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.
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.
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.
In this talk I compare the knowledge on the critical end point of the QCD phase diagram grasped from lattice calculations, with that obtained from Nambu--Jona-Lasinio (NJL) model computations. The original publication is available at http://www.sif.it/SIF/en/portal/journals
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.
The Global Colour Model (GCM) of QCD is a very successful model. Not only is it formally derivable from QCD but under various conditions it reduces to the NJL model and also to Chiral Perturbation Theory, and to other models. Results presented include the effective gluon propagator, the difference between constituent and exact quark propagators, various meson and nucleon observables, a new mass formula for the Nambu-Goldstone mesons of QCD, and the change in the MIT bag constant in nuclei.
Starting from a QCD inspired bilocal quark interaction we obtain a local effective meson lagrangian. In contrast to previous local (NJL-like) approaches, we include nonlocal corrections related to the finite meson size which we characterize by a small parameter. After bosonization using the heat-kernel method we predict the structure coefficients of the Gasser-Leutwyler $p^4$-lagrangian up to first order in this parameter. The modifications for the $L_i$ coefficients are typically of the order 10-20\%, except for $L_5$, where we find a stronger nonlocal influence.
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…
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…
We present results for dihadron fragmentation functions from the NJL-jet model evolved from the model scale to a typical experimental scale of $4 \mathrm{GeV}^2$. The numerical method used in this evolution is discussed in detail. The effect of evolution on the shapes of the dihadron fragmentation functions is discussed for a doubly favored process ($u \to π^+π^-$), as well as a singly favored ($u \to π^+K^-$) process involving light quarks. Finally, we explore the production of $K^+ K^-$ pairs from an initial $u$, $d$ or $s$ quark.
We generalize a non-local Nambu-Jona-Lasinio model to a generic representation of the gauge group. The critical temperature is given in a closed form as a function of the parameters of the theory and the cut-off. This result is generally useful in the understanding of QCD-like theories and their thermodynamical behavior.
In previous works effective non-local $SU(2)\times SU(2)$ NJL model was derived in the framework of the fundamental QCD. All the parameters of the model are expressed through QCD parameters: current light quark mass $m_0$ and average non-perturbative $α_s$. The results for scalar and pseudo-scalar mesons are in satisfactory agreement to existing data. In the present work the same model without introduction of any additional parameters is applied for a description of masses and strong decay widths of $ρ$- and $a_1$-mesons. The results for both scalar and vector sectors agree with data with only…
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…
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…
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 Euclidean-time hadronic current correlation functions, $G_P(τ, T)$ and $G_V(τ, T)$, of pseudoscalar and vector currents have recently been calculated in lattice simulations of QCD and have been used to obtain the corresponding spectral functions. We have used the Nambu-Jona-Lasinio (NJL) model to calculate such spectral functions, as well as the Euclidean-time correlators, and have made a comparison to the lattice results for the correlators. We find evidence for the type of temperature dependence of the NJL coupling parameters that we have used in previous studies of the mesonic confineme…
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…
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 …
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…
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…
Non-extensive NJL model study of QCD phase structure with chiral imbalance and strong magnetic fields
College of Mathematics and Physics, China Three Gorges University（三峡大学数学与物理学院）；Center for Astronomy and Space Sciences and Institute of Modern Physics, China Three Gorges University（三峡大学天文与空间科学中心及现代物理研究所）；Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University（华中师范大学夸克与轻子物理教育部重点实验室及粒子物理研究所）
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.
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…
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.
The Polyakov loop extended Nambu--Jona-Lasinio (PNJL) model with imaginary chemical potential is studied. The model possesses the extended ${\mathbb Z}_{3}$ symmetry that QCD does. Quantities invariant under the extended ${\mathbb Z}_{3}$ symmetry, such as the partition function, the chiral condensate and the modified Polyakov loop, have the Roberge-Weiss (RW) periodicity. The phase diagram of confinement/deconfinement transition derived with the PNJL model is consistent with the RW prediction on it and the results of lattice QCD. The phase diagram of chiral transition is also presented by the…
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 …
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.
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…
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…
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…
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…
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…
The responses of quark condensates to the chemical potential, as a function of temperature T and chemical potential μ, are calculated within the Nambu--Jona-Lasinio (NJL) model. We compare our results with those from the recent lattice QCD simulations [QCD-TARO Collaboration, Nucl. Phys. B (Proc. Suppl.) 106, 462 (2002)]. The NJL model and lattice calculations show qualitatively similar behavior, and they will be complimentary ways to study hadrons at finite density. The behavior above T_c requires more elaborated analyses.
The description of baryons as chiral solitons of the Nambu--Jona--Lasinio (NJL) model is reviewed. A motivation for the soliton description of baryons is provided from large $N_C$ QCD. Rigorous results on the spontaneous breaking of chiral symmetry in QCD are discussed. It is then argued that the NJL model provides a fair description of low--energy hadron physics. The NJL model is therefore employed to mimic the low--energy chiral flavor dynamics of QCD. The model is bosonized by functional integral techniques and the physical content of the emerging effective meson theory is discussed. In par…
Temperature dependence of pion and sigma-meson screening masses is evaluated by the Polyakov-loop extended Nambu--Jona-Lasinio model with the entanglement vertex (EPNJL model). We propose a practical way of calculating meson screening masses in the NJL-type effective models. The method based on the Pauli-Villars regularization solves the well-known difficulty that the evaluation of screening masses is not easy in the NJL-type effective models. The method is applied to analyze temperature dependence of pion screening masses calculated with state-of-the-art lattice simulations with success in re…
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.
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-…
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…
A generalization to any dimension of the fermion field transformation which allows to derive the solution of the massless Schwinger model in the path integral framework is identified. New arguments based on this transformation for a Nambu-Jona-Lasinio (NJL) like model as the low energy limit of a gauge theory in dimension greater than two are presented. Our result supports the spontaneous chiral symmetry breaking picture conjectured by Nambu many years ago and the link between QCD, NJL and chiral models.
We study a bottom-up holographic description of the QCD colour superconducting phase in the presence of higher derivative corrections. We expand this holographic model in the context of Gauss-Bonnet (GB) gravity. The Cooper pair condensate has been investigated in the deconfinement phase for different values of the GB coupling parameter $λ_{G B}$, we observe a change in the value of the critical chemical potential $μ_c$ in comparison to Einstein gravity. We find that $μ_c$ grows as $λ_{G B}$ increases. We add four fermion interactions and show that in the presence of these corrections the main…
In an effort to investigate some of the low energy properties of QCD, in particular those related to chiral symmetry breaking, as well as to obtain insights on the behavior of an interacting theory of fermions on the lattice, the two flavor Nambu--Jona-Lasinio model with $SU(2) \times SU(2)$ chiral symmetry is studied on the four--dimensional hypercubic lattice using large $N$ techniques and numerical simulations. Naive and Wilson fermions are considered and transparent results are obtained regarding the following: the scalar and pseudoscalar spectrum, the approach to the continuum and chiral …
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…
We present the bulk thermodynamic properties and phase diagram of strongly interacting matter in an extension of the 3-flavor NJL and PNJL models of QCD. Using a three momentum cut-off scheme, we have extended the multiquark interaction terms up to eight order so that the stability of the vacuum is ensured in these models. We explore the effects of various combinations of the two eight-quark couplings $g_1$ and $g_2$ and present a comparative study between the NJL and PNJL models as well as Lattice QCD data. The main effect of the eight-quark interaction term is to shift the critical end point…
Extending our recently published $SU(2)$ results for zero temperature we now compute the QCD equation of state for finite isospin density within the three flavor Nambu-Jona-Lasinio model in the mean field approximation, motivated by the recently obtained Lattice QCD results for both zero and finite temperatures. Like our previous study, here also we have considered both the commonly used Traditional cutoff Regularization Scheme and the Medium Separation Scheme. Our results are compared with recent high-precision lattice simulations as well as previously obtained results in two-flavor Nambu-Jon…
I review recent developments in the study of strongly interacting field theories with non-zero chemical potential mu. In particular I focus on (a) the determination of the QCD critical endpoint in the (mu,T) plane; (b) superfluid condensates in Two Color QCD; and (c) Fermi surface effects in the NJL model. Some remarks are made concerning the relation of superconductivity with the sign problem.
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 (…
We present a nonextensive version of the recently discussed QCD-based Nambu - Jona-Lasinio (NJL) model of many-body field theory describing behavior of strongly interacting matter. It is based on the nonextensive generalization of the Boltzmann-Gibbs (BG) statistical mechanics used in NJL model, which was taken in the form proposed by Tsallis and characterized by a dimensionless nonextensivity parameter q (for q -> 1 one recovers the usual BG case). This is a new phenomenological parameter of the model which accounts summarily for all possible (so far unspecified) effects leading to departure …
We study the QCD phase structure in the three-flavor Nambu-Jona-Lasinio model, incorporating the interplay between the chiral and diquark condensates induced by the axial anomaly. We demonstrate that for an appropriate range of parameters of the model, the interplay leads to the low temperature critical point in the phase structure predicted by a previous Ginzburg-Landau analysis. We also show that a Bose-Einstein condensate (BEC) of diquark molecules emerges in the intermediate density region, and as a result, a BEC-BCS crossover is realized with increasing quark chemical potential.
The pion and kaon properties in a nuclear medium at nonvanishing temperature as well as the 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 dependent 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 bar…
We use a numerical method, the finite-mode approach, to study inhomogeneous condensation in effective models for QCD in a general framework. Former limitations of considering a specific ansatz for the spatial dependence of the condensate are overcome. Different error sources are analyzed and strategies to minimize or eliminate them are outlined. The analytically known results for $1+1$ dimensional models (such as the Gross-Neveu model and extensions of it) are correctly reproduced using the finite-mode approach. Moreover, the NJL model in $3+1$ dimensions is investigated and its phase diagram …
Temperature dependence of pion and sigma-meson screening masses is evaluated by the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model with the entanglement vertex. We propose a practical way of calculating meson screening masses in the NJL-type effective models. The method based on the Pauli-Villars regularization solves the well-known difficulty that the evaluaton of screening masses is not easy in the NJL-type effective models.The PNJL model with the entanglement vertex and the Pauli-Villars regularization well reproduces lattice QCD results on temperature dependence of the chiral cond…
