Structure of exotic hadrons by 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 (2317), Ds1(2460), N Ω dibaryon, ΩΩ dibaryon, 3 Λ H, and 4 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 Ω dibaryon show that the range correction is important to estimate the compositeness of physical states.

Estimation of compositeness with correction terms

“…This model can also be regarded as the resonance model without the direct ψ 1 ψ 2 interaction in Refs. [17,47].…”

“…The compositeness is defined as the probability to find the hadronic molecule component in the bound state. Theoretically, the compositeness can be evaluated either from the weak-binding relation [10,[15][16][17] or from the residue of the pole of the scattering amplitude [11,12]. The internal structure of many hadrons has been studied by the compositeness [10,.…”

“…The internal structure of many hadrons has been studied by the compositeness [10,. The notion of the compositeness has also been applied to other systems, such as nuclei and atoms [17,[40][41][42].…”

“…The phenomena associated with the near-threshold states are governed by the low-energy universality [43,44]. From the universality argument, it is expected that the near-threshold states are dominated by the molecular component [17]. In fact, Ref.…”

“…In fact, the weak-binding hadrons, nuclei and atoms studied in Ref. [17] are all composite dominant states.…”