Bound states in the B-matrix formalism for the three-body scattering

Abstract

We consider a model of relativistic three-body scattering with a bound state in the two-body sub-channel. We show that the naïve K-matrix type parametrization, here referred to as the B-matrix, has nonphysical singularities near the physical region. We show how to eliminate such singularities by using dispersion relations and also show how to reproduce unitarity relations by taking into account all relevant open channels.

19 pages, 11 figures

References in corpus (16)

• Multiquark Resonances
• A relativistic, model-independent, three-particle quantization condition
• Isoscalar $\pi \pi$ scattering and the $\sigma$ meson resonance from QCD
• Is X(3872) a molecule?
• Three-body Unitarity in the Finite Volume
• Resonances in coupled $\pi K,\eta K$ scattering from lattice QCD
• Coupled-Channel $D\pi$, $D\eta$ and $D_s\bar{K}$ Scattering from Lattice QCD
• On the nature of $a_1(1420)$
• Implementing the three-particle quantization condition including higher partial waves
• Three-body Unitarity with Isobars Revisited
• Odd and Even Partial Waves of $\eta {\pi }^{-}$ and ${\eta }^{\prime }{\pi }^{-}$ in ${\pi }^{-}p\to {\eta }^{(\prime )}{\pi }^{-}p$ at $191\text{GeV}/c$
• Alternative derivation of the relativistic three-particle quantization condition
• Equivalence of relativistic three-particle quantization conditions
• Applying the relativistic quantization condition to a three-particle bound state in a periodic box
• A New Approach to the 3D Faddeev Equation for Three-Body Scattering
• Peak locations and relative phase of different decay modes of the $a_1$ axial vector resonance in diffractive production

Cited by in corpus (6)

• Multi-particle systems on the lattice and chiral extrapolations: a brief review
• Novel approaches in Hadron Spectroscopy
• Solving relativistic three-body integral equations in the presence of bound states
• Relativistic $N$-particle energy shift in finite volume
• Pole position of the $a_1(1260)$ resonance in a three-body unitary framework
• Remarks on non-perturbative three--body dynamics and its application to the $KK\bar{K}$ system