Restoration of chiral and $U(1)_A$ symmetries in excited hadrons

Abstract

The effective restoration of $SU(2)_L \times SU(2)_R$ and $U(1)_A$ chiral symmetries of QCD in excited hadrons is reviewed. While the low-lying hadron spectrum is mostly shaped by the spontaneous breaking of chiral symmetry, in the high-lying hadrons the role of the quark condensate of the vacuum becomes negligible and the chiral symmetry is effectively restored. This implies that the mass generation mechanisms in the low- and high-lying hadrons are essentially different. The fundamental origin of this phenomenon is a suppression of quark quantum loop effects in high-lying hadrons relative to the classical contributions that preserve both chiral and $U(1)_A$ symmetries. Microscopically the chiral symmetry breaking is induced by the dynamical Lorentz-scalar mass of quarks due to their coupling with the quark condensate of the vacuum. This mass is strongly momentum-dependent, however, and vanishes in the high-lying hadrons where the typical momentum of valence quarks is large. This physics is illustrated within the solvable chirally-symmetric and confining model. Effective Lagrangians for the approximate chiral multiplets at the hadron level are constructed which can be used as phenomenological effective field theories in the effective chiral restoration regime. Different ramifications and implications of the effective chiral restoration for the string description of excited hadrons, the decoupling of excited hadrons from the Goldstone bosons, the glueball - quark-antiquark mixing and the OZI rule violations are discussed.Comment: 64 pages. To appear in Physics Report