Generalized weak-binding relations of compositeness in effective field theory

TL;DR

This paper extends Weinberg's weak-binding relation within effective field theory to better analyze the internal structure of near-threshold exotic hadrons, including unstable states and CDD pole effects, validated through numerical tests.

Contribution

It introduces a generalized weak-binding relation accounting for decay channels and CDD poles, enabling more accurate internal structure analysis of near-threshold states.

Findings

Validated the generalized relation with numerical calculations.

Applied the method to Lambda(1405), f0(980), and a0(980).

Provided a systematic error evaluation approach.

Abstract

We study the compositeness of near-threshold states to investigate the internal structure of exotic hadron candidates. Within the framework of effective field theory, Weinberg's weak-binding relation is extended to more general cases by easing several preconditions. First, by evaluating the contribution from the decay channel, we obtain the generalized relation for unstable quasibound states. Next, we generalize the relation to include the nearby CDD (Castillejo-Dalitz-Dyson) pole contribution with the help of the Pade approximant. The validity of the estimation with the generalized weak-binding relations is examined by numerical calculations. The method to systematically evaluate the error in the weak-binding relation is presented. Finally, by applying the extended relation to Lambda(1405), f0(980) and a0(980), we discuss their internal structure, in comparison with other approaches.