Three-particle formalism for multiple channels: the $\eta \pi \pi +K\overline{K}\pi$ system in isosymmetric QCD

Abstract

We generalize previous three-particle finite-volume formalisms to allow for multiple three-particle channels. For definiteness, we focus on the two-channel $\eta \pi \pi$ and $K\overline{K}\pi$ system in isosymmetric QCD, considering the positive $G$ parity sector of the latter channel, and neglecting the coupling to modes with four or more particles. The formalism we obtain is thus appropriate to study the $b_1(1235)$ and $\eta (1295)$ resonances. The derivation is made in the generic relativistic field theory approach using the time-ordered perturbation theory method. We study how the resulting quantization condition reduces to that for a single three-particle channel when one drops below the upper ($K\overline{K}\pi$) threshold. We also present parametrizations of the three-particle K matrices that enter into the formalism.

arXiv comment49 pages, no figures. v2: Fixed typos, added additional comments to the conclusion, made other minor changes

References in corpus (36)

• The $XYZ$ states: experimental and theoretical status and perspectives
• Non-Standard Heavy Mesons and Baryons, an Experimental Review
• Pentaquark and Tetraquark states
• Exotics: Heavy Pentaquarks and Tetraquarks
• Finite-Volume Effects for Two-Hadron States in Moving Frames
• Multiple-channel generalization of Lellouch-Luscher formula
• Multiquark States
• A relativistic, model-independent, three-particle quantization condition
• Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude
• S and D-wave phase shifts in isospin-2 pi pi scattering from lattice QCD
• Three particles in a finite volume
• Three-particle scattering amplitudes from a finite volume formalism
• 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
• Three-body Unitarity in the Finite Volume
• Three-particle quantization condition in a finite volume: 1. The role of the three-particle force
• Three-particle systems with resonant subprocesses in a finite volume
• Implementing the three-particle quantization condition including higher partial waves
• Generalizing the relativistic quantization condition to include all three-pion isospin channels
• Numerical exploration of three relativistic particles in a finite volume including two-particle resonances and bound states
• On the Equivalence of Three-Particle Scattering Formalisms
• Energy shift of the three-particle system in a finite volume
• Volume Dependence of N-Body Bound States
• Relativistic three-particle quantization condition for nondegenerate scalars
• Alternative derivation of the relativistic three-particle quantization condition
• Equivalence of relativistic three-particle quantization conditions
• Three-particle finite-volume formalism for ${\pi }^{+}{\pi }^{+}{K}^{+}$ and related systems
• $DDK$ system in finite volume
• Solving relativistic three-body integral equations in the presence of bound states
• Relativistic-invariant formulation of the NREFT three-particle quantization condition
• Finite-volume energy shift of the three-pion ground state
• Relativistic $N$-particle energy shift in finite volume
• Implementing the three-particle quantization condition for ${\pi }^{+}{\pi }^{+}{K}^{+}$ and related systems
• Three relativistic neutrons in a finite volume
• Three-body resonances in the ${\phi }^4$ theory
• The three-pion $K$-matrix at NLO in ChPT

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