Generalized weak-binding relations of compositeness in effective field theory

We study the compositeness of near-threshold states to investigate the internal structure of exotic hadron candidates. Within the framework of effective field theory, Weinberg's weak-binding relation is extended to more general cases by easing several preconditions. First, by evaluating the contribution from the decay channel, we obtain the generalized relation for unstable quasibound states. Next, we generalize the relation to include the nearby CDD (Castillejo-Dalitz-Dyson) pole contribution with the help of the Pade approximant. The validity of the estimation with the generalized weak-binding relations is examined by numerical calculations. A method to systematically evaluate the error in the weak-binding relation is presented. Finally, by applying the extended relation to $\Lambda \left(1405\right)$, $f_0\left(980\right)$, and $a_0\left(980\right)$, we discuss their internal structure, in comparison with other approaches.