# Two-body Wave Functions, Compositeness, And The Internal Structure Of Dynamically Generated Resonances

## TL;DR

This paper discusses how to extract and interpret the two-body wave functions and compositeness of hadronic resonances, revealing their internal molecular structures through scattering amplitude analysis.

## Contribution

It presents a formulation to evaluate the two-body wave function and compositeness of resonances, applying it to several hadronic states to understand their internal structure.

## Key findings

- Compositeness deviates from unity for energy-dependent interactions.
- Two-body wave functions can be extracted from scattering amplitude residues.
- Internal structures of resonances like $f_{0}(980)$, $ ext{Lambda}(1405)$, and $ ext{Xi}(1690)$ are analyzed.

## Abstract

Recently, the compositeness, defined as the norm of a two-body wave function for bound and resonance states, has been investigated to discuss the internal structure of hadrons in terms of hadronic molecular components. From the studies of the compositeness, it has been clarified that the two-body wave function of a bound state can be extracted from the residue of the scattering amplitude at the bound state pole. Of special interest is that the two-body wave function from the scattering amplitude is automatically normalized. In particular, while the compositeness is unity for energy-independent interactions, it deviates from unity for energy-dependent interactions, which can be interpreted as a missing-channel contribution. In this manuscript, we show the formulation of the two-body wave function from the scattering amplitude, evaluate the compositeness for several dynamically generated resonances such as $f_{0} (980)$, $\Lambda (1405)$, and $\Xi (1690)$, and investigate their internal structure in terms of the hadronic molecular components.