Three-body Unitarity with Isobars Revisited

Abstract

The particle exchange model of hadron interactions can be used to describe three-body scattering under the isobar assumption. In this study we start from the 3->3 scattering amplitude for spinless particles, which contains an isobar-spectator scattering amplitude. Using a Bethe-Salpeter Ansatz for the latter, we derive a relativistic three-dimensional scattering equation that manifestly fulfills three-body unitarity and two-body unitarity for the sub-amplitudes. This property holds for energies above breakup and also in the presence of resonances in the sub-amplitudes.

18 pages, 5 figures

References in corpus (14)

• Multiquark Resonances
• The COMPASS Experiment at CERN
• A relativistic, model-independent, three-particle quantization condition
• Three particle quantization condition in a finite volume: 2. general formalism and the analysis of data
• Analytic properties of the scattering amplitude and resonances parameters in a meson exchange model
• Dispersive analysis of omega --> 3pi and phi --> 3pi decays
• On the nature of $a_1(1420)$
• Three body resonances in two meson-one baryon systems
• Eta photoproduction in a combined analysis of pion- and photon-induced reactions
• Dynamical coupled-channels model of $K^{-}p$ reactions (I): Determination of partial-wave amplitudes
• Remarks on the study of the X(3872) from Effective Field Theory with Pion-Exchange Interaction
• Relevance of complex branch points for partial wave analysis
• Faddeev-Chiral Unitary Approach to the $K^{-}d$ scattering length
• Recoil corrections in antikaon-deuteron scattering

Cited by in corpus (9)

• Three particle quantization condition in a finite volume: 2. general formalism and the analysis of data
• Three-body Unitarity in the Finite Volume
• Relativistic three-particle quantization condition for nondegenerate scalars
• Alternative derivation of the relativistic three-particle quantization condition
• Equivalence of relativistic three-particle quantization conditions
• Light Baryon Spectroscopy
• Light baryon resonances from a coupled-channel study including $\mathbf{K\Sigma }$ photoproduction
• Pole position of the $a_1(1260)$ resonance in a three-body unitary framework
• Nucleon form factors in dispersively improved Chiral Effective Field Theory I: Scalar form factor