Does One Observe Chiral Symmetry Restoration in Baryon Spectrum?

Abstract

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. We review the recent developments in this field. We demonstrate with a simple quantum-mechanical example that it is a very natural property of quantum systems that a symmetry breaking effect which is important for the low-lying spectrum of the system, can become unimportant for the highly-lying states; the highly lying states reveal a multiplet structure of nearly degenerate states. Using the well established concepts of quark-hadron duality, asymptotic freedom in QCD and validity of the operator product expansion in QCD we show that the spectral densities obtained with the local currents that are connected to each other via chiral transformations, very high in the spectrum must coincide. Hence effects of spontaneous breaking of chiral symmetry in QCD vacuum that are crucially important for the low-lying spectra, become irrelevant for the highly-lying states. Then to the extent that identifiable hadronic resonances still exist in the continuum spectrum at high excitations this implies that the highly excited hadrons must fall into multiplets associated with the representations of the chiral group. We demonstrate that this is indeed the case for meson spectra in the large N c limit. All possible parity-chiral multiplets are classified for baryons and it is demonstrated that the existing data on highly excited N and ∆ states at masses of 2 GeV and higher is consistent with approximate chiral symmetry restoration. However new experimental studies are needed to achieve any definitive conclusions.

Chiral mirror-baryon-meson model and nuclear matter beyond mean-field approximation

“…To evaluate (20) one has to specify an Ansatz for the effective action. Here we work in the local potential approximation (LPA) where the only scale-dependence stems from the effective potential, and correspondingly we use…”

Parity doublets in the baryon spectrum

“…There is a heuristic argument that supports this idea [ 4]. The argument is based on the well controlled behaviour of the two-point function (2) at the large space-like momenta Q 2 = −q 2 , where the operator product expansion (OPE) is valid and where all nonperturbative effects can be absorbed into condensates of different dimensions [ 14].…”

“…Now we will consider chiral multiplets of excited baryons [ 4]. The only possible representations of the SU(2) L × SU(2) R group that are invariant under parity are (1/2, 0) ⊕ (0, 1/2), (1/2, 1) ⊕ (1, 1/2) and (3/2, 0) ⊕ (0, 3/2).…”

“…As a consequence we do not observe any chiral or U(1) A multiplets low in the hadron spectrum. The upper part of both baryon [ 3,4] and meson [ 5] spectra almost systematically exhibits multiplets of the chiral and U(1) A groups (for a pedagogical overview see [ 6]), though a careful experimental exploration of high-lying spectra must be done for a final conclusion. This phenomenon is referred to as effective chiral symmetry restoration or chiral symmetry restoration of the second kind.…”

Chiral symmetry restoration in hadron spectra

“…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.…”