QCD symmetries in excited hadrons

TL;DR

This paper reviews recent progress on chiral and $U(1)_A$ symmetry restoration in excited hadrons, highlighting predictions, experimental correlations, and a solvable model illustrating chiral symmetry behavior in meson spectra.

Contribution

It introduces general chiral symmetry arguments predicting decay suppression, correlates these with experimental data, and presents a solvable 4D model demonstrating chiral restoration patterns.

Findings

Decay into Nπ is forbidden in strict chiral restoration.

Strong correlation between decay data and parity doublet patterns.

Chiral restoration occurs rapidly with increasing angular momentum J.

Abstract

Recent developments for chiral and $U(1)_A$ restorations in excited hadrons are reviewed. We emphasize predictions of the chiral symmetry restoration scenario for axial charges and couplings to Goldstone bosons. Using very general chiral symmetry arguments it is shown that strict chiral restoration in a given excited nucleon forbids its decay into the $N \pi$ channel. We confront this prediction with the $N^*N\pi$ coupling constants extracted from the decay widths and observe a 100 % correlation of these data with the spectroscopic parity doublet patterns. These results suggest that the lowest approximate chiral parity doublet is the $N(1440) - N(1535)$ pair. In the meson sector we discuss predictions of the chiral symmetry restoration for still missing states and a signature of the higher symmetry observed in new $\bar p p$ data. We conclude with the exactly solvable chirally symmetric and confining model that can be considered as a generalization of the 1+1 dimensional 't Hooft model to 4 dimensions. Complete spectra of $\bar q q$ mesons demonstrate a fast chiral restoration with increasing $J$ and a slow one with increasing $n$.