Pion interaction in nuclear matter and chiral symmetry restoration

This paper is devoted to the interplay between p-wave, s-wave pion-nucleon/nucleus interaction and in-medium pion-pion interaction with special emphasis on the role of the nuclear pionic scalar density driving a large amount of chiral symmetry restoration. In particular we show that the πNN coupling constant and the Goldberger-Treiman relation are preserved in the nuclear medium under certain conditions. We also discuss the related problem of the in-medium pion-pion strength function.     

Phase transitions in a saturating chiral theory of nuclear matter

The formalism of a relativistically covariant saturating chiral field theory of nuclear matter is developed in the mean field approximation, and some of the properties are studied. The theory possesses the normal saturated state of nuclear matter. The finite temperature properties are examined. A normal gas-liquid phase equilibrium region exists below T ≈ 23MeV. The maximum mass for a neutron star is calculated, and it lies well above the lower bound set by observation. In the high-temperature regime, there is a second minimum in the free energy, on which branch the effective baryon mass is very small. However, this branch is everywhere mechanically unstable, and so is not a realizable state of the theory. Above a certain critical temperature there is in fact no stable state at low baryon density. There is no density or temperature regime where chiral symmetry is restored.     

Nucleon propagation through nuclear matter in chiral effective field theory

We treat the propagation of a nucleon in nuclear matter by evaluating the ensemble average of the two-point function of the nucleon currents in the framework of chiral effective field theory. We first derive the effective parameters of the nucleon to one loop. The resulting formula for the effective mass has been known since before and gives an absurd value at normal nuclear density. We then modify it following Weinberg’s method for the two-nucleon system in the effective theory. Our results for the effective mass and the width of the nucleon are compared with those in the literature. PACS 11.30.Rd; 12.38.Lg; 12.39.Fe; 24.85.+p     

Saturating chiral field theory for the study of nuclear matter in the relativistic Hartree approximation

The bulk properties of nuclear matter are studied by considering a chirally invariant lagrangian which contains an interaction term involving scalar and vector mesons, of the form (apart from a numerical factor) used by Boguta. The calculation is performed in the relativistic Hartree approximation which includes the baryon vacuum fluctuation correction.     

Single-particle potential in a chiral approach to nuclear matter including short-range NN-terms

We extend a recent chiral approach to nuclear matter of Lutz et al.Phys. Lett. B 474, 7 (2000)) by calculating the underlying (complex-valued) single-particle potential U(p, k _f) + iW(p, k _f). The potential for a nucleon at the bottom of the Fermi sea, U(0, k _f0) = - 20.0 MeV, comes out as much too weakly attractive in this approach. Even more seriously, the total single-particle energy does not rise monotonically with the nucleon momentum p, implying a negative effective nucleon mass at the Fermi surface. Also, the imaginary single-particle potential, W(0, k _f0) = 51.1 MeV, is too large. More realistic single-particle properties together with a good nuclear-matter equation of state can be obtained if the short-range contributions of non-pionic origin are treated in mean-field approximation (i.e. if they are not further iterated with 1π-exchange). We also consider the equation of state of pure neutron matter ˉE_n(k _n) and the asymmetry energy A(k _f) in that approach. The downward bending of these quantities above nuclear-matter saturation density seems to be a generic feature of perturbative chiral pion-nucleon dynamics. Received: 19 December 2002 / Accepted: 11 February 2003 / Published online: 15 April 2003     

Effective quark masses in the chiral limit

The behavior of effective, scale dependent quark masses in the chiral limit is studied using the operator product expansion. Their relation to current and constituent quark masses is clarified. Current correlation functions are examined as an example of separating effects of spontaneous and explicit chiral symmetry breaking.     

Hypernuclei and nuclear matter in a chiral SU(3) RMF model

We develop a chiral SU(3) RMF model for octet baryons, as an extension of the recently developed chiral SU(2) RMF model with logarithmic sigma potential. For Σ -meson coupling, strong repulsion (SR) and weak repulsion (WR) cases are examined in existing atomic shift data of Σ^- . In both of these cases, we need an attractive pocket of a few MeV depth around nuclear surface.     

Dense nuclear matter: Landau Fermi-liquid theory and chiral Lagrangian with scaling

The relation between the effective chiral Lagrangian whose parameters scale according to Brown and Rho scaling (“BR scaling”) and Landau Fermi-liquid theory for hadronic matter is discussed in order to make a basis to describe the fluctuations under the extreme condition relevant to neutron stars. It is suggested that BR scaling gives the background around which the fluctuations are weak. A simple model with BR-scaled parameters is constructed and reproduces the properties of the nuclear ground state at normal nuclear matter density successfully. It shows that the tree level in the model Lagrangian is enough to describe the fluctuations around BR-scaled background. The model Lagrangian is consistent thermodynamically and reproduces relativistic Landau Fermi-liquid properties. Such points are important for dealing with hadronic matter under extreme condition. On the other hand, it is shown that the vector current obtained from the chiral Lagrangian is the same as that obtained from Landau–Migdal approach. We can determine the Landau parameter in terms of BR-scaled parameter. However, these two approaches provide different results, when applied to the axial charge. The numerical difference is small. It shows that the axial response is not included properly in the Landau–Migdal approach.     

Low-energy limit of chiral meson theory

Based on a phenomenologically successful effective chiral theory of pseudoscalar, vector, and axial-vector mesons, all the coefficients of the chiral perturbation theory are predicted. There is no new adjustable parameter in these predictions. Up to O(m ² _q) the formulas of the masses of the pseudoscalar mesons are the same as the ones obtained by ChPT. Received: 31 August 2000 / Accepted: 16 March 2001     

High density matter in the chiral bag model

We estimate the properties of dense matter in a chiral bag model, using methods previously employed for skyrmions. The bag is stabilized by the Casimir energy, and the chiral field outside the bag is described by Skyrme's model. We find that the bag radius decreases with increasing density, but that the fraction of space filled by bags increases. We also investigate the transition to quark matter.     

On the chiral phase transition in hadronic matter

A qualitative analysis of the chiral phase transition in QCD with two massless quarks and nonzero baryon density is performed. It is assumed that, at zero baryonic density, ρ=0, the temperature phase transition is of the second order. Due to a specific power dependence of baryon masses on the chiral condensate, the phase transition becomes of the first order at the temperature T=T_ph(ρ) for ρ>0. At temperatures T_cont(ρ)> _T>_Tph(ρ), there is a mixed phase consisting of the quark phase (stable) and the hadron phase (unstable). At the temperature T=T_cont(ρ), the system experiences a continuous transition to the pure chirally symmetric phase.     

Quark condensate in the nuclear matter

We calculate the quark condensate in the nuclear matter, taking into account the single-pion and two-pion exchanges between nucleons. We find the dependence of the averaged value of the quark operator¯qq on the density of the matterρ. At very low density the nonlinear terms are proportional toρ ² and increase the tendency to restoration of the chiral symmetry. At larger values of density the account of interaction inside the matter slower down the restoration of chiral symmetry compared to the gas approximation law. The leading nonlinear term in Fermi momentum power expansion becomes of the orderρ ^4/3 . The value of the condensate at the saturation value of density is obtained. The role of multinucleon effects is analyzed.     

Skyrmion in nuclear matter

The properties of Skyrmions in finite nuclei are considered. The deformation effect is taken into account through the external-field-induced distortion of the profile function of a chiral field. The masses of classical Skyrmions and the distribution of their baryon number versus the Skyrmion position within a nucleus are discussed.     

The chiral limit of quenched lattice QCD

We investigate the low mass properties of our quenched QCD data for the range of beta values: 5.70, 6.00, 6.15 and 6.30. The chiral condensate, the ground-state meson spectrum and the scaling behaviour of various quantities are examined. A criterion for assessing at what value of the quark mass finite lattice effects become intolerable is suggested.