Chiral symmetry restoration in hadron spectra

Abstract

The evidence and the theoretical justification of chiral symmetry restoration in high-lying hadrons is presented. I. CHIRAL SYMMETRY RESTORATION OF THE SECOND KINDIt 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 Π Jα of the current J α (x) (that creates from the vacuum the hadrons with the quantum numbers α) at large spacelike momenta Q 2 , 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 qq and higher dimensional condensates that are not invariant under axial transformation. At large Q 2 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 2 . At asymptotically high Q 2 , 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 2 vanishes. This is in contrast to the situation of low values of Q 2 , where the role of chiral condensates is crucial. This shows that at large spacelike momenta the correlation function becomes chirally

Eigenvalue decomposition of meson correlators

“…Analyses of hadronic spectroscopy [8,9,10,11,12,13,14] have been used to argue that excited states of the meson and baryon spectrum are effectively chirally restored, in the sense that particles of opposite parity are nearly degenerate in mass. It is argued that this "effective restoration of chiral symmetry" is a natural consequence of the soft nature of chiral symmetry breaking: generally in quantum mechanics, low excitations are sensitive to symmetry breaking but high excitations are not.…”

“…Instanton models plus lattice simulations have also been used to compute the amplitude for chiral mixing of q q correlators [6, 7]. Ref.[2] also observed that the lowest eigenvalue modes had a large autocorrelation in both density and chirality at short distance, which slowly dies away as the eigenmode rises.Analyses of hadronic spectroscopy [8,9,10,11,12,13,14] have been used to argue that excited states of the meson and baryon spectrum are effectively chirally restored, in the sense that particles of opposite parity are nearly degenerate in mass. It is argued that this "effective restoration of chiral symmetry" is a natural consequence of the soft nature of chiral symmetry breaking: generally in quantum mechanics, low excitations are sensitive to symmetry breaking but high excitations are not.…”

Parity doubling in the high baryon spectrum: near-degenerate three-quark quartets

“…By current ideas we believe that this restoration should occur for higher excitations. Glozman and collaborators [2,3,4,5,6,7,8] (see also [9]) have theoretically examined (q q) mesons, and also shown marginal empirical evidence for chiral symmetry restoration in both meson and hadron spectra, that rekindles interest on intermediate energy resonances. Chiral symmetry restoration, or more precisely, Spontaneous Chiral Symmetry Breaking Insensitivity high in the spectrum, is established as a strong prediction of the symmetry breaking pattern of QCD, and such prediction in an energy region where little else can be stated, needs to be confirmed or refuted by experiment.…”