Estimation of compositeness with correction terms

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.

Compositeness of near-threshold exotic hadrons with decay and coupled-channel effects

“…Therefore, in this section, we calculate the compositeness of the actual exotic hadrons T cc and X(3872) with the effects of the decay and coupled channels, and discuss the modification of the universality implications by channel couplings. We use the complex coupling constant to effectively take into account the decay contribution, and introduce the coupling to the isospin partner channel above the threshold [12]. In this case, X1 stands for the compositeness of the threshold channel, and X2 for that of the coupled channel [12,14].…”

“…We use the complex coupling constant to effectively take into account the decay contribution, and introduce the coupling to the isospin partner channel above the threshold [12]. In this case, X1 stands for the compositeness of the threshold channel, and X2 for that of the coupled channel [12,14].…”