We discuss the relation between the analytic structure of the scattering amplitude and the origin of an eigenstate represented by a pole of the amplitude. If the eigenstate is not dynamically generated by the interaction in the channel of interest, the residue of the pole vanishes in the zero coupling limit. Based on the topological nature of the phase of the scattering amplitude, we show that the pole must encounter with the Castillejo-Dalitz-Dyson (CDD) zero in this limit. It is concluded that the dynamical component of the eigenstate is small if a CDD zero exists near the eigenstate pole. We show that the line shape of the resonance is distorted from the Breit-Wigner form as an observable consequence of the nearby CDD zero. Finally, studying the positions of poles and CDD zeros of the $\overline{K}N\text{−}\pi \mathrm{\Sigma }$ amplitude, we discuss the origin of the eigenstates in the $\mathrm{\Lambda }(1405)$ region.

• Received 27 November 2017

DOI:https://doi.org/10.1103/PhysRevD.97.054019

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Published by the American Physical Society