Compositeness of the Delta(1232) resonance in pi N scattering

We evaluate the $πN$ compositeness of the $Δ(1232)$ resonance so as to clarify the internal structure of $Δ(1232)$ in terms of the $πN$ component. Here the compositeness is defined as contributions from two-body wave functions to the normalization of the total wave function and is extracted from the $πN$ scattering amplitude. In this study we employ the chiral unitary approach with the interaction up to the next-to-leading order plus a bare $Δ$ term in chiral perturbation theory and describe $Δ(1232)$ in an elastic $πN$ scattering. Fitting the $πN$ scattering amplitude to the solution of the partial wave analysis, we obtain a large real part of the $πN$ compositeness for $Δ(1232)$ comparable to unity and non-negligible imaginary part as well, with which we reconfirm the result in the previous study on the $πN$ compositeness for $Δ(1232)$.

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