On the three-particle analog of the Lellouch-Lüscher formula

Abstract

Using non-relativistic effective field theory, we derive a three-particle analog of the Lellouch-Lüscher formula at the leading order. This formula relates the three-particle decay amplitudes in a finite volume with their infinite-volume counterparts and, hence, can be used to study the three-particle decays on the lattice. The generalization of the approach to higher orders is briefly discussed.

arXiv comment15 pages, 3 figures

References in corpus (44)

• Renormalization of the Three-Body System with Short-Range Interactions
• The Three-Boson System with Short-Range Interactions
• Finite-Volume Effects for Two-Hadron States in Moving Frames
• Weak transition matrix elements from finite-volume correlation functions
• Multiple-channel generalization of Lellouch-Luscher formula
• A relativistic, model-independent, three-particle quantization condition
• Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude
• More Effective Field Theory for Nonrelativistic Scattering
• 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
• Finite Volume Corrections to the Two-Particle Decay of States with Non-Zero Momentum
• 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 the Timelike Pion Form Factor
• Multichannel one-to-two transition amplitudes in a finite volume
• Three-body spectrum in a finite volume: the role of cubic symmetry
• Multi-Pion Systems in Lattice QCD and the Three-Pion Interaction
• Cusps in K --> 3 pi decays
• Multichannel 0-to-2 and 1-to-2 transition amplitudes for arbitrary spin particles 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
• Implementing the three-particle quantization condition including higher partial waves
• 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
• The $\pi \pi \to \pi {\gamma }^{\star }$ amplitude and the resonant $\rho \to \pi {\gamma }^{\star }$ transition from lattice QCD
• Efimov physics in a finite volume
• The triton in a finite volume
• A framework for the calculation of the $\Delta N{\gamma }^{\ast }$ transition form factors on the lattice
• The resonant ${\pi }^{+}\gamma \to {\pi }^{+}{\pi }^0$ amplitude from Quantum Chromodynamics
• Finite-volume energy spectrum of the $K^{-}{K}^{-}{K}^{-}$ system
• Radiative corrections in K --> 3 pi decays
• Three particles in a finite volume: The breakdown of spherical symmetry
• Matrix elements of unstable states
• On the modification of the Efimov spectrum in a finite cubic box
• Cusps in K_L --> 3 pi decays
• Alternative derivation of the relativistic three-particle quantization condition
• Rescattering effects in eta {\to} 3pi decays
• Cusps in K --> 3pi decays: a theoretical framework
• Two- and three-body interactions in ${\phi }^4$ theory from lattice simulations
• The cusp effect in eta' --> eta pi pi decays
• Relativistic $N$-particle energy shift in finite volume
• The $B\to K^{\ast }$ form factors on the lattice
• Predictions for the cusp in eta->3pi0 decay

Cited by in corpus (11)

• Towards a theory of hadron resonances
• Three-body interactions from the finite-volume QCD spectrum
• Relativistic-invariant formulation of the NREFT three-particle quantization condition
• Three-body dynamics of the $a_1(1260)$ resonance from lattice QCD
• Constraining $1+\mathcal{J}\to 2$ coupled-channel amplitudes in finite-volume
• Three-body resonances in the ${\phi }^4$ theory
• Particle-dimer approach for the Roper resonance in a finite volume
• Spurious poles in a finite volume
• Emergence of the $\pi (1300)$ Resonance from Lattice QCD
• Rediscovery of Numerical Lüscher's Formula from the Neural Network
• Lellouch-Lüscher relation for ultracold few-atom systems under confinement