Range correction in the weak-binding relation for unstable states

Abstract

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.

Application of the weak-binding relation with range correction

“…namely, the larger one among R int and R eff . In fact, using the effective range model [14], we explicitly construct a system which does not follow the weak-binding relation with the correction term ( 2), but is consistent only with the improved correction term (3) [10,11]. We also show that the range correction should be introduced in the correction term, by analyzing the origin of the effective range [11].…”

“…According to the discussion in Refs. [10,11], we introduce the range correction in the weak-binding relation by the redefinition of the length scale R typ in the correction term as…”

“…We have introduced the range correction in the weakbinding relation by considering the effective range parameter, and demonstrated that the applicability of the relation can be extended by the range correction [10,11]. Here, we present the application of the weak-binding relation to the actual systems in which the range correction is important.…”

Role of the effective range in the weak-binding relation

“…In fact, it is numerically demonstrated that the improved weak-binding relation with Eq. ( 17) has larger applicability than the previous one [16]. The effective range model in the zero range limit is one of such examples.…”

“…Here we would like to focus on the finite range correction in the weak-binding relation (1), stemming from the effective range [16]. To this end, we examine the origin of the effective range in several effective field theories.…”