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

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.

Comments: 26 pages, 7 figures, 12 tables