Relevance of complex branch points for partial wave analysis

Abstract

A central issue in hadron spectroscopy is to deduce --- and interpret --- resonance parameters, namely pole positions and residues, from experimental data, for those are the quantities to be compared to lattice QCD or model calculations. However, not every structure in the observables derives from a resonance pole: the origin might as well be branch points, either located on the real axis (when a new channel comprised of stable particles opens) or in the complex plane (when at least one of the intermediate particles is unstable). In this paper we demonstrate first the existence of such branch points in the complex plane and then show on the example of the piN P11 partial wave that it is not possible to distinguish the structures induced by the latter from a true pole signal based on elastic data alone.

8 pages, 4 figures

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• Pion photoproduction in a dynamical coupled-channels model
• Light Baryon Spectroscopy
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• Novel approaches in Hadron Spectroscopy
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• Pole position of the $a_1(1260)$ resonance in a three-body unitary framework
• Model Selection for Pion Photoproduction
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• Three-body dynamics of the $a_1(1260)$ resonance from lattice QCD
• Strong decay of low-lying $S_{11}$ and $D_{13}$ nucleon resonances to pseudoscalar mesons and octet baryons
• Poles of Karlsruhe-Helsinki KH80 and KA84 solutions extracted by using Laurent+Pietarinen method
• Baryon photo-decay amplitudes at the pole
• Three-body resonances in the ${\phi }^4$ theory
• Towards the Minimal Spectrum of Excited Baryons
• Observation of the $p{\eta }^{\prime }$ Cusp in the New Precise Beam Asymmetry $\Sigma$ Data for $\gamma p\to p\eta$
• New Insights on Low Energy $\pi N$ Scattering Amplitudes
• Pole structure from energy-dependent and single-energy fits to $\pi N$ elastic scattering data
• Baryon transition form factors at the pole
• Description of $\rho (1700)$ as a $\rho K\bar{K}$ system with the fixed center approximation
• Effects of Final State Interactions on Landau Singularities
• Poles, the only true resonant-state signals, are extracted from a worldwide collection of partial wave amplitudes using only one, well controlled pole-extraction method
• Dispersive analysis of low energy ${\gamma }^{\ast }N\to \pi N$ process
• Stability of the Zagreb Carnegie-Mellon-Berkeley model
• Amplitude Analysis for Mesons and Baryons: Tools and Technology
• Signature of $N^{\star }$ resonance in mass spectrum of the $K\bar{K}N$ decay channels
• The pole structure of low energy $\pi N$ scattering amplitudes
• Spectral branch points of the Bloch-Torrey operator
• Unitarity Analyses of $\pi N$ Elastic Scattering Amplitudes
• Spectral properties of the Bloch-Torrey operator in three dimensions