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

TL;DR

This paper presents a calculation demonstrating that high-spin baryons form near-degenerate quartets of states with opposite parity, supporting the concept of chiral symmetry restoration at high energies.

Contribution

It introduces the first calculation of excited baryons with a chirally symmetric Hamiltonian, revealing the formation of parity doublets and quartets in the high baryon spectrum.

Findings

High-spin Delta states group into quartets with two states of each parity.

Splittings within quartets decrease to zero at high energies.

A 50 MeV mass measurement accuracy can confirm chiral symmetry restoration.

Abstract

We report on the first calculation of excited baryons with a chirally symmetric Hamiltonian, modeled after Coulomb gauge QCD (or upgraded from the Cornell meson potential model to a field theory in all of Fock-space) showing the insensitivity to chiral symmetry breaking. As has recently been understood, this leads to doubling between two hadrons of equal spin and opposite parity. As a novelty we show that three-quark, for example Delta states, group into quartets with two states of each parity, all four states having equal angular momentum J. Diagonalizing the chiral charge expressed in terms of quarks we show that the quartet is slightly split into two parity doublets by the tensor force, all splittings decreasing to zero high in the spectrum. Our specific calculation is for the family of maximum-spin excitations of the Delta baryon. We provide a model estimate of the experimental accuracy needed to establish Chiral Symmetry Restoration in the high spectrum. We suggest that a measurement of masses of high-partial wave Delta resonances with an accuracy of 50 MeV should be sufficient to unambiguously establish the approximate degeneracy, and test the concept of running quark mass in the infrared.