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.

arXiv comment18 pages, 5 figures

References in corpus (36)

• Multiquark Resonances
• Heavy-Quark QCD Exotica
• The COMPASS Experiment at CERN
• The Physics of the B Factories
• A relativistic, model-independent, three-particle quantization condition
• Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude
• Nucleon resonances within a dynamical coupled-channels model of pi N and gamma N reactions
• Coupled-channel dynamics in the reactions piN --> piN, etaN, KLambda, KSigma
• Three particles in a finite volume
• Relating the finite-volume spectrum and the two-and-three-particle $S$ matrix for relativistic systems of identical scalar particles
• 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
• omega --> pi0 gamma* and phi --> pi0 gamma* Transition form factors in dispersion theory
• On the nature of $a_1(1420)$
• Spectrum of three-body bound states in a finite volume
• Three body resonances in two meson-one baryon systems
• Eta photoproduction in a combined analysis of pion- and photon-induced reactions
• Three-body $D\bar{D}\pi$ dynamics for the X(3872)
• Dynamical coupled-channels model of $K^{-}p$ reactions (I): Determination of partial-wave amplitudes
• Three-body Final State Interaction in $\eta \to 3\pi$
• Towards three-body unitarity in $D^{+}\to K^{-}{\pi }^{+}{\pi }^{+}$
• Dispersion-theoretical analysis of the D^+ --> K^- pi^+ pi^+ Dalitz plot
• Unitary coupled-channels model for three-mesons decays of heavy mesons
• Remarks on the study of the X(3872) from Effective Field Theory with Pion-Exchange Interaction
• First Results from The GlueX Experiment
• Scattering of unstable particles in a finite volume: the case of pi rho scattering and the a1(1260) resonance
• Relevance of complex branch points for partial wave analysis
• Dispersion relations for ${\eta }^{\prime }\to \eta \pi \pi$
• Three-body final state interaction in $\eta \to 3\pi$ updated
• The Optical Potential on the Lattice
• Theoretical support for the $\pi (1300)$ and the recently claimed $f_0(1790)$ as molecular resonances
• Coupled-channel analysis of $D^{+}\to K^{-}{\pi }^{+}{\pi }^{+}$ decay
• Faddeev-Chiral Unitary Approach to the $K^{-}d$ scattering length
• Binding energy of the $X(3872)$ at unphysical pion masses
• Recoil corrections in antikaon-deuteron scattering

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• Numerical exploration of three relativistic particles in a finite volume including two-particle resonances and bound states
• Three-body unitarity versus finite-volume ${\pi }^{+}{\pi }^{+}{\pi }^{+}$ spectrum from lattice QCD
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• Relativistic three-particle quantization condition for nondegenerate scalars
• Alternative derivation of the relativistic three-particle quantization condition
• Equivalence of relativistic three-particle quantization conditions
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• Multi-particle systems on the lattice and chiral extrapolations: a brief review
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• Phenomenology of Relativistic $3\to 3$ Reaction Amplitudes within the Isobar Approximation
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• Consistent Dalitz plot analysis of Cabibbo-favored $D^{+}\to \bar{K}\pi {\pi }^{+}$ decays
• Pole position of the $a_1(1260)$ resonance in a three-body unitary framework
• Pole position of the $a_1(1260)$ from $\tau$-decay
• Three-body dynamics of the $a_1(1260)$ resonance from lattice QCD
• Dalitz plots and lineshape of $a_1(1260)$ from a relativistic three-body unitary approach
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• $\omega$ meson from lattice QCD
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• Nucleon form factors in dispersively improved Chiral Effective Field Theory I: Scalar form factor
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• Roles of $a_0(980)$, $\Lambda (1670)$, and $\Sigma (1385)$ in the ${\Lambda }_c^{+}\to \eta \Lambda {\pi }^{+}$ decay
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• Bound states in the B-matrix formalism for the three-body scattering
• $\Lambda (1405)$ production in the process ${\chi }_{c0}(1P)\to \bar{\Lambda }\Sigma \pi$
• Remarks on non-perturbative three--body dynamics and its application to the $KK\bar{K}$ system
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• Three-Body Unitary Coupled-Channel Analysis on $\eta (1405/1475)$
• Pole analysis for the $D^{\ast }\bar{K}$-$D\overline{K^{\ast }}$ coupled-channel system
• Unitarity and Unitarization
• $K^{-}d\to \pi \Lambda N$ reaction with in-flight kaons for studying the $\Lambda N$ interaction
• Coupled-channel contributions to the GDH sum rule from the Jülich-Bonn approach