Application of the weak-binding relation with range correction

TL;DR

This paper enhances the weak-binding relation by incorporating range correction, enabling more accurate analysis of the internal structure of shallow bound states across various physical systems.

Contribution

It introduces a range correction to the weak-binding relation, broadening its applicability to systems with significant effective ranges.

Findings

Range correction improves the applicability of the weak-binding relation.

Application to hadrons, hypernuclei, and atoms demonstrates its practical importance.

Range correction leads to more accurate structural insights in diverse systems.

Abstract

The weak-binding relation is a useful tool to study the internal structure of hadrons from the observable quantities. We introduce the range correction in the weak-binding relation for the system having a sizable magnitude of the effective range, and show that the applicability of the weak-binding relation can be enlarged by the range correction. Thanks to the low-energy universality, the weak-binding relation can be used to study the structure of shallow bound states in any systems with different length scales. We apply the weak-binding relation to actual systems, including hadrons, hypernuclei, and atoms and show the importance of the range correction.