Equivalence of relativistic three-particle quantization conditions

Abstract

We show that a recently derived alternative form of the relativistic three-particle quantization condition for identical particles can be rewritten in terms of the R matrix introduced to give a unitary representation of the infinite-volume three-particle scattering amplitude. Combined with earlier work, this shows the equivalence of the relativistic effective field theory approach of Hansen and Sharpe (Refs.[1,2]) and the "finite-volume unitarity" approach of Mai and Döring (Refs.[3,4]). It also provides a generalization of the latter approach to arbitrary angular momenta of two-particle subsystems.

arXiv comment13 pages, 2 appendices; v2--added clarifications, corrected typos; v3--further clarifications added and typos corrected, results unchanged; matches published version

References in corpus (32)

• A relativistic, model-independent, three-particle quantization condition
• Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude
• 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
• Lattice QCD and Three-particle Decays of Resonances
• Three-body spectrum in a finite volume: the role of cubic symmetry
• 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
• n-Boson Energies at Finite Volume and Three-Boson Interactions
• Implementing the three-particle quantization condition including higher partial waves
• Three pion spectrum in the $I=3$ channel from lattice QCD
• 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
• Three-boson problem at low energy and Implications for dilute Bose-Einstein condensates
• Numerical study of the relativistic three-body quantization condition in the isotropic approximation
• An solvable three-body model in finite volume
• Three-body unitarity versus finite-volume ${\pi }^{+}{\pi }^{+}{\pi }^{+}$ spectrum from lattice QCD
• Three-body Unitarity with Isobars Revisited
• On the Equivalence of Three-Particle Scattering Formalisms
• Energy shift of the three-particle system in a finite volume
• Unitarity of the infinite-volume three-particle scattering amplitude arising from a finite-volume formalism
• Variational approach to $N$-body interactions in finite volume
• Two- and three-body interactions in ${\phi }^4$ theory from lattice simulations
• Signatures of few-body resonances in finite volume
• Phenomenology of Relativistic $3\to 3$ Reaction Amplitudes within the Isobar Approximation
• Threshold expansion of the three-particle quantization condition

Cited by in corpus (26)

• Towards a theory of hadron resonances
• Finite-volume energy spectrum of the $K^{-}{K}^{-}{K}^{-}$ system
• Three-body interactions from the finite-volume QCD spectrum
• The energy-dependent ${\pi }^{+}{\pi }^{+}{\pi }^{+}$ scattering amplitude from QCD
• Relativistic three-particle quantization condition for nondegenerate scalars
• Multi-particle systems on the lattice and chiral extrapolations: a brief review
• Scattering of two and three physical pions at maximal isospin from lattice QCD
• Three-particle finite-volume formalism for ${\pi }^{+}{\pi }^{+}{K}^{+}$ and related systems
• 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
• Interactions of $\pi K$, $\pi \pi K$ and $KK\pi$ systems at maximal isospin from lattice QCD
• Decay amplitudes to three hadrons from finite-volume matrix elements
• Six-pion amplitude
• Variations on the Maiani-Testa approach and the inverse problem
• The isospin-3 three-particle $K$-matrix at NLO in ChPT
• Bound states in the B-matrix formalism for the three-body scattering
• Finite-volume energy shift of the three-nucleon ground state
• Axial-vector $D_1$ hadrons in $D^{\ast }\pi$ scattering from QCD
• Analytic expansions of multi-hadron finite-volume energies: I. Two-particle states
• Three-particle formalism for multiple channels: the $\eta \pi \pi +K\overline{K}\pi$ system in isosymmetric QCD
• The three-pion $K$-matrix at NLO in ChPT
• Spurious poles in a finite volume
• Six-meson amplitude in QCD-like theories