Compositeness of the Delta(1232) resonance in pi N scattering

TL;DR

This paper investigates the internal structure of the Delta(1232) resonance by calculating its pi-N compositeness using a chiral unitary approach, revealing a significant pi-N component in its wave function.

Contribution

It introduces a detailed calculation of the Delta(1232) compositeness within a chiral unitary framework, confirming previous findings with improved methodology.

Findings

Large real part of pi-N compositeness close to unity

Non-negligible imaginary part of the compositeness

Reconfirmation of previous pi-N compositeness results for Delta(1232)

Abstract

We evaluate the $\pi N$ compositeness of the $\Delta (1232)$ resonance so as to clarify the internal structure of $\Delta (1232)$ in terms of the $\pi N$ component. Here the compositeness is defined as contributions from two-body wave functions to the normalization of the total wave function and is extracted from the $\pi N$ scattering amplitude. In this study we employ the chiral unitary approach with the interaction up to the next-to-leading order plus a bare $\Delta$ term in chiral perturbation theory and describe $\Delta (1232)$ in an elastic $\pi N$ scattering. Fitting the $\pi N$ scattering amplitude to the solution of the partial wave analysis, we obtain a large real part of the $\pi N$ compositeness for $\Delta (1232)$ comparable to unity and non-negligible imaginary part as well, with which we reconfirm the result in the previous study on the $\pi N$ compositeness for $\Delta (1232)$.