Chiral Symmetry and Its Restoration in QCD

Abstract

We first note the peculiar property of the pion as the pseudoscalar particle, which play the essential role in realizing the basic properties of the nuclear matter such as the density/energy saturations. Then, we introduce the notion of chirality using the Dirac equation, and show how chiralities are mixed in the massive Dirac field with an emphasis on the similarity with the Bogoliubov-Valatin theory of superconductivity. After noting the approximate chiral symmetry in QCD in the light quark sector, we introduce the notion of the spontaneous symmetry breaking, and the Nambu-Goldstone theorem. A remark is given on the U(1)$_A$ anomaly and its physical consequences. Several chiral quark models of the Nambu-Jona-Lasinio type are introduced with an emphasis to the relevance to QCD, and discuss some consequences of the models. A three-flavor linear sigma model with the determinant term is examined, and discuss the origin of the mass term of the $\eta'$ meson. A parity-doublet model for nucleons is introduced, and the current active effort is described to construct the equation of state of nuclear and neutron-star matter incorporating the parity-doubling in the baryon sector and the occurrence of the restoration of chiral symmetry in the QCD matter. An intuitive account is given on how the chiral condensate may be reduced on the basis of Hellmann-Feynman theorem. We describe some experiments to explore the chiral restoration in hot and/or dense medium, such as the pionic atoms, lepton-pair production in relativistic-heavy-ion collisions, an attempt to produce $\eta'$-mesonic nuclei, and so on.