We have derived and solved numerically the Boltzmann-Vlasov transport equations that includes both two-body collisions and the chiral phase transition by mean of NJL-field dynamics. The scope is to understand if the field dynamics supply new genuine effects on the build-up of the elliptic flow $v_2$, a measure of the asymmetry in the momentum space, and in particular if it can affect the relation between $v_2$ and the shear viscosity to entropy ratio $η/s$. Solving the transport equation with a constant cross section for the condition of $Au+Au$ collisions at $\sqrt{s_{NN}}=200$ AGeV it is shown a sizable suppression of $v_2$ due to the attractive nature of the field dynamics that generates the constituent mass. However the key result is that if $η/s$ of the system is kept fixed by an appropriate local renormalization of the cross section the $v_2$ does not depend on the details of the collisional and/or field dynamics and in particular it is not affected significantly by the chiral phase transition.
The chiral phase transition and color superconductivity in an extended NJL model with eight-quark interactions are studied. The scalar-type nonlinear term hastens the chiral phase transition,the scalar-vector mixing term suppresses effects of the vector-type linear term and the scalar-diquark mixing term makes the coexisting phase wider.
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.
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.
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.
We study the solutions of the gap equation, the thermodynamic potential and the chiral susceptibility in and beyond the chiral limit at finite chemical potential in the Nambu--Jona-Lasinio (NJL) model. We give an explicit relation between the chiral susceptibility and the thermodynamic potential in the NJL model. We find that the chiral susceptibility is a quantity being able to represent the furcation of the solutions of the gap equation and the concavo-convexity of the thermodynamic potential in NJL model. It indicates that the chiral susceptibility can identify the stable state and the poss…
In this work we present a strong chiral meson Lagrangian up to and including $O(p^6)$ in the momentum expansion. It is derived from the Nambu--Jona-Lasinio (NJL) model using the heat-kernel method. Identities related to the properties of covariant derivatives of the chiral matrix $U$ as well as field transformations have been used to obtain a minimal set of linearly independent terms.
We present numerical simulations for unpolarized and polarized structure functions in a chiral soliton model. The soliton is constructed self-consistently from quark fields from which the structure functions are extracted. Central to the project is the implementation of regularizing the Dirac sea (or vacuum) contribution to structure functions from first principles. We discuss in detail how sum rules are realized at the level of the quark wave-functions in momentum space. The comparison with experimental data is convincing for the polarized structure functions but exhibits some discrepancies i…
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 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 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 …
In this paper we investigate the phase structure of a (1+1) and (3+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. It is shown that the chemical potential $μ_{I5}$ promotes the appearance of the charged PC phase with nonzero baryon density. Results of both models are qualitatively the same, this fact enhances one's confidence in %the faith in the obtained predictions. It is established that in the large-$N_c$ limit ($N_c$ is the number of colored quarks) there exists a duality corre…
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…
The branching fraction of the decay $η' \to πρ$ is calculated in the chiral quark NJL model. The decay exists due to the mass difference between $u$- and $d$-quarks leading to $π^{0}-η^{'}$ mixing. Two different approaches are applied: the approximate calculation of this process taking into account the transition $π^{0}-η^{'}$ explicitly without dioganalisation and a more precise approach consisting in the diagonalisation of the singlet and octet states leading to the physical fields $π^{0}$, $η$ and $η^{'}$. The obtained results are in satisfactory agreement with current experimental data.
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.
We study the chiral phase transition in the presence of the chiral chemical potential $μ_5$ using the two-flavor Nambu--Jona-Lasinio model. In particular, we analyze the reason why one can obtain two opposite behaviors of the chiral critical temperature as a function of $μ_5$ in the framework of different regularization schemes. We compare the modifications of the chiral condensate and the critical temperature due to $μ_5$ in different regularization schemes, analytically and numerically. Finally, we find that, for the conventional hard-cutoff regularization scheme, the increasing dependence o…
We calculate the two-loop effective potential of the non-local NJL model derived from the Sakai-Sugimoto model in string theory. In contrast to conventional NJL with 4-fermion contact interaction, the chiral symmetry was previously found to be dynamically broken for arbitrary weak coupling at the one-loop level. As a confirmation, the approximate numerical solutions to the gap equation at one loop are explicitly demonstrated for weak couplings. We then calculate the one and two-loop contribution to the effective potential of the non-local NJL model and found that the two-loop contribution is n…
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…
The quark-hadron phase transition at finite temperature and baryon chemical potential is investigated in an extended NJL model with scalar-vector eight-point interaction by comparing the pressure of symmetric nuclear matter with that of the quark matter. As a result, the extended NJL phase diagram is obtained in the temperature-baryon chemical potential plane and the effects of the scalar-vector coupling constant G_{sv}^q on the chiral phase transition are summarized. It is shown that a quarkyonic-like phase in which the chiral symmetry is restored but the elementary excitation modes are nucle…
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.
The properties of the chiral phase transition at finite temperature and chemical potential are investigated within a nonlocal covariant extension of the Nambu-Jona-Lasinio model based on a separable quark-quark interaction. We consider both the situation in which the Minkowski quark propagator has poles at real energies and the case where only complex poles appear. In the literature, the latter has been proposed as a realization of confinement. In both cases, the behaviour of the physical quantities as functions of T and μis found to be quite similar. In particular, for low values of T the chi…
We calculate the momentum dependence of three particle vertices $σγγ$, $σργ$ and $σρρ$ in the context of a Nambu Jona Lasinio type model. We show how they influence the processes $γγ\rightarrow σ\rightarrow ππ$, $ρ\rightarrow γσ$ and $γγ\rightarrow ρρ$ and how chiral symmetry shadows the presence of the $σ$.
We study the interplay of the chiral and the color superconducting phase transitions in an extended Nambu--Jona-Lasinio model with a multi-quark interaction that produces the nonlinear chiral-diquark coupling. We observe that this nonlinear coupling adds up coherently with the ω^2 interaction to produce the chiral-color superconductivity coexistence phase or cancel each other depending on its sign. We discuss that large coexistence region in the phase diagram is consistent with the quark-diquark picture for the nucleon whereas its smallness is the prerequisite for the applicability of the Ginz…
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.
We decribe properties of 2+1-dimensional Nambu-Jona-Lasinio (NJL) models at finite-temperature, beginning with the model with a discrete chiral symmetry. We then consider the model with a continuous $U(1) \times U(1)$ chiral symmetry, describing the restoration of the symmetry at finite temperature. In each case, we compute the free energy and comment on a recently proposed constraint based upon it. We conclude with a brief discussion of NJL models with larger chiral symmetries.
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…
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 study QED corrections to chiral symmetry breaking in the Nambu--Jona-Lasinio (NJL) model with two flavors of quarks. In this model, the isospin symmetry is broken by the differences between the current quark masses and the electromagnetic charges of the up and down quarks. To leading order in the 1/N expansion, we calculate the effective potential of the model with one-loop QED corrections at finite temperature. Evaluating the effective potential, we study the influence of the isospin symmetry breaking on the orientation of chiral symmetry breaking. The current quark mass plays an essential…
We discuss the net quark and isovector fluctuations as well as off-diagonal quark flavor susceptibilities along the chiral phase transition line in the Nambu--Jona-Lasinio (NJL) model. The model is formulated at non-zero quark and isospin chemical potentials with non-vanishing vector couplings in the iso-scalar and iso-vector channels. We study the influence of the quark chemical potential on the quark flavour susceptibilities in detail and the dependence of the results on model parameters as well as on the quark mass. The NJL model findings are compared with recent lattice results obtained in…
The branching fractions of the decays $τ\to a_{1} πν_τ$, $τ\to K_{1} πν_τ$ and $τ\to K_{1} K ν_τ$ are calculated in the framework of the extended $U(3)\times U(3)$ chiral Nambu--Jona-Lasinio model. There are no experimental data for these decays in the present time, thus the obtained results are considered as predictions. The comparison of these results to the theoretical results of other authors is carried out.
In the chirally symmetric Nambu--Jona-Lasinio model baryons are described as chiral solitons of mesonic quark--antiquark bound states. Hyperons are investigated in two complementary pictures: the bound state approach of Callan and Klebanov and the collective approach of Yabu and Ando. The latter is used to compute the strange vector form factors of the nucleon providing estimates for the strange electric mean square radius and the strange magnetic moment of the nucleon.
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…
The processes $τ^- \to π^- π^0 ν_τ$ and $e^{+}e^{-} \to π^{+} π^{-}$ are considered within the chiral Nambu--Jona-Lasinio model with taking into account the pion final state interactions beyond the leading $1/N_c$ approximation. The contribution of the loop correction caused by a $ρ$ meson exchange between the pions, which gives the main contribution in the P-wave channel, is caclulated. The results for both processes are in a satisfactory agreement with experimental data.
Chiral Phase Transition in Rotating Quark Matter with Chiral Imbalance: A Medium Separation Scheme Regularized NJL Model Study
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, Three Gorges University（三峡大学天体空间科学与现代物理研究所）；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）
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.
The thermodynamic potential and thermal dependence of low lying mass spectra of scalars and pseudoscalars are evaluated in a generalized Nambu -- Jona-Lasinio model, which incorporates eight-quark interactions. These are necessary to stabilize the scalar effective potential for the light and strange quark flavors, which would be otherwise unbounded from below. In addition it turns out that they are also crucial to i) lower the temperature of the chiral transition, in conformity with lattice calculations, ii) sharpen the temperature interval in which the crossover occurs, iii) or even allow for…
NJL-Chiral Soliton and the Nucleon Equation of State at supra-saturation density: Impact of Chiral Symmetry Restoration
Institut de Physique des 2 infinis de Lyon, CNRS/IN2P3, Université de Lyon, Université Claude Bernard Lyon 1（里昂二维物理研究所，CNRS/IN2P3，里昂大学，里昂第一大学）；International Research Laboratory on Nuclear Physics and Astrophysics, Michigan State University and CNRS（核物理与天体物理学国际研究实验室，密歇根州立大学和CNRS）
Chiral Magnetic Effect(CME) is usually believed not receiving higher order corrections due to the non-renormalization of AVV triangle diagram in the framework of quantum field theory. However, the CME-relevant triangle, which is obtained by expanding the current-current correlation requires zero momentum on the axial vertex, is not equivalent to the general AVV triangle when taking the zero-momentum limit owing to the infrared problem on the axial vertex. Therefore, it is still significant to check if there exists perturbative higher order corrections to the current-current correlation. In thi…
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…
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 …
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）
In this paper we develop a new method that is different from Schwinger proper time method to deduce the fermion propagator with a constant external magnetic field. In the NJL model, we use this method to find out the gap equation at zero and non-zero temperature, and give the numerical results and phase diagram between magnetic field and temperature. Beside these, we also introduce current mass to study the susceptibilities, because there is a new parameter (the strength of external magnetic field) in this problem, corresponding this new parameter, we have defined a new susceptibility $χ_B$ to…
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…
The momentum-space bosonization method of a Nambu and Jona-Lasinio type model with vector and axial-vector mesons is applied to $ππ$ scattering. Unlike the case in earlier published papers, we obtain the $ππ$ scattering amplitude using the linear and nonlinear realizations of chiral symmetry and fully taking into account the momentum dependence of meson vertices. We show the full physical equivalence between these two approaches. The chiral expansion procedure in this model is discussed in detail. Chiral expansions of the quark mass, pion mass and constant $f_π$ are obtained. The low-energy $π…
In this paper we investigate the phase structure of a (1+1)-dimensional schematic quark model with four-quark interaction and in the presence of baryon ($μ_B$), isospin ($μ_I$) and chiral isospin ($μ_{I5}$) chemical potentials. It is established that in the large-$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. The role and influence of this property on the phase structure of the model are studied. Moreover, it is shown that the chemical potential $μ_{I5}$ promotes th…
Isospin asymmetry is the well-known property of dense quark matter, which exists in the compact stars and is produced in heavy ion collisions. On the other hand, the chiral imbalance between left- and right-handed quarks is another highly anticipated phenomenon that could occur in the dense quark matter. To investigate quark matter under these conditions, we take into account baryon -- $μ_B$, isospin -- $μ_I$ and chiral isospin -- $μ_{I5}$ chemical potentials and study QCD phase portrait using NJL$_4$ model generalized to two massive quarks that could condense into the pion condensation. We ha…
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…
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.
According to the Ideal Walking Technicolor paradigm large mass anomalous dimensions arise in gauged Nambu--Jona-Lasinio (NJL) models when the four-fermion coupling is sufficiently strong to induce spontaneous symmetry breaking in an otherwise conformal gauge theory. We therefore study the $SU(2)$ gauged NJL model with two adjoint fermions using lattice simulations. The model is in an infrared conformal phase at small NJL coupling while it displays a chirally broken phase at large NJL couplings. In the infrared conformal phase we find that the mass anomalous dimension varies with the NJL coupli…
In this paper the phase structure of dense quark matter has been investigated in the presence of baryon, isospin and chiral isospin chemical potentials in the framework of (3+1)-dimensional Nambu--Jona-Lasinio model with two quark flavors. It has been shown that in the large-$N_{c}$ limit ($N_{c}$ is the number of colors of quarks) there exists a duality correspondence between the chiral symmetry breaking phase and the charged pion condensation one. The key conclusion of our studies is the fact that chiral isospin chemical potential generates charged pion condensation in dense quark matter wit…
We study QED corrections to the chiral symmetry breaking in Nambu-Jona-Lasinio (NJL) model with two flavors of quarks. In the model the isospin symmetry is broken by differences of the current quark masses and the electromagnetic charges between up and down quarks. In the leading order of the 1/N expansion we calculate the effective potential of the model with one-loop QED corrections. Evaluating the effective potential, we study an influence of the isospin symmetry breaking on the orientation of chiral symmetry breaking. The current quark mass has an important contribution for the orientation…
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）
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 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 branching fractions of the decays $τ^- \to K^- π^+ π^- ν_τ$, $τ^- \to K^- π^0 π^0 ν_τ$ and $τ^- \to \bar{K}^0 π^- π^0ν_τ$ are calculated in the $U(3)\times U(3)$ Nambu--Jona-Lasinio type chiral model. Four intermediate channels are considered: the contact channel and the channels with the intermediate axial vector, vector and pseudoscalar mesons. The additional resonance states $K^* π$ and $K ρ$ are taken into account in all channels. It is shown that the main contributions to the widths of these decays are given by the axial vector channel. In the axial vector channel, the intermediate re…
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…
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 phase diagram for quark matter is investigated within a simple Nambu-Jona-Lasinio model without vector correlations. It is found that the phase structure in the temperature-density plane depends sensitively on the parametrization of the model. We present two schemes of parametrization of the model where within the first one a first order phase transition from a phase with broken chiral symmetry to a color superconducting phase for temperatures below the triple point at T_t= 55 MeV occurs whereas for the second one a second order phase transition for temperatures below T_t = 7 MeV is found.…
