Complex phase structure of the meson-baryon $T$-matrix

Abstract

The full complex phase structure of the meson-baryon reaction amplitude in coupled channels approach is investigated, including also the photon-baryon channel. The result may be viewed as a generalization of the well-known Watson's theorem. Furthermore, the complex phase structure is exhibited for the pole and nonpole parts of the reaction amplitude in such a way that it will serve as a convenient common starting point for constructing models with different levels of approximation, in particular, for building isobar models where the basic properties of the $S$-matrix can be maintained. Such models should be useful, especially, in coupled multichannel calculations, where a large amount of experimental data are considered in resonance analyses, a situation encountered in modern baryon spectroscopy. In particular, it is shown that the unitarity of the pole part of the $T$-matrix arises automatically from the dressing mechanism inherent in the basic scattering equation. This implies that no separate conditions are required for making this part of the resonance amplitude unitary as it has been done in some of the existing isobar models.

References in corpus (41)

• A unitary isobar model for pion photo- and electroproduction on the proton up to 1 GeV
• Unitary Isobar Model - MAID2007
• Extended Partial-Wave Analysis of piN Scattering Data
• Chiral Dynamics and the $S_{11}(1535)$ Nucleon Resonance
• Properties of baryon resonances from a multichannel partial wave analysis
• Dynamical coupled-channel model of meson production reactions in the nucleon resonance region
• Nucleon resonances within a dynamical coupled-channels model of pi N and gamma N reactions
• Dynamically generated resonances from the vector octet-baryon octet interaction
• Coupled-channel dynamics in the reactions piN --> piN, etaN, KLambda, KSigma
• Analytic properties of the scattering amplitude and resonances parameters in a meson exchange model
• Gauge-invariant theory of pion photoproduction with dressed hadrons
• Chiral dynamics of the S11(1535) and S11(1650) resonances revisited
• Electromagnetic Excitation of Nucleon Resonances
• Dynamical Coupled-Channel Model of $\pi N$ Scattering in the W $\le$ 2 GeV Nucleon Resonance Region
• Coupled-channel analysis of the $\omega$-meson production in $\pi N$ and $\gamma N$ reactions for c.m. energies up to 2 GeV
• Parameterization dependence of T matrix poles and eigenphases from a fit to piN elastic scattering data
• A coupled-channel analysis of $K\Lambda$ production in the nucleon resonance region
• Eta photoproduction in a combined analysis of pion- and photon-induced reactions
• Multipole Amplitudes of Pion Photoproduction on Nucleons up to 2GeV within Dispersion Relations and Unitary Isobar Model
• Multichannel parametrization of πN scattering amplitudes and extraction of resonance parameters
• Dynamical Coupled-Channels Effects on Pion Photoproduction
• Photocouplings at the Pole from Pion Photoproduction
• Gauge-invariant approach to meson photoproduction including the final-state interaction
• The reaction pi+ p --> K+ Sigma+ in a unitary coupled-channels model
• Pion photoproduction in a dynamical coupled-channels model
• Dynamical coupled-channels model of $K^{-}p$ reactions (I): Determination of partial-wave amplitudes
• Dynamical coupled-channels model of $K^{-}p$ reactions (II): Extraction of ${\Lambda }^{\ast }$ and ${\Sigma }^{\ast }$ hyperon resonances
• Dynamical coupled-channels analysis of 1H(e,e'pi)N reactions
• Photoproduction of pions and properties of baryon resonances from a Bonn-Gatchina partial wave analysis
• The impact of ${\mathbf{K}}^{+}\mathbf{\Lambda }$ photoproduction on the resonance spectrum
• Multichannel parametrization of $\bar{K}N$ scattering amplitudes and extraction of resonance parameters
• Eta and Etaprime Photoproduction on the Nucleon with the Isobar Model EtaMAID2018
• Pion- and photo-induced transition amplitudes to $\Lambda K$, $\Sigma K$, and $N\eta$
• Nucleon resonances in the fourth resonance region
• Double and single pion photoproduction within a dynamical coupled-channels model
• Coupled-channel analysis of $K\Sigma$ production on the nucleon up to 2.0 GeV
• Towards the Minimal Spectrum of Excited Baryons
• The MAID Legacy and Future
• $2\pi$ production in the Giessen coupled-channel model
• Study of ambiguities in ${\pi }^{-}p\to \Lambda K^0$ scattering amplitudes
• The K-matrix approach to the Delta - resonance mass splitting and isospin violation in low-energy pi-N scattering