Compositness and wave function of shallow bound states in relation to scattering observables

TL;DR

This paper investigates the internal structure of exotic hadrons by relating their compositeness, defined as the probability of hadronic molecular components, to scattering observables using a coupled-channel potential model.

Contribution

It introduces a framework connecting compositeness with scattering phase shifts for shallow bound states, applied to several exotic hadrons including X(3872).

Findings

Compositeness varies with model parameters for the studied states.

Scattering phase shifts provide insights into the internal structure of exotic hadrons.

The framework successfully relates internal structure to observable scattering data.

Abstract

We study the internal structure of exotic hadrons, especially focusing on the relation between the compositeness and physical observables. Defined as the probability of finding hadronic molecular components in the wave function, compositeness serves as a quantitative measure of the internal structure of exotic hadrons. We utilize the coupled-channel potential model incorporating both quark and hadron degrees of freedom, which naturally generate the ``bare state'' responsible for the elementary component as the bound state in the quark channel. The behavior of the compositeness under the variation of the model parameters is investigated by using the $X(3872)$ as an example. In particular, we analyze the associated scattering phase shifts and the bound-state wave functions to discuss the relation between the compositeness and the scattering observables for a shallow bound state. As a phenomenological application of the present framework, the compositeness of the $X(3872)$, $T_{cc}(3875)$, $D_{s0}(2317)$, and $D_{s1}(2460)$ is discussed.