Chiral symmetry in nuclei and nuclear matter

We discuss a model for hadrons based on chiral symmetry, Hadronic masses are generated via spontaneous symmetry breaking. Within this model we investigate nuclear matter and finite nuclei. Since the model is SU_F(3)-symmetric we are also able to investigate hypernuclei. Numerical results in comparison with experimental data are presented.     

Chiral symmetry in quarkyonic matter

The 1/N _c expansion classifies nuclearmatter, deconfined quark matter, and Quarkyonic matter in low temperature region. We investigate the realization of chiral symmetry in Quarkyonic matter by taking into account condensations of chiral particle-hole pairs. It is argued that chiral symmetry and parity are locally violated by the formation of chiral spirals, $\left\langle {\bar \psi exp\left( {2i\mu _q z\gamma ^0 \gamma ^z } \right)\psi } \right\rangle$ . An extension to multiple chiral spirals is also briefly discussed.     

Chiral symmetry breaking in dense matter

The quark condensate in nuclear matter is studied. We relate it to the nuclear sigma commutator, and then treat it as sigma commutator for quasi- particles in a self-consistent way. We find that the deviation from the linear expression is large at high density. Received: 20 November 1997 / Revised version: 24 February 1998 / Published online: 16 September 1998     

Chiral symmetry restoration in excited hadrons and dense matter

We overview two interconnected topics： possible effective restoration of chiral symmetry in highly excited hadrons and possible existence of confined but chirally symmetric matter at low temperatures and high densities.     

Chiral symmetry restoration in excited hadrons and dense matter

We overview two interconnected topics: possible effective restoration of chiral symmetry in highly excited hadrons and possible existence of confined but chirally symmetric matter at low temperatures and high densities.     

Chiral symmetry and light resonances in hot and dense matter

We present a study of the π π scattering amplitude in the σ and ρ channels at finite temperature and nuclear density within a chiral unitary framework. Meson resonances are dynamically generated in our approach, which allows us to analyze the behavior of their associated scattering poles when the system is driven towards chiral-symmetry restoration. Medium effects are incorporated in three ways: (a) by thermal corrections of the unitarized scattering amplitudes, (b) by finite nuclear-density effects associated to a renormalization of the pion decay constant, and complementarily (c) by extending our calculation of the scalar–isoscalar channel to account for finite nuclear-density and temperature effects in a microscopic many-body implementation of pion dynamics. Our results are discussed in connection with several phenomenological aspects relevant for nuclear-matter and heavy-ion collision experiments, such as ρ mass scaling versus broadening from dilepton spectra and chiral restoration signals in the σ channel. We also elaborate on the molecular nature of π π resonances.     

The symmetry energy in nuclei and in nuclear matter

We discuss to what extent information on ground-state properties of finite nuclei (energies and radii) can be used to obtain constraints on the symmetry energy in nuclear matter and its dependence on the density. The starting point is a generalized Weizs?cker formula for ground-state energies. In particular, effects from the Wigner energy and shell structure on the symmetry energy are investigated. Strong correlations in the parameter space prevent a clear isolation of the surface contribution. Use of neutron skin information improves the situation. The result of the analysis appears consistent with a rather soft density dependence of the symmetry energy in nuclear matter.     

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.     

Chiral symmetry breaking and pion properties at finite temperatures

Spontaneous and explicit chiral symmetry breaking is analyzed in Coulomb gauge QCD at finite temperatures, using an instantaneous approximation for the quark interaction and incorporating confinement through a running coupling constant. The thermodynamics of the quarks is treated approximatively by assuming that the momentum-dependent constituent quark mass sets the scale for thermodynamic fluctuations of colour singlet excitations. We investigate the class of a temperature independent and a temperature dependent interaction between quarks. In the chiral limit both temperature independent and a smooth temperature dependent interaction yields a second order chiral phase transition with critical exponents close to the values for a BCS super-conductor. For explicit chiral symmetry breaking we find a nearly constant pion mass below the transition temperature, but a strongly overdamped mode above. For a first order deconfining transition in the gluonic sector also the quark sector shows a first order chiral phase transition. The relevance of our results for relativistic heavy ion collisions is briefly discussed.     

Analytical relations between nuclear symmetry energy and single-nucleon potentials in isospin asymmetric nuclear matter

Using the Hugenholtz-Van Hove theorem, we derive general expressions for the quadratic and quartic symmetry energies in terms of the isoscalar and isovector parts of single-nucleon potentials in isospin asymmetric nuclear matter. These expressions are useful for gaining deeper insights into the microscopic origins of the uncertainties in our knowledge on nuclear symmetry energies especially at supra-saturation densities. As examples, the formalism is applied to two model single-nucleon potentials that are widely used in transport model simulations of heavy-ion reactions.     

Topological symmetry breakdown and quark confinement

The manner by which topological symmetry breakdown leads to confinement in a non-Abelian gauge theory is discussed.     

Isospin symmetry breaking in relativistic mean-field theories of nuclear matter

Taking into account σ-, ω- and ρ-mesons, an expression for the interaction function of quasiparticles in non-isoscalar nuclear matter is derived. This medium resembles a state of broken symmetry, which gives rise to a Goldstone boson. It obtains nonzero mass, if the electromagnetic interaction is included. Treating the electromagnetic field self-consistently, dressing factors for the single-particle current in non-isoscalar nuclear matter are determined. As an application, the effective angular momentum g-factor for a single nucleon added at the Fermi surface is calculated.     

Chiral symmetry restoration and properties of Goldstone bosons at finite temperature

We study chiral symmetry restoration by analyzing thermal properties of QCD's(pseudo-) Goldstone bosons, especially the pion. The meson properties are obtained from the spectral densities of mesonic imaginary-time correlation functions. To obtain the correlation functions, we solve the Dyson-Schwinger equations and the inhomogeneous Bethe-Salpeter equations in the leading symmetry-preserving rainbow-ladder approximation. In chiral limit, the pion and its partner sigma degenerate at the critical temperature begin{document}$T_{rm c}$end{document}. At begin{document}$T gtrsim T_{rm c}$end{document}, it was found that the pion rapidly dissociates, which signals deconfinement phase transition. Beyond the chiral limit, the pion dissociation temperature can be used to define the pseudo-critical temperature of the chiral phase crossover, which is consistent with that obtained by the maximum point of chiral susceptibility. A parallel analysis for kaon and pseudoscalar begin{document}$ sbar{s} $end{document} suggests that heavy mesons may survive above begin{document}$T_{rm c}$end{document}.     

Chiral symmetry and nucleon-nucleon scattering

The contributions of the minimal chiral two-pion exchange nucleon-nucleon potential for some selected observables are studied by means of the variable phase method. We conclude that chiral symmetry is responsible for important cancellations, which are related to those occurring in pion-nucleon scattering.     

Neutron skin thickness and nuclear matter properties

Linear correlations are found among the isovector nuclear matter properties in both the Skyrme-Hartree-Fock (SHF) and the relativistic mean-field (RMF) models. In addition, we found a kind of correlation between the isovector nuclear matter properties and the incompressibility in the SHF model. The Skyrme parameters are related analytically to nuclear matter properties with the Thomas—Fermi approximation. By using a linear correlation between the neutron skin thickness and the pressure of the neutron matter in the SHF model, we show that the neutron skin thickness of ²⁰⁸Pb gives crucial information about not only the neutron equation of state but also the isovector nuclear matter properties and the parametrization of Skyrme interaction. The text was submitted by the authors in English.     

Chiral symmetry and excited baryons

An approach to baryons in the framework of the microscopic generalized Nambu-Jona-Lasinio chiral potential quark model is considered and quite general arguments are given in favor of the effective restoration of the chiral symmetry in excited baryons. The text was submitted by the authors in English.     

Chiral symmetry and lattice QCD

Four lectures about chiral symmetry and dynamical fermions in QCD. 1) Chiral symmetry in continuum QCD with an eye toward lattice simulations. 2) Lattice fermions with exact chiral symmetry: staggered fermions, fermions in five dimensions, chiral fermions in four dimensions. 3) A typical lattice simulation from beginning to end: the simulation algorithm, designing observables to measure some desired quantity, analyzing the data. 4) Recent lattice results relevant to chiral symmetry: a mini-review.