Phase transition and the nucleon as a soliton in the Nambu-Jona-Lasinio model at finite temperature and density

We study some bulk thermodynamical characteristics, meson properties and the nucleon as a baryon-number-one soliton in hot quark matter in the NJL model as well as in hot nucleon matter in a hybrid NJL model in which the Dirac sea of quarks is combined with a Fermi sea of nucleons. In both cases, working in the mean-field approximation, we find a chiral phase transition from the Goldstone to the Wigner phase. At finite density the chiral order parameter and the constituent quark mass have a non-monotonic temperature dependence — at finite temperatures not close to the critical one they are less affected than in cold matter. Whereas quark matter is rather soft against thermal fluctuations and the corresponding chiral phase transition is smooth, nucleon matter is much stiffer and the chiral phase transition is very sharp. The thermodynamical variables show large discontinuities which is an indication for a first-order phase transition. We solve the B = 1 solitonic sector of the NJL model in the presence of external hot quark and nucleon media. In the hot medium at intermediate temperature the soliton is more bound and less swelled than in the case of cold matter. At some critical temperature, which for nucleon matter coincides with the critical temperature for the chiral phase transition, we find no more a localized solution. According to this model scenario one should expect a sharp phase transition from nucleon to quark matter.     

Effects of Composite Pions on the Chiral Condensate within the PNJL Model at Finite Temperature

We investigate the effect of composite pions on the behaviour of the chiral condensate at finite temperature within the Polyakov-loop improved NJL model. To this end we treat quark-antiquark correlations in the pion channel (bound states and scattering continuum) within a Beth–Uhlenbeck approach that uses medium-dependent phase shifts. A striking medium effect is the Mott transition which occurs when the binding energy vanishes and the discrete pion bound state merges the continuum. This transition is triggered by the lowering of the continuum edge due to the chiral restoration transition. This in turn also entails a modification of the Polyakov-loop so that the SU(3) center symmetry gets broken at finite temperature and dynamical quarks (and gluons) appear in the system, taking over the role of the dominant degrees of freedom from the pions. At low temperatures our model reproduces the chiral perturbation theory result for the chiral condensate while at high temperatures the PNJL model result is recovered. The new aspect of the current work is a consistent treatment of the chiral restoration transition region within the Beth–Uhlenbeck approach on the basis of mesonic phase shifts for the treatment of the correlations.     

Phase diagram of two-color QCD matter at finite baryon and axial isospin densities

We study the two-color QCD matter with two fundamental quark flavors using the chiral perturbation theory and the Nambu-Jona-Lasinio(NJL)model.The effective Lagrangian is derived in terms of mesons and baryons,i.e.diquarks.The low lying excitations lie in the extended SU(4)flavor symmetry space.We compute the leading order terms of the Lagrangian as a function of the baryon and axial isospin densities.After numerically solving the gap equations in the two-color NJL model,the phase diagram is obtained in the μ−ν5 plane.     

On the chiral transition temperature in bilocal effective QCD

The breakdown of chiral symmetry in a many-quark system at finite temperature is studied by considering a bilocal quark interaction derived from a field theoretical treatment of QCD. We find that such an approach yields a chiral transition temperature which is about 30% lower compared to the standard NJL model prediction.     

Properties of the nucleon in the nuclear medium within a chiral quark-meson theory

The modifications of the nucleon structure due to the presence of an external baryon medium are investigated in a chiral quark meson theory. To that end the Nambu-Jona-Lasinio (NJL) model is combined with the projected chiral soliton model. The medium effects are incorporated using the medium modified values of the pion decay constant and the pion and sigma masses at finite density. These values are evaluated within the NJL model. Using functional integral techniques the latter is solved in a quark continuum at finite density. The effective meson values serve to fix the parameters of the linear chiral sigma model which is solved in a variational projected mean field approach in order to obtain the nucleon properties. All nucleon properties show modifications in the medium except for the pion nucleon coupling constant. The proton radius shows an increase of 19% and the nucleon mass a decrease of 17% if the medium reaches nuclear matter density. The magnetic moments and axial vector coupling constant are less modified. All form factors show remarkable reduction at finite transfer momenta.     

Meson Effects on the Chiral Condensate at Finite Density

Meson corrections on the chiral condensate up to next-to-leading order in a 1/N_c expansion at finite density are investigated in the NJL model with explicit chiral symmetry breaking. Compared with mean-field results, the chiral phase transition is still of the first order while the properties near the critical density for chiral phase transition are found to change significantly.     

Chiral phase transition at finite temperature in the linear sigma model

We study the chiral phase transition at finite temperature in the linear sigma model by employing a self-consistent Hartree approximation. This approximation is introduced by imposing self-consistency conditions on the effective meson mass equations which are derived from the finite temperature one-loop effective potential. It is shown that in the limit of vanishing pion mass, namely when the chiral symmetry is exact, the phase transition becomes a weak first order accompanying a gap in the order parameter as a function of temperature. This is caused by the long range fluctuations of meson fields whose effective masses become small in the transition region. It is shown, however, that with an explicit chiral symmetry breaking term in the Lagrangian which generates the realistic finite pion mass the transition is smoothed out irrespective of the choice of coupling strength. Recieved: 19 September 1997 / Revised version: 30 October 1997     

Meson Effects on the Chiral Condensate at Finite Density

Meson corrections on the chiral condensate up to next-to-leading order in a 1/Nc expansion at finite densityare investigated in the NJL model with explicit chiral symmetry breaking. Compared with mean-field results, the chiralphase transition is still of the first order while the properties near the critical density for chiral phase transition are foundto change significantly.     

Pion and σ-meson Properties in a Strong Magnetic Field

With the Nambu-Jona-Lasinio (NJL) model we calculate the properties of pion and σ-meson at finite temperature and finite magnetic field. The obtained temperature and magnetic field strength dependence of the constituent quark mass M, the pion and σ-meson masses and the neutral pion decay constant indicates that, in the simple four fermion interaction model, there exists the magnetic catalysis effect. It also shows that the Gell-Mann-Oakes-Renner relation is violated obviously with the increasing of the temperature, and the effect of the magnetic field becomes pronounced only around the critical temperature. The deviation of the critical temperatures obtained with different criteria indicates that the chiral phase transition driven by the temperature in the magnetic field strength region we have considered is in fact a crossover.     

Chiral crossover characterized by Mott transition at finite temperature

We discuss the proper definition for the chiral crossover at finite temperature,based on Goldstone's theorem.Different from the commonly used maximum change in chiral condensate,we propose defining the crossover temperature using the Mott transition of pseudo-Goldstone bosons,which,by definition,guarantees Goldstone's theorem.We analytically and numerically demonstrate this property in the frame of a Pauli-Villars regularized NJL model.In an external magnetic field,we find that the Mott transition temperature shows an inverse magnetic catalysis effect.     

On the phase structure of QCD in a finite volume

The chiral phase transition in QCD at finite chemical potential and temperature can be characterized for small chemical potential by its curvature and the transition temperature. The curvature is accessible to QCD lattice simulations, which are always performed at finite pion masses and in finite simulation volumes. We investigate the effect of a finite volume on the curvature of the chiral phase transition line. We use functional renormalization group methods with a two flavor quark-meson model to obtain the effective action in a finite volume, including both quark and meson fluctuation effects. Depending on the chosen boundary conditions and the pion mass, we find pronounced finite-volume effects. For periodic quark boundary conditions in spatial directions, we observe a decrease in the curvature in intermediate volume sizes, which we interpret in terms of finite-volume quark effects. Our results have implications for the phase structure of QCD in a finite volume, where the location of a possible critical endpoint might be shifted compared to the infinite-volume case.     

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

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

Chiral phase transition from the Dyson-Schwinger equations in a finite spherical volume

Within the framework of the Dyson-Schwinger equations and by means of Multiple Reflection Expansion,we study the effect of finite volume on the chiral phase transition in a sphere, and discuss in particular its influence on the possible location of the critical end point(CEP). According to our calculations, when we take a sphere instead of a cube, the influence of finite volume on phase transition is not as significant as previously calculated. For instance,as the radius of the spherical volume decreases from infinite to 2 fm, the critical temperature T c, at zero chemical potential and finite temperature, drops only slightly. At finite chemical potential and finite temperature, the location of CEP shifts towards smaller temperature and higher chemical potential, but the amplitude of the variation does not exceed 20%. As a result, we find that not only the size of the volume but also its shape have a considerable impact on the phase transition.     

Calculations of θ（p^6） Resonance Coupling Constants in Scalar Sector of ENJL Model

We derive the scalar resonance coupling constants of resonance chiral theory from the extended Nambu Jona-Lasinio model by using heat-kernel expansion.     

Transport coefficients near chiral phase transition

We analyze the transport properties of relativistic fluid composed of constituent quarks at finite temperature and density. We focus on the shear and bulk viscosities and study their behavior near chiral phase transition. We model the constituent quark interactions through the Nambu–Jona-Lasinio Lagrangian. The transport coefficients are calculated within kinetic theory under relaxation time approximation including in-medium modification of quasi-particles dispersion relations. We quantify the influence of the order of chiral phase transition and the critical end point on dissipative phenomena in such a medium.     

Chiral susceptibility and chiral phase transition in Nambu–Jona-Lasinio model

We give a general relation between the chiral susceptibility and the thermodynamical potential and a relation between the chiral susceptibility and the condition for furcations to appear in the Wigner solution(s) in the Nambu–Jona-Lasinio (NJL) model. We find that the chiral susceptibility is a quantity able to represent the appearance of furcation in the solution(s) of the gap equation and the concavo–convexity of the thermodynamical potential in the NJL model. It indicates that the chiral susceptibility can identify the stability of the states and the chiral phase transition in NJL model. We propose that analyzing the chiral susceptibility may play an important role in studying the chiral phase transition in approaches superior to the NJL model.     

Phase transitions in quark matter and behaviour of physical observables in the vicinity of the critical end point

We study the chiral phase transition at finite T and μ _B within the framework of the SU(3) Nambu-Jona-Lasinio (NJL) model. The QCD critical end point (CEP) and the critical line at finite temperature and baryonic chemical potential are investigated: the study of physical quantities, such as the baryon number susceptibility near the CEP, will provide complementary information concerning the order of the phase transition. We also analyze the information provided by the study of the critical exponents around the CEP.     

引入Polyakov环路的手征模型中的涨落与相变

We explore the NJL model with Polyakov loops for a system of three colors and two flavors within the mean-field approximation, where both chiral symmetry and confinement are taken into account. We focus on the phase structure of the model and study the chiral and Polyakov loop susceptibilities.     

Chiral Phase Transition at Finite Isospin Density in Linear Sigma Model

Using the linear sigma model, we have introduced the pion isospin chemical potential. The chiral phase transition is studied at finite temperatures and finite isospin densities. We have studied the μ-T phase diagram for the chiral phase transition and found the transition cannot happen below a certain low temperature because of the Bose-Einstein condensation in this system. Above that temperature, the chiral phase transition is studied by the isotherms of pressure versus density. We indicate that the transition, in the chiral limit, is a first-order transition from a low-density phase to a high-density phase like a gas-liquid phase transition.