Role of the effective range in the weak-binding relation

TL;DR

This paper investigates how the effective range influences the weak-binding relation in hadronic physics, showing that it arises from derivative interactions and channel coupling, and proposing its inclusion in uncertainty estimates.

Contribution

The study clarifies the origin of the effective range in effective field theories and introduces its correction into the weak-binding relation's uncertainty analysis.

Findings

Effective range originates from derivative coupling and channel coupling.

Range correction affects the weak-binding relation's accuracy.

Proposes including range correction in uncertainty estimates.

Abstract

We study the range correction in the weak-binding relation, which relates the internal structure of hadrons with the scattering length and the binding energy. Utilizing the effective field theories, we show that the effective range originates from the derivative coupling interaction as well as from the channel coupling to the bare state, and that the different contributions are not distinguishable. By examining the compositeness in the effective field theories, it is demonstrated that the effective range induces the finite range correction for the weak-binding relation in addition to the previously known contributions. We thus propose to include the range correction in the uncertainty terms of the weak-binding relation.