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.

arXiv comment19 pages, 11 figures

References in corpus (61)

• Observation of a narrow charmonium-like state in exclusive B+ -> K+ pi+pi- J/psi decays
• Observation of a New Narrow Charmonium State in Exclusive B+-->K+ pi+pi- J/psi Decays
• Hadronic molecules
• Multiquark Resonances
• Non-Standard Heavy Mesons and Baryons, an Experimental Review
• Heavy-Quark QCD Exotica
• The Three-Boson System with Short-Range Interactions
• Scattering processes and resonances from lattice QCD
• A relativistic, model-independent, three-particle quantization condition
• Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude
• Isoscalar $\pi \pi$ scattering and the $\sigma$ meson resonance from QCD
• Is X(3872) a molecule?
• Nucleon-Deuteron Scattering from an Effective Field Theory
• Relating the finite-volume spectrum and the two-and-three-particle $S$ matrix for relativistic systems of identical scalar particles
• Three-body Unitarity in the Finite Volume
• Resonances in coupled $\pi K,\eta K$ scattering from lattice QCD
• Lattice QCD and Three-particle Decays of Resonances
• An $a_0$ resonance in strongly coupled $\pi \eta$, $K\overline{K}$ scattering from lattice QCD
• Coupled-Channel $D\pi$, $D\eta$ and $D_s\bar{K}$ Scattering from Lattice QCD
• Isoscalar $\pi \pi ,K\overline{K},\eta \eta$ scattering and the $\sigma ,f_0,f_2$ mesons from QCD
• Finite-volume spectrum of ${\pi }^{+}{\pi }^{+}$ and ${\pi }^{+}{\pi }^{+}{\pi }^{+}$ systems
• Three-particle systems with resonant subprocesses in a finite volume
• Two- and three-pion finite-volume spectra at maximal isospin from lattice QCD
• $I=3$ three-pion scattering amplitude from lattice QCD
• On the nature of $a_1(1420)$
• The $I=1$ pion-pion scattering amplitude and timelike pion form factor from $N_{\mathrm{f}}=2+1$ lattice QCD
• Implementing the three-particle quantization condition including higher partial waves
• Generalizing the relativistic quantization condition to include all three-pion isospin channels
• Three pion spectrum in the $I=3$ channel from lattice QCD
• 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
• Three-body $D\bar{D}\pi$ dynamics for the X(3872)
• Numerical study of the relativistic three-body quantization condition in the isotropic approximation
• Different pole structures in line shapes of the $X(3872)$
• Three-body Unitarity with Isobars Revisited
• The elastic $I=3/2$ $p$-wave nucleon-pion scattering amplitude and the $\Delta (1232)$ resonance from $N_{\mathrm{f}}=2+1$ lattice QCD
• On the Equivalence of Three-Particle Scattering Formalisms
• Odd and Even Partial Waves of $\eta {\pi }^{-}$ and ${\eta }^{\prime }{\pi }^{-}$ in ${\pi }^{-}p\to {\eta }^{(\prime )}{\pi }^{-}p$ at $191\text{GeV}/c$
• Light isovector resonances in ${\pi }^{-}p\to {\pi }^{-}{\pi }^{-}{\pi }^{+}p$ at 190 GeV/$c$
• Observation of a new narrow axial-vector meson $a_1(1420)$
• Unitarity of the infinite-volume three-particle scattering amplitude arising from a finite-volume formalism
• Extraction of isoscalar $\pi \pi$ phase-shifts from lattice QCD
• Determination of $s$- and $p$-wave $I=1/2$ $K\pi$ scattering amplitudes in $N_{\mathrm{f}}=2+1$ lattice QCD
• Scattering of an Ultrasoft Pion and the X(3872)
• The $b_1$ resonance in coupled $\pi \omega$, $\pi \varphi$ scattering from lattice QCD
• Alternative derivation of the relativistic three-particle quantization condition
• Measurement of the beam asymmetry $\Sigma$ for ${\pi }^0$ and $\eta$ photoproduction on the proton at $E_{\gamma }=9$ GeV
• Equivalence of relativistic three-particle quantization conditions
• Resonance Production and $\pi \pi$ S-wave in ${\pi }^{-}+p\to {\pi }^{-}{\pi }^{-}{\pi }^{+}+p_{recoil}$ at 190 GeV/c
• Two- and three-body interactions in ${\phi }^4$ theory from lattice simulations
• Dynamically-coupled partial-waves in $\rho \pi$ isospin-2 scattering from lattice QCD
• Applying the relativistic quantization condition to a three-particle bound state in a periodic box
• First Results from The GlueX Experiment
• Pion scattering in the isospin I=2 channel from elongated lattices
• Phenomenology of Relativistic $3\to 3$ Reaction Amplitudes within the Isobar Approximation
• Vector and scalar charmonium resonances with lattice QCD
• Dalitz plots and lineshape of $a_1(1260)$ from a relativistic three-body unitary approach
• Three-body scattering: Ladders and Resonances
• 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
• One-pion exchange in the X(3872) revisited

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