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.     

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     

Lowering Critical Temperature in the Extended Quark Sigma Model at Finite Temperature

A phase transition, a critical temperature, and meson masses are studied in the extended quark sigma model, in which the effective mesonic potential is extended to include eighth-order mesonic interactions. The second derivative of the effective mesonic potential is applied to calculate the effective sigma and pion masses as functions of temperature. We find that the critical temperature assumes a lower value in comparison with that of original quark sigma model. A comparison with recent calculations of lattice QCD is introduced. The behavior of the phase transition remains unchanged when the higher-order mesonic interactions are included. We find that the spontaneous symmetry-breaking condition is necessary to satisfy the Goldstone theorem at low temperatures.     

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.     

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.     

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.     

N-Midpoint Rule for Calculating the Effective Mesonic Potential at Finite Temperature

The temperature dependence of meson properties is studied by using the effective potential formalism. The effective mesonic potential is numerically calculated using the n-midpoint rule at finite temperature. The meson masses, the phase transition, and the energy density are investigated as functions of temperature. The obtained results are compared with those from other works. The present technique is compared with the Hartree approximation and the imaginary time formalism. We conclude that the calculated effective potential successfully predicts the meson properties, the phase transition, and the critical temperature in comparison with other models and avoid the difficulty that found in the Hartree approximation which depends on cutoff technique.     

Electromagnetic radiation from hot and dense hadronic matter

The modifications of hadronic masses and decay widths at finite temperature and baryon density are investigated using a phenomenological model of hadronic interactions in the Relativistic Hartree Approximation. We consider an exhaustive set of hadronic reactions and vector meson decays to estimate the photon emission from hot and dense hadronic matter. The reduction in the vector meson masses and decay widths is seen to cause an enhancement in the photon production. It is observed that the effect of p-decay width on photon spectra is negligible. The effects on dilepton production from pion annihilation are also indicated.     

Strong coupling expansion of meson propagator in finite temperature lattice gauge theories

We consider Susskind fermions on a (d+1)-dimensional lattice interacting with aU(n) gauge field at finite temperature. We calculate the meson propagator in an expansion in 1/g ² and 1/d and determine the meson masses. To the order considered the results are identical to those obtained at zero temperature.     

Nuclear Matter in a Chiral SU(3) Quark Mean-Field Model

A quark meson coupling model based on SU(3)_L×SU(3)_R symmetry and scale invariance is proposed. The quarks and mesons get masses through symmetry broken. We apply this SU(3) chiral constituent quark model to investigating the nuclear matter at finite temperature and density. The effective baryon masses, compression modulus and hyperon potentials are all reasonable. The critical temperature of liquid-gas phase transition is also calculated in this model.     

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.     

Finite-temperature effect on broken UA(1) symmetry and the η′ mass

The U_A(1) symmetry-breaking effective lagrangian mediated by the instanton is calculated in the semiclassical approximation at finite temperature. It is found that the strength of the effective vertex decreases with increasing temperature up to the QCD scale. Also, we discuss the possible variation of the η′ and other pseudoscalar meson masses.     

Quark matter and meson properties in a Nonlocal SU(3) chiral quark model at finite temperature

We study the finite temperature behavior of light scalar and pseudoscalar meson properties in the context of a three-flavor nonlocal chiral quark model. The model includes mixing with active strangeness degrees of freedom, and takes care of the effect of gauge interactions by coupling the quarks with a background color field. We analyze the chiral restoration and deconfinement transitions, as well as the temperature dependence of meson masses, mixing angles, and decay constants.     

Low energy theorems in a nonlocal chiral quark model at finite temperature

We solve the Dyson equation and the Bethe-Salpeter equation for a nonlocal effective quark interaction kernel which is instantaneous and separable. The momentum-dependent dynamical quark mass, the scalar and pseudoscalar meson masses, the pion decay constant and the quark meson coupling constant are calculated at finite temperature in the Hartree approximation for the quark self energy. We obtain relations between these quantities, which coincide to leading order in the current quark mass (m ₀/Δm) with the basic low energy theorems: the Goldstone theorem, the Gell-Mann-Oakes-Renner relation and the Goldberger-Treimann relation at finite temperature. A formula for the σ?π mass gap is obtained which exhibits an additional contribution from the momentum dependence of the quark mass.     

Properties of vector and axial-vector mesons from a generalized Nambu-Jona-Lasinio model

We construct a generalized Nambu-Jona-Lasinio lagrangian including scalar, pseudoscalar, vector and axial-vector mesons. We specialize to the two-flavor case. The properties of the structured vacuum as well as meson masses and coupling constants are calculated giving an overall agreement within 20% of the experimental data. We investigate the meson properties at finite density. In contrast to the mass of the scalar σ-meson, which decreases sharply with increasing density, the vector meson masses are almost independent of density. Furthermore, the vector-meson-quark coupling constants are also stable against density changes. We point out that these results imply a softening of the nuclear equation of state at high densities. Furthermore, we discuss the breakdown of the KFSR relation on the quark level as well as other deviations from phenomenological concepts such as universality and vector meson dominance.     

Behavior of the topological susceptibility at finite T and <Emphasis Type="Italic">μ</Emphasis> and signs of restoration of chiral symmetries

We investigate the possible restoration of chiral and axial symmetries across the phase transition at finite temperature and chemical potential, by analyzing the behavior of several physics quantities, such as the quark condensates and the topological susceptibility, the respective derivatives with respect to the chemical potential, and the masses of meson chiral partners. We discuss whether only chiral symmetry or both chiral and axial symmetries are restored and what the role of the strange quark is. The results are compared with recent lattice results.     

Properties of lightest mesons at finite temperature and quark/baryon chemical potential in the instanton model of the QCD vacuum

The paper is focused on calculating the finite temperature and quark/baryon chemical potential dependencies of the quark condensate and the π-and σ-meson masses in the subcritical region in the instanton model of the QCD vacuum. The impact of phononlike excitation of instanton liquid on the characteristics of the σ meson in such an environment is also examined.     

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.     

Lightest scalar in the SU(L)2 x SU(R)2 linear sigma model

We consider the lightest scalar meson in the frame of the SU(L)2 x SU(R)2 linear sigma model, keeping in mind that this model could be the low energy realization of two-flavor QCD. We show that the sigma field is described by its four-quark component at least in the sigma resonance energy (virtuality) region and the sigma-->gammagamma decay is the four-quark transition. We emphasize that residues of the sigma pole in the pipi-->pipi and gammagamma-->pipi amplitudes do not give an idea about the sigma meson nature, and the progress in studying the sigma meson production mechanisms in different processes could essentially further us in understanding its nature.