Structure of hadron resonances with a nearby zero of the amplitude

TL;DR

This paper explores how the analytic structure of scattering amplitudes, especially CDD zeros, reveals whether hadron resonances like Lambda(1405) are dynamically generated or have a different origin, affecting their observed line shapes.

Contribution

It establishes a topological relation between poles and CDD zeros in scattering amplitudes, linking the resonance structure to the eigenstate's origin and shape distortions.

Findings

Resonance line shape distortion due to nearby CDD zero.

Pole-zero relation indicating non-dynamical origin of certain states.

Application to Lambda(1405) clarifies its eigenstate nature.

Abstract

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.