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Structure of hadron resonances with a nearby zero of the amplitude
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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 KbarN-piSigma amplitude, we discuss the origin of the eigenstates in the Lambda(1405) region.
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Cited by 1 Pith paper
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Eigenstates in coupled-channel scattering amplitude and their effects on spectrum
In coupled-channel scattering, the observable above-threshold resonance originates from the virtual-state pole, while the subthreshold quasibound state becomes a shadow pole, an interchange shown and applied to Xi resonances.
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