Unified study of nucleon and $\Delta$ baryon spectra and their strong decays with chiral dynamics

TL;DR

This study uses a unified quark model with chiral dynamics to analyze the mass spectra and strong decays of nucleon and Delta resonances, explaining mass orderings, configuration mixing, and the nature of missing resonances.

Contribution

It provides a comprehensive framework that simultaneously describes spectra and decay properties, explaining phenomena like mass reversal and the weak coupling of certain resonances.

Findings

Good description of decay properties of nucleon and Delta resonances.

Explanation of mass reversal between specific resonances.

Identification of weakly coupled 'missing' resonances with potential for detection in $N extpi extpi$ channels.

Abstract

In this work we systematically study both the mass spectra and strong decays of the nucleon and $\Delta$ resonances up to the $N=2$ shell within a unified quark model framework with chiral dynamics. In this framework we achieve a good description of the strong decay properties of the well-established nucleon and $\Delta$ resonances. Meanwhile, the mass reversal between $N(1440)1/2^{+}$ as the first radial excitation state and the $1P$-wave nucleon resonances can be explained. We show that the three-body spin-orbit potential arising from the one-gluon exchange can cause a large configuration mixing between $N(1520)3/2^-$ and $N(1700)3/2^-$, and is also responsible for the large splitting between $\Delta(1600)1/2^-$ and $\Delta(1700)3/2^-$. Some of these baryon resonances turn to weakly couple to the $N\pi$, $N\eta$, $K\Lambda$, and $K\Sigma$ channels, which may answer the question why they have not been established in these channels via the $\pi N$ and $\gamma N$ scatterings. It shows that these ``missing resonances" may have large potentials to be established in the $N\pi\pi$ final state due to their large decay rates into either the $\Delta(1232)$ or $1P$-wave nucleon resonances via the pionic decays. Further experimental search for their signals in charmonium decays at BESIII is thus strongly recommended.