Compositeness of baryonic resonances: Applications to the Delta(1232), N(1535), and N(1650) resonances

TL;DR

This paper develops a method to quantify the meson-baryon molecular structure of baryonic resonances and applies it to analyze the compositeness of specific resonances using scattering data.

Contribution

It introduces a relation between scattering amplitude residues and two-body wave functions to define and evaluate the compositeness of baryonic resonances.

Findings

The $ riangle(1232)$ resonance has a significant $ ext{pi-N}$ component.

The $N(1535)$ and $N(1650)$ resonances have negligible $ ext{pi-N}$, $ ext{eta-N}$, $ ext{K} ext{-} ext{Lambda}$, and $ ext{K} ext{-} ext{Sigma}$ components.

The method supports previous findings about the $ riangle(1232)$ structure.

Abstract

We present a formulation of the compositeness for baryonic resonances in order to discuss the meson-baryon molecular structure inside the resonances. For this purpose, we derive a relation between the residue of the scattering amplitude at the resonance pole position and the two-body wave function of the resonance in a sophisticated way, and we define the compositeness as the norm of the two-body wave functions. As applications, we investigate the compositeness of the $\Delta (1232)$, $N (1535)$, and $N (1650)$ resonances from precise $\pi N$ scattering amplitudes in a unitarized chiral framework with the interaction up to the next-to-leading order in chiral perturbation theory. The $\pi N$ compositeness for the $\Delta (1232)$ resonance is evaluated in the $\pi N$ single-channel scattering, and we find that the $\pi N$ component inside $\Delta (1232)$ in the present framework is nonnegligible, which supports the previous work. On the other hand, the compositeness for the $N (1535)$ and $N (1650)$ resonances is evaluated in a coupled-channels approach, resulting that the $\pi N$, $\eta N$, $K \Lambda$ and $K \Sigma$ components are negligible for these resonances.