How much is the compositeness of a bound state constrained by $a$ and $r_0$? The role of the interaction range

TL;DR

This paper introduces a method to assess the compositeness of molecular states by incorporating the interaction range, improving upon Weinberg's formula, and applies it to deuteron and certain meson states to determine their structure.

Contribution

The paper develops a formalism that includes the interaction range to better estimate the compositeness of bound states, extending beyond the zero-range approximation.

Findings

Effective range significantly influences compositeness estimates.

The method provides reliable results even for non-small binding energies.

Application to deuteron and meson states yields specific compositeness ranges.

Abstract

We present an approach that allows one to obtain information on the compositeness of molecular states from combined information of the scattering length of the hadronic components, the effective range, and the binding energy. We consider explicitly the range of the interaction in the formalism and show it to be extremely important to improve on the formula of Weinberg obtained in the limit of very small binding and zero range interaction. The method allows obtaining good information also in cases where the binding is not small. We explicitly apply it to the case of the deuteron and the $D^{*}_{s0}(2317)$ and $D^{*}_{s1}(2460)$ states and determine simultaneously the value of the compositeness within a certain range, as well as get qualitative information on the range of the interaction.