Structure of exotic hadrons by a weak-binding relation with finite-range correction

TL;DR

This paper improves the weak-binding relation to better analyze the internal structure of exotic hadrons, nuclei, and atomic systems by including finite-range corrections, enabling more accurate estimations of their compositeness.

Contribution

The authors introduce a finite-range correction to the weak-binding relation, extending its applicability to systems with large effective ranges and providing a method to estimate uncertainties.

Findings

Range correction enlarges the applicable region of the weak-binding relation.

Improved relation yields more accurate compositeness estimates for hadrons and nuclei.

Range correction is crucial for reliable analysis of physical states like X(3872) and NΩ dibaryon.

Abstract

The composite nature of a shallow bound state is studied by using the weak-binding relation, which connects the compositeness of the bound state with observables. We first show that the previous weak-binding relation cannot be applied to the system with a large effective range. To overcome this difficulty, we introduce the finite-range correction by redefining the typical length scale in the weak-binding relation. A method to estimate the uncertainty of the compositeness is proposed. It is numerically demonstrated that the range correction enlarges the applicable region of the weak-binding relation. Finally, we apply the improved weak-binding relation to the actual hadrons, nuclei, and atomic systems [deuteron, $X(3872)$, $D^{*}_{s0}(2317)$, $D_{s1}(2460)$, $N\Omega$ dibaryon, $\Omega\Omega$ dibaryon, ${}^{3}_{\Lambda}{\rm H}$, and ${}^{4}{\rm He}$ dimer] to discuss their internal structure from the compositeness. We present a reasonable estimation of the compositeness of the deuteron by properly taking into account the uncertainty. The results of $X(3872)$ and the $N\Omega$ dibaryon show that the range correction is important to estimate the compositeness of physical states.