Estimation of compositeness with correction terms

Department of Physics, Tokyo Metropolitan University, Hachioji 192-0397, Japan

^* e-mail: kinugawa-tomona@ed.tmu.ac.jp
^** e-mail: hyodo@tmu.ac.jp

Published online: 9 November 2022

Abstract

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.