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.

The compositeness is defined as the weight of the hadronic molecule in the hadron wave function. We can determine the internal structure of the weak-binding system without any specific models from the compositeness. In order to estimate the compositeness of the system with a large effective range, we introduce the range correction to Weinberg's weak-binding relation by modifying the correction terms. We study the applicability of the weak-binding relations by the numerical calculation and show that the improved relation can be applied to a larger parameter region compared with the previous one.

The compositeness is defined as the weight of the hadronic molecule in the hadron wave function. We can determine the internal structure of the weak-binding system without any specific models from the compositeness. In order to estimate the compositeness of the system with a large effective range, we introduce the range correction to Weinberg's weak-binding relation by modifying the correction terms. We study the applicability of the weak-binding relations by the numerical calculation and show that the improved relation can be applied to a larger parameter region compared with the previous one.

The compositeness X is defined as the probability to observe the composite structure such as the hadronic molecule component in a bound state. One of the model-independent approaches to calculate X is the weak-binding relation. However, when the scattering length a0 is larger than the radius of the bound state R, the central value of the compositeness X becomes larger than unity, which cannot be interpreted as a probability. For the systems with a0 > R, we need to estimate the compositeness with the correction terms. For the reasonable determination of the compositeness, we first present the quantitative estimation of the correction terms. Because the exact value of the compositeness should be contained in its definition domain 0 ≤ X ≤ 1, we propose the reasonable estimation method with the uncertainty band by excluding the region outside of the definition domain of the compositeness. We finally estimate the compositeness of physical systems, and obtain the result which we can interpret as the fraction of the composite component.

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