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We present a formulation of the compositeness for baryonic resonances inorder to discuss the meson-baryon molecular structure inside the resonances.For this purpose, we derive a relation between the residue of the scatteringamplitude at the resonance pole position and the two-body wave function of theresonance in a sophisticated way, and we define the compositeness as the normof the two-body wave functions. As applications, we investigate thecompositeness of the $\Delta (1232)$, $N (1535)$, and $N (1650)$ resonancesfrom precise $\pi N$ scattering amplitudes in a unitarized chiral frameworkwith the interaction up to the next-to-leading order in chiral perturbationtheory. The $\pi N$ compositeness for the $\Delta (1232)$ resonance isevaluated in the $\pi N$ single-channel scattering, and we find that the $\piN$ component inside $\Delta (1232)$ in the present framework is nonnegligible,which supports the previous work. On the other hand, the compositeness for the$N (1535)$ and $N (1650)$ resonances is evaluated in a coupled-channelsapproach, resulting that the $\pi N$, $\eta N$, $K \Lambda$ and $K \Sigma$components are negligible for these resonances.

Compositeness of baryonic resonances: Applications to the Delta(1232), N(1535), and N(1650) resonances