DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: 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.

Authors:
ORCiD logo; ORCiD logo
Publication Date:
Research Org.:
Univ. of Washington, Seattle, WA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP)
OSTI Identifier:
1668118
Alternate Identifier(s):
OSTI ID: 1705739; OSTI ID: 1774029
Grant/Contract Number:  
SC0011637
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Name: Physical Review D Journal Volume: 102 Journal Issue: 5; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; effective field theory; few-body systems; lattice field theory; nuclear physics; particles & fields

Citation Formats

Blanton, Tyler D., and Sharpe, Stephen R. Equivalence of relativistic three-particle quantization conditions. United States: N. p., 2020. Web. doi:10.1103/physrevd.102.054515.
Blanton, Tyler D., & Sharpe, Stephen R. Equivalence of relativistic three-particle quantization conditions. United States. https://doi.org/10.1103/physrevd.102.054515
Blanton, Tyler D., and Sharpe, Stephen R. Mon . "Equivalence of relativistic three-particle quantization conditions". United States. https://doi.org/10.1103/physrevd.102.054515.
@article{osti_1668118,
title = {Equivalence of relativistic three-particle quantization conditions},
author = {Blanton, Tyler D. and Sharpe, Stephen R.},
abstractNote = {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.},
doi = {10.1103/physrevd.102.054515},
journal = {Physical Review D},
number = 5,
volume = 102,
place = {United States},
year = {2020},
month = {9}
}

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

Energy shift of the three-particle system in a finite volume
journal, April 2019


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


Finite-Volume Spectrum of π + π + and π + π + π + Systems
journal, February 2019


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


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

  • Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R.
  • Physical Review D, Vol. 95, Issue 7
  • DOI: 10.1103/PhysRevD.95.074510

Signatures of few-body resonances in finite volume
journal, September 2018


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


Generalizing the relativistic quantization condition to include all three-pion isospin channels
journal, July 2020

  • Hansen, Maxwell T.; Romero-López, Fernando; Sharpe, Stephen R.
  • Journal of High Energy Physics, Vol. 2020, Issue 7
  • DOI: 10.1007/JHEP07(2020)047

Variational approach to N -body interactions in finite volume
journal, November 2018


Three particles on the lattice
conference, August 2020

  • Rusetsky, Akaki
  • Proceedings of 37th International Symposium on Lattice Field Theory — PoS(LATTICE2019)
  • DOI: 10.22323/1.363.0281

Equivalence of three-particle scattering formalisms
journal, August 2019

  • Jackura, A. W.; Dawid, S. M.; Fernández-Ramírez, C.
  • Physical Review D, Vol. 100, Issue 3
  • DOI: 10.1103/PhysRevD.100.034508

Lattice QCD and Three-Particle Decays of Resonances
journal, October 2019


Two- and Three-Pion Finite-Volume Spectra at Maximal Isospin from Lattice QCD
journal, October 2019


Two- and three-body interactions in $$\varphi ^4$$ φ 4 theory from lattice simulations
journal, October 2018


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

Numerical exploration of three relativistic particles in a finite volume including two-particle resonances and bound states
journal, October 2019

  • Romero-López, Fernando; Sharpe, Stephen R.; Blanton, Tyler D.
  • Journal of High Energy Physics, Vol. 2019, Issue 10
  • DOI: 10.1007/JHEP10(2019)007

Three pion spectrum in the I = 3 channel from lattice QCD
journal, June 2020


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


Numerical study of the relativistic three-body quantization condition in the isotropic approximation
journal, July 2018

  • Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R.
  • Physical Review D, Vol. 98, Issue 1
  • DOI: 10.1103/PhysRevD.98.014506

Implementing the three-particle quantization condition including higher partial waves
journal, March 2019

  • Blanton, Tyler D.; Romero-López, Fernando; Sharpe, Stephen R.
  • Journal of High Energy Physics, Vol. 2019, Issue 3
  • DOI: 10.1007/JHEP03(2019)106

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


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


Phenomenology of relativistic $$\mathbf {3}\rightarrow \mathbf {3}$$ 3 → 3 reaction amplitudes within the isobar approximation
journal, January 2019


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


Unitarity of the infinite-volume three-particle scattering amplitude arising from a finite-volume formalism
journal, September 2019


I = 3 Three-Pion Scattering Amplitude from Lattice QCD
journal, January 2020


Three-particle systems with resonant subprocesses in a finite volume
journal, January 2019

  • Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R.
  • Physical Review D, Vol. 99, Issue 1
  • DOI: 10.1103/PhysRevD.99.014516