Equivalence of three-particle scattering formalisms

Jackura, A. W.; Dawid, S. M.; Fernández-Ramírez, C.; Mathieu, V.; Mikhasenko, M.; Pilloni, A.; Sharpe, S. R.; Szczepaniak, A. P.

doi:10.1103/PhysRevD.100.034508

Title: Equivalence of three-particle scattering formalisms

Abstract

In recent years, different on-shell 3→3 scattering formalisms have been proposed to be applied to both lattice QCD and infinite volume scattering processes. We prove that the formulation in the infinite volume presented by Hansen and Sharpe in Phys.~Rev.~D92, 114509 (2015) and subsequently Briceño, Hansen, and Sharpe in Phys.~Rev.~D95, 074510 (2017) can be recovered from the B-matrix representation, derived on the basis of S-matrix unitarity, presented by Mai {\em et al.} in Eur.~Phys.~J.~A53, 177 (2017) and Jackura {\em et al.} in Eur.~Phys.~J.~C79, 56 (2019). Therefore, both formalisms in the infinite volume are equivalent and the physical content is identical. Additionally, the Faddeev equations are recovered in the non-relativistic limit of both representations.

Authors:: Jackura, A. W.; Dawid, S. M.; Fernández-Ramírez, C.; Mathieu, V.; Mikhasenko, M.; Pilloni, A.; Sharpe, S. R.; Szczepaniak, A. P.; Joint Physics Analysis Center

Publication Date:: 2019-08-13

Research Org.:: Univ. of Washington, Seattle, WA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF)

Contributing Org.:: Joint Physics Analysis Center

OSTI Identifier:: 1557359

Alternate Identifier(s):: OSTI ID: 1557621; OSTI ID: 1595143

Report Number(s):: JLAB-THY-19-2947; DOE/OR/23177-4683; arXiv:1905.12007
Journal ID: ISSN 2470-0010; PRVDAQ; 034508

Grant/Contract Number:: SC0011637; AC05-06OR23177; FG02-87ER40365; PHY-1415459; IA101819; 251817; A1-S-21389

Resource Type:: Published Article

Journal Name:: Physical Review D

Additional Journal Information:: Journal Name: Physical Review D Journal Volume: 100 Journal Issue: 3; 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; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Lattice QCD; Particles & Fields; Nuclear Physics

Citation Formats


                    Jackura, A. W., Dawid, S. M., Fernández-Ramírez, C., Mathieu, V., Mikhasenko, M., Pilloni, A., Sharpe, S. R., Szczepaniak, A. P., and Joint Physics Analysis Center. Equivalence of three-particle scattering formalisms.  United States: N. p., 2019. 
Web.  doi:10.1103/PhysRevD.100.034508.

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                    Jackura, A. W., Dawid, S. M., Fernández-Ramírez, C., Mathieu, V., Mikhasenko, M., Pilloni, A., Sharpe, S. R., Szczepaniak, A. P., & Joint Physics Analysis Center. Equivalence of three-particle scattering formalisms.  United States.  https://doi.org/10.1103/PhysRevD.100.034508

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                    Jackura, A. W., Dawid, S. M., Fernández-Ramírez, C., Mathieu, V., Mikhasenko, M., Pilloni, A., Sharpe, S. R., Szczepaniak, A. P., and Joint Physics Analysis Center. Tue .  
"Equivalence of three-particle scattering formalisms".  United States.  https://doi.org/10.1103/PhysRevD.100.034508.

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@article{osti_1557359,

  title        = {Equivalence of three-particle scattering formalisms},

  author       = {Jackura, A. W. and Dawid, S. M. and Fernández-Ramírez, C. and Mathieu, V. and Mikhasenko, M. and Pilloni, A. and Sharpe, S. R. and Szczepaniak, A. P. and Joint Physics Analysis Center},

  abstractNote = {In recent years, different on-shell 3→3 scattering formalisms have been proposed to be applied to both lattice QCD and infinite volume scattering processes. We prove that the formulation in the infinite volume presented by Hansen and Sharpe in Phys.~Rev.~D92, 114509 (2015) and subsequently Briceño, Hansen, and Sharpe in Phys.~Rev.~D95, 074510 (2017) can be recovered from the B-matrix representation, derived on the basis of S-matrix unitarity, presented by Mai {\em et al.} in Eur.~Phys.~J.~A53, 177 (2017) and Jackura {\em et al.} in Eur.~Phys.~J.~C79, 56 (2019). Therefore, both formalisms in the infinite volume are equivalent and the physical content is identical. Additionally, the Faddeev equations are recovered in the non-relativistic limit of both representations.},

  doi          = {10.1103/PhysRevD.100.034508},

  journal      = {Physical Review D},

  number       = 3,

  volume       = 100,

  place        = {United States},

  year         = {2019},

  month        = {8}

}

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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

Poincaré Invariant Three-Body Scattering
journal, March 2009

Elster, Ch.; Lin, T.; Polyzou, W. N.
Few-Body Systems, Vol. 45, Issue 2-4
DOI: 10.1007/s00601-009-0019-6

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

Pang, Jin-Yi; Wu, Jia-Jun; Hammer, Hans-Werner
Physical Review D, Vol. 99, Issue 7
DOI: 10.1103/PhysRevD.99.074513

Ab Initio Determination of Light Hadron Masses
journal, November 2008

Durr, S.; Fodor, Z.; Frison, J.
Science, Vol. 322, Issue 5905
DOI: 10.1126/science.1163233

Finite-Volume Spectrum of $π^{+} π^{+}$ and $π^{+} π^{+} π^{+}$ Systems
journal, February 2019

Mai, M.; Döring, M.
Physical Review Letters, Vol. 122, Issue 6
DOI: 10.1103/PhysRevLett.122.062503

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

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

Mai, M.; Döring, M.
The European Physical Journal A, Vol. 53, Issue 12
DOI: 10.1140/epja/i2017-12440-1

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

Dudek, Jozef J.; Edwards, Robert G.; Thomas, Christopher E.
Physical Review Letters, Vol. 113, Issue 18
DOI: 10.1103/PhysRevLett.113.182001

Scattering processes and resonances from lattice QCD
journal, April 2018

Briceño, Raúl A.; Dudek, Jozef J.; Young, Ross D.
Reviews of Modern Physics, Vol. 90, Issue 2
DOI: 10.1103/RevModPhys.90.025001

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

Hansen, Maxwell T.; Sharpe, Stephen R.
Physical Review D, Vol. 93, Issue 1
DOI: 10.1103/PhysRevD.93.014506

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 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

$ρ$ meson form factors in a confining Nambu–Jona-Lasinio model
journal, July 2015

Carrillo-Serrano, Manuel E.; Bentz, Wolfgang; Cloët, Ian C.
Physical Review C, Vol. 92, Issue 1
DOI: 10.1103/PhysRevC.92.015212

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

Hansen, Maxwell T.; Sharpe, Stephen R.
Physical Review D, Vol. 95, Issue 3
DOI: 10.1103/PhysRevD.95.034501

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

Light mesons in QCD and unquenching effects from the 3PI effective action
journal, February 2016

Williams, Richard; Fischer, Christian S.; Heupel, Walter
Physical Review D, Vol. 93, Issue 3
DOI: 10.1103/PhysRevD.93.034026

Deuteron and exotic two-body bound states from lattice QCD
journal, March 2012

Beane, S. R.; Chang, E.; Detmold, W.
Physical Review D, Vol. 85, Issue 5
DOI: 10.1103/PhysRevD.85.054511

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

Hansen, Maxwell T.; Sharpe, Stephen R.
Physical Review D, Vol. 90, Issue 11
DOI: 10.1103/PhysRevD.90.116003

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

Döring, M.; Hammer, H. -W.; Mai, M.
Physical Review D, Vol. 97, Issue 11
DOI: 10.1103/PhysRevD.97.114508

Three particles in a finite volume
journal, May 2012

Polejaeva, K.; Rusetsky, A.
The European Physical Journal A, Vol. 48, Issue 5
DOI: 10.1140/epja/i2012-12067-8

Coupled $π π$ , $K \bar{K}$ scattering in $P$ -wave and the $ρ$ resonance from lattice QCD
journal, November 2015

Wilson, David J.; Briceño, Raúl A.; Dudek, Jozef J.
Physical Review D, Vol. 92, Issue 9
DOI: 10.1103/PhysRevD.92.094502

Three-body unitarity with isobars revisited
journal, September 2017

Mai, M.; Hu, B.; Döring, M.
The European Physical Journal A, Vol. 53, Issue 9
DOI: 10.1140/epja/i2017-12368-4

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

Jackura, A.; Fernández-Ramírez, C.; Mathieu, V.
The European Physical Journal C, Vol. 79, Issue 1
DOI: 10.1140/epjc/s10052-019-6566-1

Nucleon resonances in Compton scattering
journal, November 2018

Eichmann, Gernot; Ramalho, G.
Physical Review D, Vol. 98, Issue 9
DOI: 10.1103/PhysRevD.98.093007

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

Hansen, Maxwell T.; Sharpe, Stephen R.
Physical Review D, Vol. 92, Issue 11
DOI: 10.1103/PhysRevD.92.114509

Baryons as relativistic three-quark bound states
journal, November 2016

Eichmann, Gernot; Sanchis-Alepuz, Hèlios; Williams, Richard
Progress in Particle and Nuclear Physics, Vol. 91
DOI: 10.1016/j.ppnp.2016.07.001

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

First order relativistic three-body scattering
journal, July 2007

Lin, T.; Elster, Ch.; Polyzou, W. N.
Physical Review C, Vol. 76, Issue 1
DOI: 10.1103/PhysRevC.76.014010

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Similar Records

Title: Equivalence of three-particle scattering formalisms

Abstract

Citation Formats

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

Poincaré Invariant Three-Body Scattering journal, March 2009

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

Ab Initio Determination of Light Hadron Masses journal, November 2008

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

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

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

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

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

ρ meson form factors in a confining Nambu–Jona-Lasinio model journal, July 2015

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

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

Light mesons in QCD and unquenching effects from the 3PI effective action journal, February 2016

Deuteron and exotic two-body bound states from lattice QCD journal, March 2012

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

Three particles in a finite volume journal, May 2012

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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

Nucleon resonances in Compton scattering journal, November 2018

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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
journal, February 2019

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

Resonances in Coupled $π K − η K$ Scattering from Quantum Chromodynamics
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Scattering processes and resonances from lattice QCD
journal, April 2018

Perturbative results for two- and three-particle threshold energies in finite volume
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Three-particle quantization condition in a finite volume: 2. General formalism and the analysis of data
journal, October 2017

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

$ρ$ meson form factors in a confining Nambu–Jona-Lasinio model
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Applying the relativistic quantization condition to a three-particle bound state in a periodic box
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Implementing the three-particle quantization condition including higher partial waves
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Light mesons in QCD and unquenching effects from the 3PI effective action
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Deuteron and exotic two-body bound states from lattice QCD
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