Chiral multiplets versus parity doublets in highly excited baryons

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 restoration for these states. We argue how the idea of chiral symmetry restoration high in the spectrum is consistent with the concept of quark-hadron duality. If chiral symmetry is effectively restored for highly lying states, then the baryons should fall into representations of ${\mathrm{SU}(2)}_{L}\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}(2)}_{R}$ that are compatible with the given parity of the states---the parity-chiral multiplets. We classify all possible parity-chiral multiplets: (i) $(1/2,0)\ensuremath{\bigoplus}(0,1/2)$ that contain parity doublet for nucleon spectrum, (ii) $(3/2,0)\ensuremath{\bigoplus}(0,3/2)$ consists of the parity doublet for delta spectrum, (iii) $(1/2,1)\ensuremath{\bigoplus}(1,1/2)$ contains one parity doublet in the nucleon spectrum and one parity doublet in the delta spectrum of the same spins that are degenerate in mass. Here we show that the available spectroscopic data for nonstrange baryons in the $\ensuremath{\sim}2 \mathrm{GeV}$ range are consistent with all possibilities, but the approximate degeneracy of parity doublets in nucleon and delta spectra support the latter possibility with excited baryons approximately falling into $(1/2,1)\ensuremath{\bigoplus}(1,1/2)$ representation of ${\mathrm{SU}(2)}_{L}\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}(2)}_{R}$ with approximate degeneracy between positive and negative parity N and $\ensuremath{\Delta}$ resonances of the same spin.