Chiral Symmetry Restoration in Hadron

The evidence and the theoretical justification of chiral symmetry restoration in high-lying hadrons is presented. I. CHIRAL SYMMETRY RESTORATION OF THE SECOND KIND It has recently been suggested that the parity doublet structure seen in the spectrum of highly excited baryons may be due to effective chiral symmetry restoration for these states [1]. This phenomenon can be understood in very general terms from the validity of the operator product expansion (OPE) in QCD at large space-like momenta and the validity of the dispersion relation for the two-point correlator, which connects the spacelike and timelike regions (i.e. the validity of Källen-Lehmann representation) [2,3]. Consider a two-point correlator ΠJα of the current Jα(x) (that creates from the vacuum the hadrons with the quantum numbers α) at large spacelike momenta Q, where the language of quarks and gluons is adequate and where the OPE is valid. The only effect that chiral symmetry breaking can have on the correlator is through the nonzero value of condensates associated with operators which are chirally active (i.e. which transform nontrivially under chiral transformations). To these belong 〈q̄q〉 and higher dimensional condensates that are not invariant under axial transformation. At large Q only a small number of condensates need be retained to get an accurate description of the correlator. Contributions of these condensates are suppressed by inverse powers of Q. At asymptotically high Q, the correlator is well described by a single term—the perturbative term. The essential thing to note from this OPE analysis is that the perturbative contribution knows nothing about chiral symmetry breaking as it contains no chirally nontrivial condensates. In other words, though the chiral symmetry is broken in the vacuum and all chiral noninvariant condensates are not zero, their influence on the correlator at asymptotically high Q vanishes. This is in contrast to the situation of low values of Q, where the role of chiral condensates is crucial. This shows that at large spacelike momenta the correlation function becomes chirally symmetric. In other words, two correlators ΠJ1(Q ) and ΠJ2(Q ), where J1 = UJ2U , Invited talk given at International School on Nuclear Physics ”Quarks in Hadrons and Nuclei”,16th -24th September 2002, Erice/Sicily/Italy; to appear in Progr. Part. Nucl. Phys., vol.