Structure of exotic hadrons by a weak-binding relation with finite-range correction

Abstract

The composite nature of a shallow bound state is studied by using the weak-binding relation, which connects the compositeness of the bound state with observables. We first show that the previous weak-binding relation cannot be applied to the system with a large effective range. To overcome this difficulty, we introduce the finite-range correction by redefining the typical length scale in the weak-binding relation. A method to estimate the uncertainty of the compositeness is proposed. It is numerically demonstrated that the range correction enlarges the applicable region of the weak-binding relation. Finally, we apply the improved weak-binding relation to the actual hadrons, nuclei, and atomic systems [deuteron, $X(3872)$, $D_{s0}^{\ast }(2317)$, $D_{s1}(2460)$, $N\Omega$ dibaryon, $\Omega \Omega$ dibaryon, ${}_{\Lambda }^3\mathrm{H}$, and ${}^4\mathrm{He}$ dimer] to discuss their internal structure from the compositeness. We present a reasonable estimation of the compositeness of the deuteron by properly taking into account the uncertainty. The results of $X(3872)$ and the $N\Omega$ dibaryon show that the range correction is important to estimate the compositeness of physical states.

18 pages, 11 figures, 5 tables, published version

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