An effective lagrangian with broken scale and chiral symmetry III. Mesons at finite temperature

We investigate the finite temperature behavior of the meson sector of an effective Lagrangian which describes nuclear matter. A method is developed for evaluating the logarithmic terms in the effective potential which involves expansion and resummation; the result is written in terms of the exponential integral. In the absence of explicit chiral symmetry breaking, a phase transition restores the symmetry at a temperature of 190 MeV; when the pion has a mass the transition is smooth. At a much higher temperature a first order phase transition restores scale symmetry.     

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     

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.     

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.     

Dissolving of mesons and soliton baryons in 2-dimensional gauge theories

We analyse two-dimensional fermionic models with a nonabelian gauge and chiral symmetry in the largeN limit. We show that there is a transition temperature at which the chiral symmetry is restored. At this transition temperature the meson bound states and the chiral solitons, the baryons of the model, dissolve. We interpret this as a simultaneous chiral symmetry restoration and deconfinement transition.     

Current algebra derivation of temperature dependence of hadron couplings with currents

The vector and the axial-vector meson couplings with the vector and the axial-vector currents respectively at finite temperature were obtained by calculating all the relevant one-loop Feynman graphs with vertices obtained from the effective chiral Lagrangian. On the other hand, the same couplings were also derived by applying the method of current algebras and the hypothesis of partial conservation of axial-vector currents. The latter method appears to miss certain terms; in the case of the vector meson coupling with the vector current, for example, a term containing the ρωπ coupling is missed. A similar situation would also appear for the nucleon coupling with the nucleon current. In this note we resolve these differences.     

Quark potential in a quark–meson plasma

We investigate the effect of the restoration of chiral symmetry on the quark potential in a quark–meson plasma by considering meson exchanges in the two flavor Nambu–Jona-Lasinio model at finite temperature and density. There are two possible oscillations in the chiral restoration phase; one is the Friedel oscillation due to the sharp quark Fermi surface at high density, and the other is the Yukawa oscillation driven by the complex meson poles at high temperature. The quark–meson plasma is strongly coupled in the temperature region 1≤T/T _c≤3, with T _c being the critical temperature of the chiral phase transition. The maximum coupling in this region is located at the phase transition point.     

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.     

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.     

The chiral phase transition at high baryon density from nonperturbative flow equations

We investigate the chiral phase transition at high baryon number density within the linear quark meson model for two flavors. The method we employ is based on an exact renormalization group equation for the free energy. Truncated nonperturbative flow equations are derived at nonzero chemical potential and temperature. Whereas the renormalization group flow leads to spontaneous chiral symmetry breaking in vacuum, we find a chiral symmetry restoring first order transition at high density. Combined with previous investigations at nonzero temperature, the result implies the presence of a tricritical point with long–range correlations in the phase diagram. Received: 24 August 1999 / Published online: 17 February 2000     

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.     

Effective meson lagrangian with chiral and heavy quark symmetries from quark flavor dynamics

By bosonization of an extended NJL model we derive an effective meson theory which describes the interplay between chiral symmetry and heavy quark dynamics. This effective theory is worked out in the low-energy regime using the gradient expansion. The resulting effective lagrangian describes strong and weak interactions of heavy B and D mesons with pseudoscalar Goldstone bosons and light vector and axial-vector mesons. Heavy meson weak decay constants, coupling constants and the Isgur-Wise function are predicted in terms of the model parameters partially fixed from the light quark sector. Explicit SU(3)_F symmetry breaking effects are estimated and, if possible, confronted with experiment.     

Proton decay in terms of an effective baryon-lepton transition

We calculate the two-body decay rates for the hadronic and electromagnetic decays of proton and neutron in terms of the effective baryon-lepton transition matrix element. Further ingredients like PCAC and vector meson dominance are used. We compute these transition amplitudes within the framework of a relativistic quark model involving Bethe-Salpeter amplitudes and present the nucleon lifetimes and branching ratios of various decay modes for three different grand unification models.     

Effective Lagrangian Approach to pion photoproduction from the nucleon

We present a pion photoproduction model on the free nucleon based on an Effective Lagrangian Approach (ELA) which includes the nucleon resonances (Δ(1232), N(1440), N(1520), N(1535), Δ(1620), N(1650), and Δ(1700)), in addition to Born and vector meson exchange terms. The model incorporates a new theoretical treatment of spin-3/2 resonances, first introduced by Pascalutsa, avoiding pathologies present in previous models. Other main features of the model are chiral symmetry, gauge invariance, and crossing symmetry. We use the model combined with modern optimization techniques to assess the parameters of the nucleon resonances on the basis of world data on electromagnetic multipoles. We present results for electromagnetic multipoles, differential cross-sections, asymmetries, and total cross-sections for all one pion photoproduction processes on free nucleons. We find overall agreement with data from threshold up to 1 GeV in laboratory frame.     

Mesons in the Quark Model of Superconductivity Type

On the basis of a quark model of superconductivity type, effective chiral Lagrangians are obtained for strong, electromagnetic and weak interactions of scalar, pseudoscalar, vector and axial vector meson nonets at low energies. The spontaneous breaking of chiral symmetry plays an important role. The form factors of strong and electromagnetic vertices, meson masses and different types of meson decaysare discussed.     

Vector manifestation of chiral symmetry

We propose "vector manifestation" (VM) of the Wigner realization of chiral symmetry in which the symmetry is restored at the critical point by the massless degenerate pion (and its flavor partners) and the rho meson (and its flavor partners) as the chiral partner, in sharp contrast to the traditional manifestation á la the linear sigma model where the symmetry is restored by the degenerate pion and the scalar meson. The application to the chiral phase transition of large N(f) QCD is performed using the hidden local symmetry Lagrangian. Combined with the Wilsonian matching proposed recently, VM determines the critical number of massless flavors N(f) approximately equal to 5 without much ambiguity.     

Complete set of electromagnetic corrections to the nucleon mass in the Nambu-Jona-Lasinio model

We show how to derive the complete set of electromagnetic corrections to the Nambu-Jona-Lasinio3 (NJL) model of the nucleon. Our results enable an accurate estimate of the electromagnetic contribution to the neutron-proton mass difference within this model. At the same time, our procedure demonstrates the way to calculate the complete set of meson corrections to the NJL model that maintains chiral symmetry.     

Relationship between the symmetry energy and the single-nucleon potential in isospin-asymmetric nucleonic matter

When skyrmions representing nucleons are put on crystal lattice and compressed to simulate high density, there is a transition above the normal nuclear matter density (n₀) from a matter consisting of skyrmions with integer baryon charge to a state of half-skyrmions with half-integer baryon charge. We exploit this observation in an effective field theory framework to access dense baryonic system. We find that the topology change involved in the transition implies changeover from a Fermi liquid structure to a non-Fermi liquid with the chiral condensate in the “melted-off” nucleon. The ～ 80% of the nucleon mass that remains “unmelted”, invariant under chiral transformation, points to the possible origin of the (bulk of) proton mass that is not encoded in the standard mechanism of spontaneously broken chiral symmetry. The topology change engenders a drastic modification of the nuclear tensor forces, thereby non-trivially affecting the EoS, in particular, the symmetry energy, for compact star matter. It brings in stiffening of the EoS needed to accommodate a neutron star of ～ 2 solar mass. The strong effect on the EoS in general and in the tensor force structure in particular will also have impact on processes that could be measured at RIB-type accelerators.