Structure of hadron resonances with a nearby zero of the amplitude

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.

7 pages, 3 figures, v2: published version

References in corpus (8)

• Effective Kbar N interaction based on chiral SU(3) dynamics
• Constraints on the chiral unitary $\bar{K}N$ amplitude from $\pi \Sigma K^{+}$ photoproduction data
• Comprehensive analysis of the wave function of a hadronic resonance and its compositeness
• New insights into antikaon-nucleon scattering and the structure of the Lambda(1405)
• Interplay of quark and meson degrees of freedom in a near-threshold resonance
• Hadron mass scaling near the s-wave threshold
• Generalized weak-binding relations of compositeness in effective field theory
• Quark mass dependence of H-dibaryon in $\Lambda \Lambda$ scattering

Cited by in corpus (5)

• Construction of a local barK N-pi Sigma-pi Lambda potential and composition of the Lambda(1405)
• Compositeness of hadrons, nuclei, and atomic systems
• Two-body wave functions and compositeness from scattering amplitudes: II. Application to the physical $N^{\ast }$ and ${\Delta }^{\ast }$ resonances
• Universal physics of the few-body system of two neutrons and one flavored meson
• Structure of proton based on the classical string model