Solution of a symmetry conserving chiral soliton model for nucleon and delta

The linear chiral soliton model is solved for nucleon and delta by constructing Fock states in the coherent pair approximation with correct spin and isospin properties. The quark configurations are those arising from theSU(2)×SU(2) coupling of three quarks in 1s-orbits. The overall Fock state is formed by the vector coupling of the quark configurations with the pion coherent state and thus avoids the use of the hedgehog ansatz. The sigma field is treated in the mean field approximation. Equations of motion for the quark, sigma and pion fields are solved in the static approximation. Soliton solutions are found with properties that are in reasonable agreement with those observed for the nucleon and delta including the axial vector coupling constant. With only components having zero and one unpaired pion in the coherent pair approximation the nucleon mass is found to be larger than that using the projected hedgehog approach.     

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.     

H-particle in a chiral quark model

In this paper we discuss the binding energy of the H-particle using a chiral quark model, where pion exchange plays an important role to reproduce the mass difference between the nucleon and Δ resonance. Since the main source for the bound H-particle is believed to be the color magnetic interaction, which gives the nucleon and Δ mass difference, it is very interesting to investigate whether the chiral quark model gives rise to the bound H-particle or not. We employ an extended resonating group method in order to take into account the possibility of a change of baryon wave functions when two baryons interact with each other. We found that a change of baryon size together with the Hamiltonian which consists of gluon, pseudoscalar meson and sigma meson exchange potentials gives rise to the bound H-particle. The binding energy is found to be about 25 MeV in a hybrid chiral quark model. Differences between the ordinary gluon dominant model and chiral quark models are also investigated. It is found that a pure chiral model has no bound state when the widely used sigma-quark coupling strength is employed.     

The Dyson-Schwinger Method of the NJL Model Beyond the Mean Field Approximation

By making use of the generating functional method we derive the Dyson-Schwinger equations in the NJL model and obtain the revised quark gap equation due to the meson dressing effects (usually called beyond the mean-field correction), and finally analyze its influence on the meson properties as well as the nucleon sigma term.     

Chiral symmetry restoration and parity mixing

We derive the expressions of the vector and axial current from a chiral Lagrangian restricted to nucleons and pions. They display mixing terms between the axial and vector currents. We study the modifications in the nuclear medium of the coupling constants of the axial current, namely the pion decay constant and the nucleonic axial one due to the requirements of chiral symmetry. We express the renormalizations in terms of the local scalar pion density. The latter also governs the quark condensate evolution and we discuss the link between this evolution and the renormalizations. In the case of the nucleon axial coupling constant this renormalization corresponds to a new type of pion exchange currents, with two exchanged pions. We give an estimate for the resulting quenching. Although moderate it helps explaining the quenching experimentally observed.     

核介质中强子性质的手征σ模型研究

采用手征σ模型描述核多体系统,考虑真空极化的影响,首先由核物质的饱和性质确定模型参数,进一步研究了强子性质在核介质中的变化。手征σ模型的研究结果给出,核子和ω介子的有效质量随核物质密度的增大而减小,但σ介子的有效质量随密度的增大而增大。这些结果与不满足手征对称性的Walecka模型结果进行了比较。计算中采用的重整化方法会对结果有一定的影响。The modification of hadron masses in nuclear medium is studied by using the chiral sigma model, which is extended to generate the omega meson mass by the sigma condensation in the vacuum in the same way as the nucleon mass. The chiral sigma model provides proper equilibrium properties of nuclear matter. It is shown that the effective masses of both nucleons and omega mesons decrease in nuclear medium, while the effective mass of sigma mesons increases at finite density in the chiral sigma model. The resuits obtained in the chiral sigma model are compared with those obtained in the Walecka model, which includes sigma and omega mesons in a non-chiral fashion.     

Dispersion Relation of σ Meson and Pion at Finite Nuclear Density in Chiral σ Model

The propagators of pion and sigma meson at a finite nuclear density and zero temperature are studied in chiral σ model. Their dispersion relations are calculated numerically in one-loop approximation. In order to avoid the so-called tachyon pole appearing in the one-loop propagators of pion and sigma meson, we regard the mass of sigma meson m_σ as a free parameter and adjust it to fit the nuclear saturation properties. For m_σ equal to 3075 MeV, the tachyon pole does not appear at the normal nuclear density. Thus the dispersion relation can be calculated in chiral σ model in one-loop level for the first time.     

Pion properties at finite isospin chemical potential with isospin symmetry breaking

Pion properties at finite temperature, finite isospin and baryon chemical potentials are investigated within the SU(2) NJL model. In the mean field approximation for quarks and random phase approximation fpr mesons, we calculate the pion mass, the decay constant and the phase diagram with different quark masses for the u quark and d quark, related to QCD corrections, for the first time. Our results show an asymmetry between μI 0 and μI 0 in the phase diagram, and different values for the charged pion mass(or decay constant) and neutral pion mass(or decay constant) at finite temperature and finite isospin chemical potential. This is caused by the effect of isospin symmetry breaking, which is from different quark masses.     

Parametrization of a nonlocal chiral quark model in the instantaneous three-flavor case. Basic formulas and tables

We describe the basic formulation of the parametrization scheme for the instantaneous nonlocal chiral quark model in the three-flavor case. We choose to discuss the Gaussian, Lorentzian-type, Woods-Saxon, and sharp cutoff (NJL) functional forms of the momentum dependence for the form factor of the separable interaction. The four parameters, light and strange quark masses and coupling strength (G _S) and range of the interaction (Λ), have been fixed by the same phenomenological inputs: pion and kaon masses and the pion decay constant and light quark mass in vacuum. The Woods-Saxon and Lorentzian-type form factors are suitable for an interpolation between sharp cutoff and soft momentum dependence. Results are tabulated for applications in models of hadron structure and quark matter at finite temperatures and chemical potentials, where separable models have been proven successfully. The text was submitted by the authors in English.     

Meson Cloud Effect on △(1232) Resonance Transition Properties with a Relativistic Quark Model Approach

Based on a relativistic quark model approach, the transition properties of the first nucleon resonance △(1232), and the coupling constants gπNN, g△πN are investigated. Tvo different vays to remove the center of mass motion are considered. The results of the relativistic approaches with and without center ofmass correction are compared with those of nonrelativistic constituent quark model. Moreover, pion meson cloud effect on these calculated observables is explicitly addressed. Better results are obtained by taking the pion meson cloud into account.     

Meson Cloud Effect on Δ(1232) Resonance Transition Properties with a Relativistic Quark Model Approach

Based on a relativistic quark model approach, the transition properties of the first nucleon resonance Δ(1232), and the coupling constants g_πNN, g_ΔπN are investigated. Two different ways to remove the center of mass motion are considered. The results of the relativistic approaches with and without center of mass correction are compared with those of nonrelativistic constituent quark model. Moreover, pion meson cloud effect on these calculated observables is explicitly addressed. Better results are obtained by taking the pion meson cloud into account.     

The equation of state of quarks and mesons in a renormalization group flow picture

Non-perturbative flow equations within an effective linear sigma model coupled to constituent quarks for two quark flavours are derived and solved. A heat kernel regularization is employed for a renormalization group improved effective potential. We determine the initial values of the coupling constants in the effective potential at zero temperature. Solving the evolution equations with the same initial values at finite temperature in the chiral limit, we find a second-order phase transition at T_c≈150 MeV. Due to the smooth decoupling of massive modes, we can directly link the low-temperature four-dimensional theory to the three-dimensional high-temperature theory. We calculate the equation of state in the chiral limit and for finite pion masses and determine universal critical exponents.     

Finite size effect on dissociation and diffusion of chiral partners in Nambu-Jona-Lasinio model

The masses of pion and sigma meson modes, along with their dissociation in the quark medium, provide detailed spectral structures of the chiral partners. Collectivity has been observed in pA and pp systems both at LHC and RHIC. In this research, we studied the restoration of chiral symmetry by investigating the finite size effect on the detailed structure of chiral partners in the framework of the Nambu-Jona-Lasinio model. Their diffusion and conduction have been studied using this dissociation mechanism. It is determined that the masses, widths, diffusion coefficients, and conductivities of chiral partners merge at different temperatures in the restoration phase of chiral symmetry. However, merging points are shifted to lower temperatures when finite size effect is introduced into the picture. The strengths of diffusions and conductions are also reduced once the finite size is introduced in the calculations.     

Massive Meson Fluctuation in NJL Model

Based on the self-consistent scheme beyond the mean-field approximation in the large N_c expansion, including current quark mass explicitly, a general scheme of SU(2) NJL model is developed. To ensure the quark self-energy expanded in the proper order of N_c,an approximate internal meson propagator is deduced, which is in order of O(l/N_c). In our scheme, adopting the method of external momentum expansion, all the Feynman diagrams are calculated in a unified way by only expanding the quark propagator. Our numerical results show that, different &om the mean-field approximation in which the explicitly chiral symmetry breaking is invisible, the effect of finite pion mass can be seen clearly when beyond the meanfield approximation.     

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     

Sea quark effects in non-topological chiral soliton models and the Nambu-Jona-Lasinio approach

The Nambu-Jona-Lasinio model (NJL) in the chiral invariant SU (2)-sector with scalar couplings is solved numerically in the Hartree approximation (zero boson loop) for baryon number B=1. To this end first the polarized vacuum solution (B=0) is constructed using appropriately parametrized non-dynamic meson fields on the chiral circle. The cut-off Λ is fixed to reproduce the pion decay constant. With this choice a full treatment of the polarized vacuum is shown in second-order gradient expansion to be equivalent to considering kinetic energies of the mesons. Solutions of the NJL model with baryon number B=1 are obtained by adding N_c=3 valence quarks to the full polarized vacuum and subjecting them to the same meson fields. If one adds the valence quarks to the kinetic energy of the mesons the usual chiral soliton model with valence quarks (CSM) is obtained. For both, NJL and CSM, the equilibrium radii of the B=1 solution are evaluated and shown to be rather close to each other. The present approach shows no vacuum instabilities. The resulting radii are different from those of the renormalized one-quark-loop model.     

Meson Properties at Finite Temperature in the Linear Sigma Model

The meson masses are investigated at finite temperature in the framework of the linear sigma model with an explicit chiral symmetry breaking term. The imaginary-time thermo-field dynamics and effective potential have been used for the calculation of the meson masses. We found that the behavior of the sigma and pion masses at finite temperature is in agreement with previous works. The critical temperature, the order of the phase transition, and the dependence of the meson fields on the temperature are discussed.     

An effective lagrangian with broken scale and chiral symmetry IV: Nucleons and mesons at finite temperature

We study the finite temperature properties of an effective chiral Lagrangian which describes nuclear matter. Thermal fluctuations in both the nucleon and the meson fields are considered. The logarithmic and square root terms in the effective potential are evaluated by expansion and resummation with the result written in terms of the exponential integral and the error function, respectively. In the absence of explicit chiral symmetry breaking a phase transition restores the symmetry, but when the pion has a mass the transition is smooth. The nucleon and meson masses as a functions of density and temperature are discussed.