We explore the effect of including quantum fluctuations in the two flavor Nambu$-$Jona-Lasinio model at finite temperature. This is accomplished, in a symmetry preserving way, by including collective and noncollective modes in the one-meson-loop gap equation which originate from poles and branch cuts in the complex plane, respectively. The inclusion of a boson cutoff, $Λ_b$, is necessary to regularize the meson-loop momenta. This new parameter is used to study the influence of going beyond the usual mean field approximation in the quark condensate. As the temperature increases, chiral symmetry tends to get restored, the collective modes melt and only noncollective modes contribute to the quark condensate. With the inclusion of such modes, the quark condensate at finite temperature has a different behavior than at mean field level that will be explored.
Within the general framework of SU(2) Nambu-Jona-Lasinio model beyond mean-field approximation, the S-wave $π- π$ scattering lengths $a_0^0$ and $a_0^2$ are calculated. The numerical results are in agreement with that analyzed from recent experiment $πN \to ππN$ data by using Chew-Low-Goebel technique, and the corresponding chiral condensate $<{\bar q}q>$ is around $-(250 {\rm MeV})^3$, which is close to the ones obtained from lattice and sum rules.
To obtain the equation of state of quark matter and construct hybrid stars, we calculate the thermodynamic potential in the three-flavor Nambu-Jona-Lasinio model including the tensor-type four-point interaction and the Kobayashi-Maskawa-'t Hooft interaction. To construct the hybrid stars, it is necessary to impose the beta-equilibrium and charge neutrality conditions on the system. It is shown that tensor condensed phases appear at large chemical potential. Under the possibility of the existence of the tensor condensates, the relationship between the radius and mass of hybrid stars is estimate…
We study the beahviour of the dual quark condensate $Σ_1$ in the Nambu-Jona-Lasinio (NJL) model and its nonlocal variant. In quantum chromodynamics $Σ_1$ can be realted to the breaking of the center symmetry and is therefore an (approximate) order parameter of confinement. The deconfinement transition is then signaled by a strong rise of $Σ_1$ as a function of temperature. However, a similar behaviour is also seen in the NJL model, which is known to have no confinement. Indeed, it was shown that in this model the rise of $Σ_1$ is triggered by the chiral phase transition. In order to shed more …
The influence of the magnetic field on the pion superfluidity and the phase structure is analyzed in the framework of the two-flavor Nambu--Jona-Lasinio(NJL) model. To do this, we first derive the thermodynamic potential from the Lagrangian density of the NJL model in the mean field approximation. Using this thermodynamic potential, we get the gap equation of the chiral condensate and the pion condensate. The effect of external magnetic field on the pion condensate is not simple promotion or suppression, which we will discuss in detail in the paper. It is shown that the tricritical point on th…
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 discuss the quark condensate of the vacuum inside the baryon. We analyze the 1+1 dimensional chiral bag in analogy with the realistic 3+1 dimensional one. The Nambu--Jona-Lasinio (NJL) type interaction is used to investigate the quark condensate in the chiral bag. Considering the strong meson-quark coupling, we solve the mean field solution to the scalar and pseudoscalar channels by including the chiral Casimir effects. The self-consistent equation allows a finite value of the quark condensate and hence a finite dynamical quark mass inside the bag. It is shown that an approximate Cheshire C…
We use a Nambu-Jona Lasinio type model to investigate the phase diagram of dense quark matter under neutron star conditions in mean field approximation. The model contains selfconsistently determined quark masses and allows for diquark condensation in the scalar as well as in the pseudoscalar channel. The latter gives rise to the possibility of K^0 condensation in the CFL phase. In agreement with earlier studies we find that this CFLK^0 phase covers large regions of the phase diagram and that the predominant part of this phase is fully gapped. We show, however, that there exists a region at ve…
We present results from a lattice Monte Carlo study of the Nambu - Jona-Lasinio model in 3+1 dimensions with a baryon chemical potential mu=/=0. As mu is increased there is a transition from a chirally-broken phase to relativistic quark matter, in which baryon number symmetry appears spontaneously broken by a diquark condensate at the Fermi surface, implying a superfluid ground state. Finite volume corrections to this relativistic BCS scenario, however, are anomalously large.
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 …
The Nambu--Jona-Lasinio (NJL) model is one of the most useful tools to study non-perturbative strong interaction matter. Because it is a nonrenormalizable model, the choosing of regularization is a subtle issue. In this paper, we discuss one of the general things of the regularization in the NJL model, which is whether we need to use the regularization on the thermal part by evaluating the quark chiral condensate and thermal properties in the two-flavor NJL model. The calculations in this work include three regularization schemes that contain both gauge covariant and invariant schemes. We foun…
We formulate the nonlocal NJL model with a momentum dependent constituent quark mass and calculate pion light cone wave functions of twist 2 and 3. The leading twist wave function is not asymptotic and agrees well with the new CLEO data. Normalization conditions for the twist 3 wave functions are used to calculate the quark condensate. A prescription to calculate the gluon condensate is proposed. The numerical value of the gluon condensate nicely agrees with the phenomenological value, whereas the quark condensate is larger than the phenomenological value of $-(250$ MeV$)^3$. The relation betw…
Investigations of deconfined quark matter within NJL-type models are reviewed, focusing on the regime of low temperatures and ``moderate'' densities, which is not accessible by perturbative QCD. Central issue is the interplay between chiral symmetry restoration and the formation of color superconducting phases. In order to lay a solid ground for this analysis, we begin with a rather detailed discussion of two and three-flavor NJL models and their phase structure, neglecting the possibility of diquark pairing in a first step. An important aspect of this part is a comparison with the MIT bag mod…
In this contribution, we summarize our recent studies on the chiral invariant mass and the chiral condensates in neutron star matter. We construct a unified equations of state assuming the crossover phase transition from hadronic matter described by a parity doublet model to quark matter by an Nambu--Jona-Lasinio type quark model. We first show that the chiral invariant mass is constrained to be 600 MeV $\lesssim m_0 \lesssim$ 900 MeV from recent observations of neutron stars. We then determine the density dependence of the chiral condensate in the crossover description, and show that the chir…
We study the chiral condensates in neutron star matter from nuclear to quark matter domain. We describe nuclear matter with a parity doublet model (PDM), quark matter with the Nambu--Jona-Lasino (NJL) model, and a matter at the intermediate density by interpolating nuclear and quark matter equations of state. The model parameters are constrained by nuclear physics and neutron star observations. Various condensates in the interpolated domain are estimated from the chemical potential dependence of the condensates at the boundaries of the interpolation. The use of the PDM with substantial chiral …
We investigate the phase structure of the Nambu--Jona-Lasinio model at zero temperature, allowing for a two-dimensional spatial dependence of the chiral condensate. Applying the mean-field approximation, we consider various periodic structures with rectangular and hexagonal geometries, and minimize the corresponding free energy. We find that these two-dimensional chiral crystals are favored over homogeneous phases in a certain window in the region where the phase transition would take place when the analysis was restricted to homogeneous condensates. It turns out, however, that in this regime …
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.
We present results of numerical simulations of the 3+1d Nambu - Jona-Lasinio model with a non-zero baryon chemical potential mu, with particular emphasis on the superfluid diquark condensate and associated susceptibilities. The results, when extrapolated to the zero diquark source limit, are consistent with the existence of a non-zero BCS condensate at high baryon density. The nature of the infinite volume and zero temperature limits are discussed.
We analyze the thermodynamical properties, at finite density and nonzero temperature, of the (1+1)-dimensional chiral Gross-Neveu model (the NJL_2 model), using the exact inhomogeneous (crystalline) condensate solutions to the gap equation. The continuous chiral symmetry of the model plays a crucial role, and the thermodynamics leads to a broken phase with a periodic spiral condensate, the "chiral spiral", as a thermodynamically preferred limit of the more general "twisted kink crystal" solution of the gap equation. This situation should be contrasted with the Gross-Neveu model, which has a di…
Density screening effects in the NJL model: Chiral condensate, speed of sound, and the Critical End Point
Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo（米却肯自治大学物理与数学研究所）；Facultad de Ingeniería Eléctrica, Universidad Michoacana de San Nicolás de Hidalgo（米却肯自治大学电气工程学院）；Centro de Ciencias Exactas, Universidad del Bío-Bío（比奥比奥大学精确科学中心）；Universidad Aeronáutica en Queretaro（克雷塔罗航空大学）
The influence of a constant uniform external chromomagnetic field $H$ on the formation of color superconductivity has been investigated. The consideration was performed in the framework of a (2+1)-dimensional Nambu--Jona-Lasinio model with two different four-fermionic structures responsible for $<\bar qq>$ and diquark $<qq>$ condensates. In particular, it was shown that there exists a critical value $H_c$ of the external chromomagnetic field such that at $H>H_c$ a nonvanishing diquark condensate is dynamically created (the so-called chromomagnetic catalysis effect of color superconductivity). …
Temperature dependence of the quark condensate is studied in the Nambu--Jona-Lasinio model with meson loops. Substantial differences are found compared to the results with quark loops only.
We consider the color spin locking (CSL) phase of two-flavor quark matter at zero temperature for nonlocal instantaneous, separable interactions. We employ a Lorentzian-type form factor allowing a parametric interpolation between the sharp (Nambu-Jona-Lasinio (NJL) model) and very smooth (e.g. Gaussian) cut-off models for systematic studies of the influence on the CSL condensate the deviation from the NJL model entails. This smoothing of the NJL model form factor shows advantageous features for the phenomenology of compact stars: (i) a lowering of the critical chemical potential for the onset …
The Nambu--Jona-Lasinio (NJL) model has been extensively studied by many researchers. In previous work we have generalized the NJL model to include a covariant model of confinement. In the present work we consider further modification of the model so as to reproduce the type of Euclidean-space momentum- dependent quark mass values obtained in lattice simulations of QCD. This may be done by introducing a nonlocal interaction, while preserving the chiral symmetry of the Lagrangian. In other work on nonlocal models, by other researchers, the momentum dependence of the quark self-energy is directl…
We consider how does the introduction of a Polyakov loop affects the spatially inhomogeneous quark condensate. The primary result of our work is that the existence of the spatially non-uniform chiral phase is confirmed within the Polyakov NJL model in a chiral limit. These findings are obtained both in a 3d-cutoff and in a Schwinger (proper time) regularization schemes.
We study the phase structure of the two-flavor Nambu--Jona-Lasinio (NJL) model in the chiral limit, extending a previous study of the competition of an inhomogeneous chiral phase and a two-flavor color-superconducting (2SC) phase [1, 2]. There, an analytic expression for the dispersion relations for quasiparticle excitations in the presence of both a particular inhomogeneous chiral condensate, the so-called chiral density wave (CDW), and a homogeneous 2SC condensate was found. In this work we show how to determine the dispersion relations for arbitrary modulations of the chiral condensate in t…
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 chiral phase transition of a hot and dense system of quarks is studied within a modified SU(3) NJL lagrangian that implements the QCD scale anomaly. The u- and s-quark condensates can feel or not the same chiral restoration depending on the considered region of the 3-dimension space T_c(μ_uc,μ_sc). The temperature behaviour of the pressure and of the energy and entropy densities of the u- and s-quark system is investigated. At high temperature, the non-vanishing bare s-quark mass only modifies slightly the usual behaviour associated with an ideal quark gas.
A schematic NJL-type model is employed to investigate kaon and pion condensation in deconfined quark matter in the color-flavor locked (CFL) phase, explicitly referring to quark degrees of freedom. To that end we allow for non-vanishing pseudoscalar diquark condensates in addition to the scalar ones which constitute the CFL phase. Color neutrality is ensured by the appropriate choice of color chemical potentials. The dependence of the free energy in the Goldstone condensed phases on quark masses and charge chemical potentials is found to be in good qualitative -- in most cases also quantitativ…
We give an introduction to the dynamical symmetry breaking with large anomalous dimension. This is the basis of tightly bound composite Higgs models such as walking technicolor, strong ETC technicolor and top quark condensate, which are all characterized by the large anomalous dimension, γ_m \simeq 1 (walking technicolor), 1<γ_m<2 (strong ETC technicolor) and γ_m \simeq 2 (top quark condensate) due to nontrivial short distance dynamics of the gauged Nambu-Jona-Lasinio (NJL) models (gauge theories plus four-fermion interactions). Particular emphasis will be placed on the top quark condensate in…
Our understanding of the dynamics and the phase structure of dense strong-interaction matter is to a large extent still built on the analysis of low-energy models, such as those of the Nambu-Jona-Lasinio-type. In this work, we analyze the emergence of the latter class of models at intermediate and low energy scales from fundamental quark-gluon interactions. To this end, we study the renormalization group flow of a Fierz-complete set of four-quark interactions and monitor their strength at finite temperature and quark chemical potential. At small quark chemical potential, we find that the scala…
The general quasiparticle propagator in dense quark matter is derived for equal mass quarks. Specialized to an NJL model, this propagator includes one new condensate, $Δ_3$, in addition to the usual CFL condensate, $Δ_1$. The gap equation is solved in two NJL models and the dependence on the quark mass of the condensates and the gap is presented. Analytic approximations for the condensates are obtained and compared to exact numerical solutions. The results are shown to differ from those obtained by neglecting $Δ_3$, especially for smaller values of $Δ_1$. The two different NJL models presented…
In this paper, the NJL-type model is used to investigate the color superconductivity. The four-fermion interactions of the NJL-type model are Fierz-transformed into two different classes, i.e., the quark-antiquark and the quark-quark interaction channels, associated with the chiral symmetry breaking and color superconductivity respectively. We conclude that the weighting factor between quark-antiquark and quark-quark interaction channels has significance on the phase structure when the mean-field approximation is employed, and the baryon number density gives a tight constraint on the weighting…
We study pion condensation and the phase structure in a two-flavor Nambu-Jona-Lasinio model in the presence of baryon chemical potential $μ$ and isospin chemical potential $μ_I$at zero and finite temperature. There is a competition between the chiral condensate and a Bose-Einstein condensate of charged pions. In the chiral limit, the chiral condensate vanishes for any finite value of the isospin chemical potential, while there is a charged pion condensate that depends on the chemical potentials and the temperature. At the physical point, the chiral condensate is always nonzero, while the charg…
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.
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.
We consider an extended Nambu--Jona-Lasinio (NJL) model for the light meson sector of QCD where unphysical quark production thresholds are excluded by an infrared cut-off on the momentum integration within quark loop diagrams. This chiral quark model conserves the low energy theorems. The infrared cut-off is fixed selfconsistently by the dynamically generated quark mass (quark condensate). The masses and decay widths of the σ- and ρ-mesons are described in the 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…
We study the holographic Dynamic AdS/QCD description of a SU($N_c$) non-abelian gauge theory with $N_f$ fermions in the fundamental representation which also have Nambu-Jona-Lasinio interactions included using Witten's multi-trace prescription. In particular here we study aspects of the dynamics in and near the conformal window of the gauge theory as described by the two loop running of the gauge theory. If the number of flavours is such that the IR fixed point lies with the anomalous dimension, $γ$, of the quark bilinear above one then chiral symmetry breaking occurs. Here we display a spiral…
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…
Starting from a NJL-type model with N fermion species fermion and difermion condensates and their associated phase structures are considered at nonzero chemical potential $μ$ and zero temperature in spaces with nontrivial topology of the form $S^1\otimes S^1\otimes S^1$ and $R^2\otimes S^1$. Special attention is devoted to the generation of the superconducting phase. In particular, for the cases of antiperiodic and periodic boundary conditions we have found that the critical curve of the phase transitions between the chiral symmetry breaking and superconducting phases as well as the correspond…
Dynamical symmetry breaking and the formation of scalar condensates in the SU(2)XU(1) Nambu-Jona-Lasinio model with two coupling constants has been studied in the framework of the mean field approximation. The bosonization procedures of the model are performed using the functional integration method. The possibility of the spontaneous CP symmetry breaking in the model under consideration has been shown. The mass spectrum of the bound states of fermions, as well as the effective Lagrangian of interacting scalar and pseudoscalar mesons are obtained.
Anomalous magnetic moment (AMM) of quarks in presence of an external magnetic field has been explored using a nonlocal Nambu\textemdash Jona-Lasinio (NJL) model. Various strengths of AMM differing in orders of magnitude are used in the literature. We explore them in our nonlocal framework to decide on their strength. We checked the validity of using constant AMM of quarks and investigate two different temperature and magnetic field dependent forms. The forms are taken as the AMM being proportional to the i) meanfield and the ii) square of the meanfield. On comparison with the lattice data for …
With the help of the functional integration method, the formation of scalar, pseudoscalar condensates, and dynamical symmetry breaking in the U(3) four-fermion model has been investigated. We show the possibility of spontaneous CP symmetry violation in the model under consideration. The bosonization procedures of the model are performed; the propagators of quarks, scalar and pseudoscalar fields are calculated in one loop approximation. The masses of the scalar and pseudoscalar mesons are evaluated.
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…
We elucidate how the color neutrality is harmed in the Polyakov Nambu-Jona Lasinio (PNJL) model at finite density within the adopted mean field approximation. Also we point out how usual assumption about the diagonal form of the Wilson loop may fail in the presence of the diquark condensate on several grounds.
We study the regularization dependence of the Nambu-Jona--Lasinio model (NJL) predictions for some properties of magnetized quark matter at zero temperature (and baryonic density) in the mean field approximation. The model parameter dependence for each regularization procedure is also analyzed in detail. We calculate the average and difference of the quark condensates using different regularization methods and compare with recent lattice results. In this context, the reliability of the different regularization procedures is discussed.
The quark propagator is calculated in the Nambu-Jona-Lasinio (NJL) model in a self-consistent 1/Nc-expansion at next-to-leading order. The calculations are carried out iteratively in Euclidean space. The chiral quark condensate and its dependence on temperature and chemical potential is calculated directly and compared with the mean-field results. In the chiral limit, we find a second-order phase transition at finite temperature and zero chemical potential, in agreement with universality arguments. At zero temperature and finite chemical potential, the phase transition is first order. In compa…
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.
In this paper, we study the possibility of an inhomogeneous quark condensate in the 1+1 dimensional Nambu-Jona-Lasinio model in the large-$N_c$ limit at finite temperature $T$ and quark chemical potential $μ$ using dimensional regularization. The phase diagram in the $μ$--$T$ plane is mapped out. At zero temperature, an inhomogeneous phase with a chiral-density wave exists for all values of $μ>μ_c$. Performing a Ginzburg-Landau analysis, we show that in the chiral limit, the critical point and the Lifschitz point coincide. We also consider the competition between a chiral-density wave and a co…
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 chiral phase transition of quark matter under rotation in two-flavor Nambu--Jona-Lasinio (NJL) model. It is found that, in the rotating frame, the angular velocity plays the similar role as the baryon chemical potential and suppresses the chiral condensate, thus the chiral phase transition shows a critical end point not only in the temperature-chemical potential $T-μ$ plane, but also in the temperature-angular momentum $T-ω$ plane. One interesting observation is that in the $T-μ$ plane, the presence of the angular momentum only shifts down the critical temperature $T^E$ of the CEP…
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…
In this paper we investigate the phase structure of a (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. Spatially inhomogeneous chiral density wave (for chiral condensate) and single wave (for charged pion condensate) approaches are used. It is established that in the large-$N_c$ limit ($N_c$ is the number of colored quarks) there exists a duality correspondence between the chiral symmetry breaking phase and the charged pion condensation (PC) one. Moreover, it is shown that inhomog…
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 …
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…
Meson corrections on chiral condensate up to next-to-leading order in $1/N_c$ expansion at finite density are investigated in NJL model with chiral symmetry explicitly breaking. Compared with the mean-field results, the chiral phase transition is still of first order, while the properties at the critical density of chiral phase transition are found to change significantly.
In this talk we present investigation of the phase structure of a (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. Spatially homogeneous and inhomogeneous (chiral density wave (for chiral condensate) and single wave (for charged pion condensate)) condensates are considered. It is established that in the large-$N_c$ limit ($N_c$ is the number of colored quarks) there exists a duality correspondence between the chiral symmetry breaking phase and the charged pion condensation one. Th…
