催化现象形成明显的对比。这种“逆磁催化”发生在Sakai-Sugimoto模型中，对于足够大的耦合，发生在NJL模型中，并且与最低朗道能级的物理学有关。虽然在大多数情况下，我们的讨论是以前发表的结果的教学审查，我们包括新的分析结果的NJL的方法和彻底的比较，在这两种方法中的逆磁催化。
Inverse magnetic catalysis in the (2+1)-flavor Nambu--Jona-Lasinio and Polyakov--Nambu--Jona-Lasinio models
在三味Nambu-Jona-Lasinio（NJL）模型和带Polyakov环的NJL模型（PNJL）中研究了外加磁场作用下零化学势、有限温度下的QCD相图.考虑了一个依赖于磁场强度的标量耦合参数。通过对标量耦合的拟合，再现了格点量子色动力学赝临界手征转变温度，并且在大磁场的极限下，手征转变温度随磁场强度的倒数而减小。耦合的这种依赖性允许再现关于夸克凝聚和波利亚科夫环的格点量子色动力学结果：由于磁场，夸克凝聚在低温和高温下被增强，而在接近转变温度的温度下被抑制，并且波利亚科夫环随着磁场的增加而增加。
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。
Chromomagnetic Catalysis of Chiral Symmetry Breaking and Color Superconductivity
在扩展的NJL模型的框架下，证明了即使在夸克间引力最弱的情况下，某些类型的外色磁场也会引起动力学手征对称性破缺或色对称性破缺.我们还认为，外部色磁场，模拟真正的QCD真空色磁胶子凝聚，可能会显着影响色超导形成。
BEC-BCS crossover in a cold and magnetized two color NJL model
本文研究外磁场下带双夸克相互作用的NJL模型的BEC-BCS渡越，对比不同正则化方案，发现BEC相变有明显反磁催化，BEC-BCS渡越在低场下反磁催化弱、高场下呈强磁催化。
We investigate the screening masses of neutral pions and sigma mesons in hot and magnetized quark matter in the framework of a two-flavor lattice-improved Nambu-Jona-Lasinio (NJL) model with a magnetic field dependent coupling constant, which is determined by utilizing the results from lattice QCD simulations. Since such model can well reproduce inverse magnetic catalysis (IMC), by comparing with the standard NJL model, we systemically analyze the impacts of IMC on the temperature and magnetic field dependences of the longitudinal and transverse screening masses of the chiral partners, i.e. π^…
Some of the advances made in the literature to understand the phase transitions of quark matter in the presence of strong magnetic field and finite temperature (zero quark chemical potential) are reviewed. We start by discussing the physics behind the Magnetic catalysis (MC) at zero/finite temperature and then focus on the lattice predictions for inverse magnetic catalysis (IMC) at high temperature and strong magnetic fields. Possible explanations for the IMC are covered as well. Finally, we discuss recent efforts to modify QCD (quantum chromodynamics) effective models in order to reproduce th…
Exploring $U_A(1)$ symmetry restoration in a magnetic field by meson screening masses in the NJL model
该研究在NJL模型中通过介子屏蔽质量探讨磁场下$U_A(1)$对称性恢复，发现纵向与横向质量差对磁场的响应不同，但赝临界温度均随磁场降低。
Topological susceptibility and axion properties in the presence of a strong magnetic field within the three-flavor NJL model
该研究在含类 't Hooft 味混合项的三味 NJL 模型中，引入磁场相关耦合以描述逆磁催化，系统考察强磁场、温度和密度对拓扑极化率、轴子性质及相变的影响，并与格点 QCD 等结果对比。
By comparing the two- and three-flavor Nambu--Jona-Lasinio (NJL) models, we demonstrate that the naively expected vacuum superconductivity (VSC) in constant magnetic field ${\bf B}=B\hat z$ is disfavored due to the splitting magnetic catalysis effect (MCE) to chiral condensates with different quark flavors. Based on the simple two-flavor NJL model, we illuminate, in the lowest Landau level approximation, the similar origins of $π^0$ and $\barρ^+_1$ ($ρ^+$ meson with spin $S_z=1$) mass reductions with smaller $B$ and their different features at larger $B$. With the full Landau levels, the two-f…
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.
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。
Dimensional Reduction and Catalysis of Dynamical Symmetry Breaking by a Magnetic Field
结果表明，在3+1和2+1维中，恒定的磁场是动力学手征对称性破缺的强催化剂，即使在费米子之间的吸引相互作用最弱的情况下，也会导致费米子动力学质量的产生.这种效应的实质是磁场中费米子配对动力学中的降维$D\to D-2$。Nambu-Jona-Lasinio（NJL）模型和量子电动力学（QED）说明了这种效应。在磁场中的NJL模型中，导出了低能有效作用量和长波集体激发谱。在QED中（在阶梯和改进的阶梯近似中），费米子的动力学质量（费米子谱中的能隙）被确定。这种效果及其扩展到非均匀场配置的可能应用进行了讨论。
Thermal Conductivity in 3D NJL Model Under External Magnetic Field
在平均场近似下，计算了（2+1）维NJL模型在恒定磁场作用下的热导率，并分析了其不同的渐近区域。考虑到由于磁催化现象的费米子质量的动态生成，它表明，对于理论的参数（粒子宽度，温度和磁场）之间的某些关系，与所施加的场的热导率的轮廓表现出扭结和平台状的行为。我们指出可能的应用平面凝聚态物质。
Magnetic catalysis is the enhancement of a condensate due to the presence of an external magnetic field. Magnetic catalysis at $T=0$ is a robust phenomenon in low-energy theories and models of QCD as well as in lattice simulations. We review the underlying physics of magnetic catalysis from both perspectives. The quark-meson model is used as a specific example of a model that exhibits magnetic catalysis. Regularization and renormalization are discussed and we pay particular attention to a consistent and correct determination of the parameters of the Lagrangian using the on-shell renormalizatio…
Quark matter under strong magnetic fields in SU(2) NJL-type models: parameter dependence of the cold dense matter phase diagram
在双味Nambu-Jona-Lasinio模型的框架下分析了磁化冷夸克物质的相结构，特别注意了在唯象允许的范围内，不同参数对磁化冷夸克物质相结构的影响。我们首先讨论较简单的手征极限情况，然后讨论更现实的有限电流质量的情况。我们表明，尽管在一些过渡的性质的差异，这两种情况下是相似的，并表现出相当丰富的相结构的一个显着的范围内的可接受的参数。一个简化的相结构的参数，导致更大的值在真空中的缀饰夸克质量被认为是获得。最后，我们考虑了所谓的“逆催化效应”，这表明在某些阶段，它意味着一个实际的序参量的磁场增加减少。
Magnetic field driven instability in planar NJL model in real-time formalism
已知在磁场B中的2+1维Nambu-Jona-Lasinio模型的对称（无质量）态不是零温时系统的基态，这是由于存在负的、线性的In &| σ+iπ| $, term in the effective potential for the composite fields $ σ \sim \bar ψψ $ and $ π \sim \bar ψiγ^5ψ $, while the quadratic term is always positive (a tachyon is absent). We find that finite temperature is a necessary ingredient for the tachyonic instability of the symmetric state to occur. Utilizing the Schwinger--Keldysh real-time formalism we calculate the dispersion relations for the fluctuation modes of the composite fields $ σ $ and $ π$。我们证明了存在的快速子不稳定性的对称态的耦合常数，超过一定的临界值，消失的温度趋于零，根据磁催化现象。
Vacuum to nuclear matter phase transition has been studied in presence of constant external background magnetic field with the mean field approximation in Walecka model. The anomalous nucleon magnetic moment has been taken into account using the modified "weak" field expansion of the fermion propagator having non-trivial correction terms for charged as well as for neutral particles. The effect of nucleon magnetic moment is found to favour the magnetic catalysis effect at zero temperature and zero baryon density. However, extending the study to finite temperatures, it is observed that the anoma…
Magnetic catalysis in hot and dense quark matter and quantum fluctuations
我们分析了在零温度和有限温度以及夸克化学势下，外磁场中夸克物质的手征对称性破缺。我们首先给出一个简要的概述内的平均场近似的分析结果。在那里，手性恢复的临界温度由于磁场效应而增加。然后我们研究了物质和量子涨落对磁催化的影响。更具体地说，我们计算的临界耦合的磁场和温度的函数为零和有限夸克化学势的量子涨落的存在下。一旦打开非零温度和/或密度，长程相关性就会被屏蔽，临界耦合不再消失。我们将我们的动力学结果扩展到导致非局域四费米耦合的领先阶气泡再确认之外。这包括在更定量的水平上的介质介子效应。
Gluon interaction introduces remarkable corrections to the magnetic polarization effects on the chiral fermions, which is known as the inverse magnetic catalysis. It is a natural speculation that the vorticity, which has many similar properties as magnetic field, would bring non-negligible contribution to the chiral rotational suppression. Using the intuitive semi-classical background field method we studied the rotation dependence of the effective strong interaction coupling. Contrary to the magnetic field case the rotation increases the effective coupling which leads to slowing down the cond…
Phase transition and thermodynamics of a hot and dense system in a scaled NJL model
在修正的SU（3）NJL拉格朗日量中研究了热稠密夸克系统的手征相变，该拉格朗日量实现了QCD标度反常。在三维空间T_c（μ_uc，μ_sc）中，u夸克凝聚和s夸克凝聚的手征恢复是否相同取决于所考虑的区域。本文研究了u-和s-夸克系统的压力、能量密度和熵密度的温度行为。在高温下，不为零的裸s夸克质量只会稍微改变与理想夸克气体相关的通常行为。
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-…
Employing a field dependent three-momentum cut-off regularization technique, we study the phase structure and mesonic masses using the $2$-flavour Nambu-Jona Lasinio model at finite temperature and density in presence of arbitrary external magnetic field. This approach is then applied to incorporate the effects of the anomalous magnetic moment(AMM) of quarks on constituent quark mass and thermodynamic observables as a function of temperature/baryonic density. The critical temperature for transition from chiral symmetry broken to the restored phase is observed to decrease with the external magn…
Extended Nambu--Jona-Lasinio model with eight quark interactions
本文综述了在SU（3）味Nambu-Jona-Lasinio（NJL）和6-夸克（6 q）t Hooft相互作用的组合拉格朗日量中加入最普遍的0-自旋8-夸克（8 q）相互作用对真空性质和磁催化的影响。
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。
Pion superfluid phase transition under external magnetic field including the inverse magnetic catalysis (IMC) effect is investigated by the Pauli-Villars regularized NJL model. Based on the Goldstone's theorem, we apply the massless Goldstone boson ($π^+$ meson) to determine the onset of pion superfluid phase. The inverse magnetic catalysis effect is introduced by the magnetic field dependent coupling $G(eB)$, which is a decreasing function of magnetic field. At fixed temperature and baryon chemical potential, the critical isospin chemical potential for pion superfluid phase transition includi…
Model analysis on thermal UV-cutoff effects on the critical boundary in hot QCD
本文研究了有限温度下QCD中手征相变在夸克质量平面上的临界边界。我们指出，从格点量子色动力学模拟和手征有效模型得到的临界边界是显着不同的，在（Polyakov环耦合）Nambu-Jona-Lasinio（NJL）模型中，我们发现，临界质量是约一个数量级的值小于在格点量子色动力学的情况下报告。在格点量子色动力学研究中，我们知道临界质量在连续极限中沿时间方向变小。为了定量地研究时间UV截止效应，我们考虑了（P）NJL模型，求和时只取有限个$N_τ$松原频率.我们证实，在这样一个UV驯服的NJL模型的临界质量变得更大的减少$N_τ$，这表明了一个正确的趋势，以解释之间的差异格点量子色动力学和手征模型的结果。
A magnetic field independent regularization scheme (zMFIR) based on the Hurwitz-Riemann zeta function is introduced. The new technique is applied to the regularization of the mean-field thermodynamic potential and mass gap equation within the SU(2) Nambu-Jona-Lasinio model in a hot and magnetized medium. The equivalence of the new and the standard MFIR scheme is demonstrated. The neutral meson pole mass is calculated in a hot and magnetized medium and the advantages of using the new regularization scheme are shown.
Chiral MHD description of a perfect magnetized QGP using the effective NJL model in a strong magnetic field
为了研究强磁场对强磁化夸克胶子等离子体（QGP）中平面波声速的影响，采用手征磁流体动力学（MHD）方法描述了一个理想的（非耗散）QGP表现出动力学手征对称性破缺（D $χ$ SB）是利用有限温度下QCD的Nambu-Jona-Lasinio（NJL）模型的有效作用量发展起来的，有限重子化学势和强磁场的存在下。在这里，D $χ$ SB由于磁催化现象而产生。除了一个有趣的频率依赖性，对于平面波在横向或纵向传播的$B$场，声速是各向异性的，并取决于相应的波矢量和$B$场的方向之间的角度。此外，对于在横向（纵向）方向上传播到外部$B$场的平面波，声速在$T<T_{c}$处具有最大值（最小值），在$T\sim T_{c}$处达到局部最小值（最大值），并且在$T\gtrsim T_{c}$处保持恒定。这里，$T_{c}$是手性相变的临界温度。因此，在$T \gtrsim T_{c}$处的常数值$v_{s}\sim 1.5 c_{s}$被证明是相对于外部$B$场在横向（纵向）方向上传播的波的下（上）界。这里，$c_{s}=1/\sqrt{3}$是理想气体中的声速。
Effect of chiral imbalance on the electrical conductivity of hot and dense quark matter using Green-Kubo Method within the 2-flavour gauged NJL model
本文在2味规范NJL模型中引入手征化学势，利用Green-Kubo方法和有限温度场论计算了热且密集夸克物质的电导率，发现电导率与温度的比值在低温区显著依赖于手征化学势。
The mass and spectral function of scalar and pseudoscalar mesons in a hot and chirally imbalanced medium using the two-flavor NJL model
该研究采用两味NJL模型和实时热场论，分析有限手征化学势下σ与π⁰介子的质量、谱函数及Landau割，揭示多重极点解和Mott温度降低等效应。
Spectral properties of $ω$, $ρ$ and $A_1$ mesons in hot magnetized matter: effects of (inverse) magnetic catalysis
本文在QCD求和规则与手征SU(3)模型框架下，研究热磁化核物质中(逆)磁催化对ω、ρ和A1介子质量、谱函数及产生截面的影响，并计算A1→ρπ介质内衰变宽度。
In this article we study a nonlocal Nambu--Jona-Lasinio (nNJL) model with a Gaussian regulator in presence of a uniform magnetic field. We take a mixed approach to the incorporation of temperature in the model, and consider aspects of both real and imaginary time formalisms. We include confinement in the model through the quasiparticle interpretation of the poles of the propagator. The effect of the magnetic field in the deconfinement phase transition is then studied. It is found that, like with chiral symmetry restoration, magnetic catalysis occurs for the deconfinement phase transition. It i…
In this work, we consider the effect of a constant anomalous magnetic moment (AMM) of quarks in the SU(2) Nambu--Jona-Lasinio model in the mean field approximation. To this end, we use the Schwinger {\it ansatz}, which represents a linear magnetic field term in the Lagrangian. A regularization method inspired in the vacuum magnetic regularization (VMR) is adopted to avoid ultraviolet divergences. Our results indicate a smooth decrease of the pseudocritical temperature and quark condensates for magnetic fields $B \leq 0.1$ GeV$^2$ when a sizable AMM is considered. We found only a small window f…
Dilepton production rate (DPR) from hot and dense quark matter is studied in the presence of an arbitrary external magnetic field using the 2-flavour Nambu--Jona-Lasinio (NJL) model. The anomalous magnetic moment (AMM) of the quarks is taken into consideration while calculating the constituent quark mass as well as the DPR from the thermo-magnetic medium. An infinite number of quark Landau levels is incorporated so that no approximations are made on the strength of the background magnetic field. The analytic structure of the two point vector current correlation function in the complex energy p…
We review in detail recent advances in our understanding of the phase structure and the phase transitions of hadronic matter in strong magnetic fields $B$ and zero quark chemical potentials $μ_f$. Many aspects of QCD are described using low-energy effective theories and models such as the MIT bag model, the hadron resonance gas model, chiral perturbation theory, the Nambu-Jona-Lasinio (NJL) model, the quark-meson (QM) model and Polyakov-loop extended versions of the NJL and QM models. We critically examine their properties and applications. This includes mean-field calculations as well as appr…
Shear and bulk viscous coefficients of a hot and chirally imbalanced quark matter using NJL model
本研究基于两味NJL模型，通过单圈Green-Kubo形式主义和实时有限温度场论，计算了含手征化学势的热手征不平衡夸克物质的剪切与体黏滞系数，分析了其温度和手征化学势依赖特性。
Forty-fifth anniversary of the Nambu-Jona-Lasinio model
对Nambu-Jona-Lasinio（NJL）模型的发展作了简要的回顾。本文考虑SU（2）× SU（2）和U（3）× U（3）定域夸克NJL模型。给出了手征对称性自发破缺和矢量占优的机制。局域NJL模型使我们能够描述赝标、标量、矢量和轴矢量介子四种基态九重态的质量谱和主要的强衰变和电弱衰变。讨论了该模型在热重介质中介子描述中的应用。结果表明，为了解决与介子径向激发和夸克禁闭的描述连接的问题，有必要考虑NJL模型的非局部扩展。主要注意力被吸引到NJL模型的不同版本中使用的方法的描述。在这些模型中得到的低能强子物理结果可以在所引用的文献中找到。
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…
Inverse magnetic catalysis in dense holographic matter
在Sakai-Sugimoto模型下研究了有限温度和化学势的磁场中的手征相变。我们考虑的味道D8-膜，这对应于一个对偶场论的Nambu-JonaLasinio（NJL）模型的一个小的分离的限制。在磁场强度、夸克化学势和温度的参数空间中绘制手征相变的表面，我们发现，对于小的温度，磁场的加入降低了手征对称性恢复的临界化学势--与化学势消失的情况相反，在这种情况下，根据熟悉的磁催化现象，磁场有利于手性断裂相位。这种“逆磁催化”（IMC）似乎与先前发现的手性对称相内的磁相变有关，该相变与最低朗道能级的过渡具有有趣的相似性。我们估计IMC在低温下持续高达10^{19} G。
Magnetic Catalysis and Fermion Mass Generation in de Sitter Spacetime
该研究利用NJL模型，结合Bunch–Davies真空条件，分析de Sitter时空中带电费米子的动力学，发现曲率恢复手征对称性、磁场增强手征对称性破缺，还揭示了相关相结构。
We have calculated the electromagnetic spectral function (SF) vis-à-vis the dilepton rate (DR) by evaluating the one-loop photon polarisation tensor for a strongly magnetised hot and dense medium. The calculation is performed in the ambit of mean field models namely Nambu\textendash Jona-Lasinio (NJL) and its Polyakov loop extended version (PNJL) in the lowest Landau level approximation. These models allow for a dynamical generation of quark mass which, evidently, gets affected in the presence of a magnetised medium. We have shown that the strength of the SF gets boosted because of the presenc…
Pseudoscalar Mesons in Asymmetric Matter
在SU（3）Nambu-Jona-Lasinio [NJL]和扩大的Nambu-Jona-Lasinio [ENJL]（包括矢量伪矢量相互作用）模型中研究了模拟中子物质的热非奇异夸克物质中的K ~+和π ~+的行为。在零温时，发现在相变为一级的NJL模型中，出现了K-，Pi+量子数的低能模，它们是费米海的粒子-空穴激发。在ENJL模型和有限温度下的NJL中没有发现这样的模式。升高的温度也具有减少电荷多重态之间的分裂的效果。
Quark anomalous magnetic moments and neutral pseudoscalar meson dynamics with three-flavor NJL model in magnetized quark matter
本研究基于三味NJL模型，探讨了夸克反常磁矩对中性赝标介子质量谱及QCD相图的影响，发现其能引发轻夸克一阶相变、重塑相变特性并诱导与格点QCD一致的逆磁催化效应。
Two-flavor color superconductivity at finite temperature, chemical potential and in the presence of strong magnetic fields
利用扩展的双味Nambu-JonaLasinio（NJL）模型，研究了QCD相图中中等重子密度下外加磁场对双味色超导相（2SC）的影响.扩展的NJL模型的有效作用量由两个质量隙组成，这两个质量隙是温度、夸克化学势和外部磁场三个强度量的函数。质量间隙的非零值，手征和双夸克凝聚，诱导自发的手征和色对称性破缺，分别，并作为一个结果，两个不同阶段的夸克物质出现。我们找到了这些相位之间的过渡曲线以及QCD相图中的临界点。在这两个相上施加一个恒定的强磁场，我们发现质量隙随着磁场的增加而增加，QCD相图中的对称性破缺区域甚至扩大到更大的温度和夸克化学势值。这种现象是磁催化动力学对称性破缺的结果，这在以前已经被证明。
We study the two flavour non-local Nambu\textemdash Jona-Lasinio (NJL) model in the presence of a magnetic field and explore the chiral crossover in presence of a non-local form of the 't Hooft determinant term. Its coupling is governed by a dimensionless parameter $c$. This term is responsible for the explicit breaking of $U(1)_A$ symmetry. We have attempted a systematic analysis of the model parameters by fitting to self-consistent lattice QCD calculations. Three parameters of the model are fixed by $eB=0$ results from published lattice QCD on the chiral condensate, the pion decay constant (…
The deconfinement phase transition, hadronization and the NJL model
量子色动力学的一个可靠预言是，在足够高的温度和/或密度下，强子物质应该经历热力学相变，变成物质的色消限态--通常称为夸克-胶子等离子体（QGP）。在低能有效量子色动力学（QCD）理论中，人们通常讨论手征跃迁，手征跃迁存在一个明确的序参量。用Nambu-JonaLasinio（NJL）模型研究了热夸克物质介质中π介子和K介子的离解。π介子和K介子的衰变宽度很大，但在远高于手征（或解除禁闭）跃迁的临界温度的温度下是有限的，K介子的衰变宽度要大得多。因此，在如此高温下，π介子甚至K介子（密度比π介子低）都可以与夸克和胶子共存。在此前提下，我们研究了夸克-胶子等离子体中的强子化过程，并着重讨论了这一过程是否对可接受的低能有效QCD理论有所启示。
Phase transition and nucleon as soliton in the Nambu-Jona-Lasinio model at finite temperature and density
本文研究了NJL模型中热夸克物质和混合NJL模型中热核物质中的体材料性质、介子性质和核子作为重子一号孤子的性质。在这两种情况下，在平均场近似下，我们发现一个手征相变从Goldstone维格纳相。在有限密度的手征序参量和组分夸克质量有一个非单调的温度依赖性-在有限的温度不接近临界一个，他们比在冷物质的影响较小。夸克物质相对于热涨落是相当软的，相应的手征相变是平滑的，而核子物质则硬得多，手征相变非常尖锐。化学变量显示出大的不连续性，这是一阶相变的指示。我们解决了B=1孤子扇区的NJL模型中存在的外部热夸克和核子介质。在中温热介质中，孤立子比冷物质中的孤立子束缚得更多，膨胀得更少。在某个临界温度，即核子物质的临界温度与手征相变的临界温度相一致时，我们不再发现定域解。根据这个模型，我们可以预期从核子到夸克物质会有一个急剧的相变。
In this paper we investigate in the large-$N_c$ limit ($N_c$ is the number of colored quarks) the phase structure of a massless (1+1)-dimensional quark model with four-quark interaction and in the presence of baryon ($μ_B$), isospin ($μ_I$) and chiral isospin ($μ_{I5}$) chemical potentials as well as at nonzero temperature. It is established that chiral isospin chemical potential leads to the generation of charged pion condensation (PC) in dense (nonzero baryon density) and chiral asymmetric quark matter for a wide range of isospin densities. It is shown that there exists a duality corresponde…
We determine the baryon spectrum of 1 + 1 + 1-flavor QCD in the presence of strong background magnetic fields using lattice simulations at physical quark masses for the first time. Our results show a splitting within multiplets according to the electric charge of the baryons and reveal, in particular, a reduction of the nucleon masses for strong magnetic fields. This first-principles input is used to define constituent quark masses and is employed to set the free parameters of the Polyakov loop-extended Nambu-Jona-Lasinio (PNJL) model in a magnetic field-dependent manner. The so constructed mo…
$η- η'$ in a hot and dense medium
在SU（3）Nambu-Jona-Lasinio [NJL]模型下，研究了热奇异夸克物质中$η$和$η'$的行为.恢复对称性的可能表现形式，由温度或密度，在$η$和$η'$的行为进行了讨论。分析了温度和密度的综合作用对相变和介子行为的影响。
The effect of anomalous magnetic moment of quarks on thermodynamic properties of the chiral condensate is studied, using of a two-flavor Nambu--Jona-Lasinio model at finite temperature $T$, chemical potential $μ$, and in the presence of a uniform magnetic field $eB$. To this purpose, the Schwinger linear-in-$B$ ansatz for the quark anomalous magnetic moment in term of the nonperturbative Bohr magneton is considered. In a two-dimensional flavor space, it leads to the correction $\hat{T}_{Sch}=\hatκ\hat{Q} eB$ in the energy dispersion relation of quarks. Here, $\hat{Q}$ is the quark charge matri…
Chiral quark model with infrared cut-off for the description of meson properties in hot matter
构造了一个具有夸克禁闭机制的Nambu-Jona-Lasinio（NJL）型简单手征夸克模型，用于描述有限温度下QCD的轻介子部分。NJL模型中的非物理夸克产生阈值被夸克环图中动量积分的红外截止所排除。这种手征夸克模型满足低能定理。用π介子和ρ介子的真空质量和衰变宽度固定模型参数，导出了σ介子的性质。在Matsubara形式主义中，该模型被系统地推广到有限温度下，当π介子Mott温度T_c=186 MeV时，由于组分夸克质量下降而导致的手征对称性恢复导致红外截止消失（解除禁闭）。除了π介子质量和弱衰变常数外，还研究了热物质中σ介子和ρ介子的质量、耦合常数和衰变宽度。轻介子的夸克-反夸克衰变通道只在T>T_c时才打开，而在ρ介子时变得特别强。在T_c以下，ρ介子的2 π介子衰变通道的宽度在T_c之前几乎不变，而σ介子的2 π介子衰变通道在T_c以下关闭，从而得到宽度为零的标量介子态，作为手征/解除束缚跃迁的前兆。
Minimal-Length Deformations of Chiral Quark Matter in a 2+1-Flavor NJL Model
在2+1味NJL模型中，构建受最小长度启发的热密手征夸克物质变形模型，揭示紫外相空间抑制对动力学手征对称性破缺及相变边界的影响，完成耦合能隙方程的自洽求解。
Vacuum structure and chiral symmetry breaking in strong magnetic fields for hot and dense quark matter
在包含Kobayashi Maskawa t-Hooft（KMT）行列式项的3味Nambu Jona Lasinio（NJL）模型中，利用夸克反夸克凝聚的基态的显式结构，研究了有限温度和密度下强磁场中的手征对称性破缺.自洽求解质量间隙方程，并用于计算热力学势。我们还导出了奇异夸克物质在强磁场存在下的状态方程，这可能与原中子星有关。~
Nambu-Jona-Lasinio-type models are often employed as low-energy models for the theory of the strong interaction to analyze its phase structure at finite temperature and quark chemical potential. In particular at low temperature and large chemical potential, where the application of fully first-principles approaches is currently difficult at best, this class of models still plays a prominent role to guide our understanding of the dynamics of dense strong-interaction matter. In this work, we consider a Fierz-complete version of the Nambu-Jona-Lasinio model with two massless quark flavors and stu…
We study the behavior of two-flavor dense quark matter under the influence of an external magnetic field in the framework of a nonlocal chiral quark model with separable interactions. The nonlocality is incorporated in the model by using a Gaussian form factor. It is found that for low and moderate values of magnetic field there is a decrease of the critical chiral restoration chemical potential $μ_c$, i.e. an inverse magnetic catalysis effect is observed. For larger values of $eB$ the behavior of $μ_c$ becomes more or less flat, depending on the parametrization. Within the considered parametr…
It is analyzed the effects of a hot and magnetized medium on the axion mass, self-coupling and topological susceptibility when in presence of an anisotropic external magnetic field along the $z$-direction, within the Nambu--Jona-Lasinio effective model for quantum chromodynamics. The effects of both Magnetic Catalysis and Inverse Magnetic Catalysis are explicitly taken into account through appropriate matching of parameters with those from lattice Monte-Carlo numerical simulations. It is also analyzed the dependence of the results with respect to different model parametrizations in the context…
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