Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude

2015/04/30 by Maxwell T. Hansen, Stephen R. Sharpe · 8 citations
Physics and Astronomy · #Amplitude #Computational physics #Finite volume method #Geology #High-Energy Particle Collisions Research #Optics #Particle (ecology) #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #Quantum electrodynamics #Quantum mechanics #Scattering #Scattering amplitude #Spectrum (functional analysis) #Volume (thermodynamics) #hep-lat

paper · pdf · doi:10.1103/physrevd.92.114509

published as Phys. Rev. D 92, 114509 (2015) · 24 pages, 6 figures, v2: added motivation in the introduction, added figure to clarify explanations, results unchanged---matches published version

openalex publication_date 2015/12/16 · arxiv created 2016/01/04 · arxiv updated 2016/01/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

In this article we complete our formalism relating the finite-volume energy spectrum of a scalar quantum field theory to the three-to-three scattering amplitude, M₃. In previous work [Phys. Rev. D 90, 116003 (2014)], we found a quantization condition relating the spectrum to a nonstandard infinite-volume quantity, denoted K_df,3. Here we present the relation between K_df,3 and M₃. We then discuss briefly how our now completed formalism can be practically implemented to extract M₃ from the finite-volume energy spectrum.

Citations

• Three-boson problem at low energy and implications for dilute Bose-Einstein condensates
• Spectrum of Three-Body Bound States in a Finite Volume

Cited by

• Hadron-hadron interactions from N f = 2 + 1 + 1 lattice QCD: isospin-2 ππ scattering length
• Numerical exploration of three relativistic particles in a finite volume including two-particle resonances and bound states
• Lattice model of heavy-light three-body system
• Testing the threshold expansion for three-particle energies at fourth order in ϕ4 theory
• Role of boundary conditions in quantum computations of scattering observables
• Chiral extrapolations of the ρ(770) meson in Nf=2+1 lattice QCD simulations
• Relating the finite-volume spectrum and the two-and-three-particle S matrix for relativistic systems of identical scalar particles
• Bound states in the B-matrix formalism for the three-body scattering
• On the effect of excited states in lattice calculations of the nucleon axial charge