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Title: Numerical study of the relativistic three-body quantization condition in the isotropic approximation

Abstract

We present numerical results showing how our recently proposed relativistic three-particle quantization condition can be used in practice. Using the isotropic (generalized s-wave) approximation, and keeping only the leading terms in the effective range expansion, we show how the quantization condition can be solved numerically in a straightforward manner. In addition, we show how the integral equations that relate the intermediate three-particle infinite-volume scattering quantity, Kdf,3, to the physical scattering amplitude can be solved at and below threshold. We test our methods by reproducing known analytic results for the 1/L expansion of the threshold state, the volume dependence of three-particle bound-state energies, and the Bethe-Salpeter wavefunctions for these bound states. We also find that certain values of Kdf,3 lead to unphysical finite-volume energies, and give a preliminary analysis of these artifacts.

Authors:
; ;
Publication Date:
Research Org.:
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Univ. of Washington, Seattle, WA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP); USDOE Office of Science (SC), High Energy Physics (HEP)
OSTI Identifier:
1459751
Alternate Identifier(s):
OSTI ID: 1460364; OSTI ID: 1595810
Report Number(s):
JLAB-THY-18-2657; DOE/OR/23177-4359; arXiv:1803.04169; CERN-TH-2018-046
Journal ID: ISSN 2470-0010; PRVDAQ; 014506
Grant/Contract Number:  
SC0011637; AC05-06OR23177
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Name: Physical Review D Journal Volume: 98 Journal Issue: 1; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats

Briceño, Raúl A., Hansen, Maxwell T., and Sharpe, Stephen R. Numerical study of the relativistic three-body quantization condition in the isotropic approximation. United States: N. p., 2018. Web. doi:10.1103/PhysRevD.98.014506.
Briceño, Raúl A., Hansen, Maxwell T., & Sharpe, Stephen R. Numerical study of the relativistic three-body quantization condition in the isotropic approximation. United States. doi:https://doi.org/10.1103/PhysRevD.98.014506
Briceño, Raúl A., Hansen, Maxwell T., and Sharpe, Stephen R. Wed . "Numerical study of the relativistic three-body quantization condition in the isotropic approximation". United States. doi:https://doi.org/10.1103/PhysRevD.98.014506.
@article{osti_1459751,
title = {Numerical study of the relativistic three-body quantization condition in the isotropic approximation},
author = {Briceño, Raúl A. and Hansen, Maxwell T. and Sharpe, Stephen R.},
abstractNote = {We present numerical results showing how our recently proposed relativistic three-particle quantization condition can be used in practice. Using the isotropic (generalized s-wave) approximation, and keeping only the leading terms in the effective range expansion, we show how the quantization condition can be solved numerically in a straightforward manner. In addition, we show how the integral equations that relate the intermediate three-particle infinite-volume scattering quantity, Kdf,3, to the physical scattering amplitude can be solved at and below threshold. We test our methods by reproducing known analytic results for the 1/L expansion of the threshold state, the volume dependence of three-particle bound-state energies, and the Bethe-Salpeter wavefunctions for these bound states. We also find that certain values of Kdf,3 lead to unphysical finite-volume energies, and give a preliminary analysis of these artifacts.},
doi = {10.1103/PhysRevD.98.014506},
journal = {Physical Review D},
number = 1,
volume = 98,
place = {United States},
year = {2018},
month = {7}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: https://doi.org/10.1103/PhysRevD.98.014506

Citation Metrics:
Cited by: 10 works
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Works referenced in this record:

Three-particle quantization condition in a finite volume: 1. The role of the three-particle force
journal, September 2017

  • Hammer, Hans-Werner; Pang, Jin-Yi; Rusetsky, Akaki
  • Journal of High Energy Physics, Vol. 2017, Issue 9, 23 p.
  • DOI: 10.1007/JHEP09(2017)109

Spectrum of Three-Body Bound States in a Finite Volume
journal, March 2015


Erratum: Threshold expansion of the three-particle quantization condition [Phys. Rev. D 93 , 096006 (2016)]
journal, August 2017


Relating the finite-volume spectrum and the two-and-three-particle S matrix for relativistic systems of identical scalar particles
journal, April 2017


Three-body unitarity in the finite volume
journal, December 2017


Multiple-channel generalization of Lellouch-Lüscher formula
journal, July 2012


n -boson energies at finite volume and three-boson interactions
journal, October 2007


Moving multichannel systems in a finite volume with application to proton-proton fusion
journal, November 2013


Resonances in Coupled π K η K Scattering from Quantum Chromodynamics
journal, October 2014


Timelike pion form factor in lattice QCD
journal, March 2015


Efimov physics in a finite volume
journal, March 2009


Scattering processes and resonances from lattice QCD
journal, April 2018


Perturbative results for two- and three-particle threshold energies in finite volume
journal, January 2016


Three-particle quantization condition in a finite volume: 2. General formalism and the analysis of data
journal, October 2017

  • Hammer, Hans-Werner; Pang, Jin-Yi; Rusetsky, Akaki
  • Journal of High Energy Physics, Vol. 2017, Issue 10, 31 p.
  • DOI: 10.1007/JHEP10(2017)115

Elastic I = 3 / 2 p -wave nucleon-pion scattering amplitude and the Δ ( 1232 ) resonance from N f = 2 + 1 lattice QCD
journal, January 2018


Applying the relativistic quantization condition to a three-particle bound state in a periodic box
journal, February 2017


Resonance scattering phase shifts on a non-rest-frame lattice
journal, September 1995


Are two nucleons bound in lattice QCD for heavy quark masses? Consistency check with Lüscher’s finite volume formula
journal, August 2017


Two-particle states on a torus and their relation to the scattering matrix
journal, May 1991


Relativistic, model-independent, three-particle quantization condition
journal, December 2014


Three-body spectrum in a finite volume: The role of cubic symmetry
journal, June 2018


Erratum: Spectrum of Three-Body Bound States in a Finite Volume [Phys. Rev. Lett. 114 , 091602 (2015)]
journal, August 2016


Three particles in a finite volume
journal, May 2012


A solvable three-body model in finite volume
journal, November 2017


Three-particle scattering amplitudes from a finite volume formalism
journal, May 2013


Threshold expansion of the three-particle quantization condition
journal, May 2016


Three-body unitarity with isobars revisited
journal, September 2017


π π π γ * amplitude and the resonant ρ π γ * transition from lattice QCD
journal, June 2016


Finite-volume effects for two-hadron states in moving frames
journal, October 2005


Two-particle multichannel systems in a finite volume with arbitrary spin
journal, April 2014


Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude
journal, December 2015


Multichannel 1 2 transition amplitudes in a finite volume
journal, February 2015


Testing the threshold expansion for three-particle energies at fourth order in ϕ 4 theory
journal, September 2017


Multichannel 0 2 and 1 2 transition amplitudes for arbitrary spin particles in a finite volume
journal, October 2015


Volume dependence of the energy spectrum in massive quantum field theories: II. Scattering states
journal, June 1986

  • Lüscher, M.
  • Communications in Mathematical Physics, Vol. 105, Issue 2
  • DOI: 10.1007/BF01211097

Three particles in a finite volume: The breakdown of spherical symmetry
journal, July 2012


Volume dependence of the energy spectrum in massive quantum field theories: I. Stable particle states
journal, June 1986

  • Lüscher, M.
  • Communications in Mathematical Physics, Vol. 104, Issue 2
  • DOI: 10.1007/bf01211589

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    Equivalence of three-particle scattering formalisms
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    b 1 resonance in coupled π ω , π ϕ scattering from lattice QCD
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    Unitarity of the infinite-volume three-particle scattering amplitude arising from a finite-volume formalism
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    Consistency checks for two-body finite-volume matrix elements: Conserved currents and bound states
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    Long-range electroweak amplitudes of single hadrons from Euclidean finite-volume correlation functions
    journal, January 2020


    Three-body unitarity versus finite-volume π + π + π + spectrum from lattice QCD
    journal, March 2020


    Three-particle bound states in a finite volume: Unequal masses and higher partial waves
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    Variational approach to N -body interactions in finite volume
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    Pole position of the a 1 ( 1260 ) from τ -decay
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    Three-particle systems with resonant subprocesses in a finite volume
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    Energy shift of the three-particle system in a finite volume
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    Finite-Volume Spectrum of π + π + and π + π + π + Systems
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    Two- and Three-Pion Finite-Volume Spectra at Maximal Isospin from Lattice QCD
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    Opportunities for Lattice QCD in quark and lepton flavor physics
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    Phenomenology of relativistic $$\mathbf {3}\rightarrow \mathbf {3}$$ 3 → 3 reaction amplitudes within the isobar approximation
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