Three-body unitarity in the finite volume
Abstract
We present the physical interpretation of lattice QCD simulations, performed in a small volume, requires an extrapolation to the infinite volume. A method is proposed to perform such an extrapolation for three interacting particles at energies above threshold. For this, a recently formulated relativistic $$3\to 3$$ amplitude based on the isobar formulation is adapted to the finite volume. The guiding principle is two- and three-body unitarity that imposes the imaginary parts of the amplitude in the infinite volume. In turn, these imaginary parts dictate the leading power-law finite-volume effects. It is demonstrated that finite-volume poles arising from the singular interaction, from the external two-body sub-amplitudes, and from the disconnected topology cancel exactly leaving only the genuine three-body eigenvalues. Lastly, the corresponding quantization condition is derived for the case of three identical scalar-isoscalar particles and its numerical implementation is demonstrated.
- Authors:
-
- George Washington Univ., Washington, DC (United States)
- George Washington Univ., Washington, DC (United States) ; Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
- Publication Date:
- Research Org.:
- Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP)
- OSTI Identifier:
- 1416327
- Report Number(s):
- JLAB-THY-17-2554; DOE/OR/23177-4221; arXiv:1709.08222
Journal ID: ISSN 1434-6001; PII: 12440; TRN: US1800924
- Grant/Contract Number:
- AC05-06OR23177; SC001658
- Resource Type:
- Accepted Manuscript
- Journal Name:
- European Physical Journal. A
- Additional Journal Information:
- Journal Volume: 53; Journal Issue: 12; Journal ID: ISSN 1434-6001
- Publisher:
- Springer
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Citation Formats
Mai, M., and Döring, M. Three-body unitarity in the finite volume. United States: N. p., 2017.
Web. doi:10.1140/epja/i2017-12440-1.
Mai, M., & Döring, M. Three-body unitarity in the finite volume. United States. https://doi.org/10.1140/epja/i2017-12440-1
Mai, M., and Döring, M. Mon .
"Three-body unitarity in the finite volume". United States. https://doi.org/10.1140/epja/i2017-12440-1. https://www.osti.gov/servlets/purl/1416327.
@article{osti_1416327,
title = {Three-body unitarity in the finite volume},
author = {Mai, M. and Döring, M.},
abstractNote = {We present the physical interpretation of lattice QCD simulations, performed in a small volume, requires an extrapolation to the infinite volume. A method is proposed to perform such an extrapolation for three interacting particles at energies above threshold. For this, a recently formulated relativistic $3\to 3$ amplitude based on the isobar formulation is adapted to the finite volume. The guiding principle is two- and three-body unitarity that imposes the imaginary parts of the amplitude in the infinite volume. In turn, these imaginary parts dictate the leading power-law finite-volume effects. It is demonstrated that finite-volume poles arising from the singular interaction, from the external two-body sub-amplitudes, and from the disconnected topology cancel exactly leaving only the genuine three-body eigenvalues. Lastly, the corresponding quantization condition is derived for the case of three identical scalar-isoscalar particles and its numerical implementation is demonstrated.},
doi = {10.1140/epja/i2017-12440-1},
journal = {European Physical Journal. A},
number = 12,
volume = 53,
place = {United States},
year = {Mon Dec 18 00:00:00 EST 2017},
month = {Mon Dec 18 00:00:00 EST 2017}
}
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Figure 1: Red dashed line (green dotted line): Real (imaginary) part of the infinite-volume S-wave projection of the potential B0 from Eq. (6) with M = 138 MeV, λ = 3476 and β = 5000 MeV. In comparison, the finite-volume projection B A+111 from Eq. (10) for the transition frommore »
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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.
Connecting physical resonant amplitudes and lattice QCD
journal, June 2016
- Bolton, Daniel R.; Briceño, Raúl A.; Wilson, David J.
- Physics Letters B, Vol. 757
Quartet S wave neutron deuteron scattering in effective field theory
journal, May 2000
- Bedaque, Paulo F.; Grießhammer, Harald W.
- Nuclear Physics A, Vol. 671, Issue 1-4
Spectrum of Three-Body Bound States in a Finite Volume
journal, March 2015
- Meißner, Ulf-G.; Ríos, Guillermo; Rusetsky, Akaki
- Physical Review Letters, Vol. 114, Issue 9
Coupled-channel scattering on a torus
journal, July 2013
- Guo, Peng; Dudek, Jozef J.; Edwards, Robert G.
- Physical Review D, Vol. 88, Issue 1
Multiple-channel generalization of Lellouch-Lüscher formula
journal, July 2012
- Hansen, Maxwell T.; Sharpe, Stephen R.
- Physical Review D, Vol. 86, Issue 1
Relating the finite-volume spectrum and the two-and-three-particle 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
A method to measure the antikaon–nucleon scattering length in lattice QCD
journal, November 2009
- Lage, Michael; Meißner, Ulf-G.; Rusetsky, Akaki
- Physics Letters B, Vol. 681, Issue 5
On the modification of the Efimov spectrum in a finite cubic box
journal, January 2010
- Kreuzer, S.; Hammer, H. -W.
- The European Physical Journal A, Vol. 43, Issue 2
Coupled-channel approach to strangeness S = -2 baryon-bayron interactions in lattice QCD
journal, September 2015
- Sasaki, K.; Aoki, S.; Doi, T.
- Progress of Theoretical and Experimental Physics, Vol. 2015, Issue 11
The B → K ⁎ form factors on the lattice
journal, September 2016
- Agadjanov, Andria; Bernard, Véronique; Meißner, Ulf-G.
- Nuclear Physics B, Vol. 910
Moving multichannel systems in a finite volume with application to proton-proton fusion
journal, November 2013
- Briceño, Raúl A.; Davoudi, Zohreh
- Physical Review D, Vol. 88, Issue 9
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.
Relativistic, model-independent, multichannel transition amplitudes in a finite volume
journal, July 2016
- Briceño, Raúl A.; Hansen, Maxwell T.
- Physical Review D, Vol. 94, Issue 1
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
Analytic properties of the scattering amplitude and resonances parameters in a meson exchange model
journal, October 2009
- Döring, M.; Hanhart, C.; Huang, F.
- Nuclear Physics A, Vol. 829, Issue 3-4
Chiral extrapolations of the meson in lattice QCD simulations
journal, August 2017
- Hu, B.; Molina, R.; Döring, M.
- Physical Review D, Vol. 96, Issue 3
Relativistic, model-independent, three-particle quantization condition
journal, December 2014
- Hansen, Maxwell T.; Sharpe, Stephen R.
- Physical Review D, Vol. 90, Issue 11
A solvable three-body model in finite volume
journal, November 2017
- Guo, Peng; Gasparian, Vladimir
- Physics Letters B, Vol. 774
Three particles in a finite volume
journal, May 2012
- Polejaeva, K.; Rusetsky, A.
- The European Physical Journal A, Vol. 48, Issue 5
Coupled , scattering in -wave and the resonance from lattice QCD
journal, November 2015
- Wilson, David J.; Briceño, Raúl A.; Dudek, Jozef J.
- Physical Review D, Vol. 92, Issue 9
Three-particle scattering amplitudes from a finite volume formalism
journal, May 2013
- Briceño, Raúl A.; Davoudi, Zohreh
- Physical Review D, Vol. 87, Issue 9
High-statistics study of the reaction γp → p2π0
journal, August 2015
- Sokhoyan, V.; Gutz, E.; Crede, V.
- The European Physical Journal A, Vol. 51, Issue 8
Two-particle multichannel systems in a finite volume with arbitrary spin
journal, April 2014
- Briceño, Raúl A.
- Physical Review D, Vol. 89, Issue 7
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
Multichannel transition amplitudes in a finite volume
journal, February 2015
- Briceño, Raúl A.; Hansen, Maxwell T.; Walker-Loud, André
- Physical Review D, Vol. 91, Issue 3
Pion-nucleon scattering in the Roper channel from lattice QCD
journal, January 2017
- Lang, C. B.; Leskovec, L.; Padmanath, M.
- Physical Review D, Vol. 95, Issue 1
Multichannel and transition amplitudes for arbitrary spin particles in a finite volume
journal, October 2015
- Briceño, Raúl A.; Hansen, Maxwell T.
- Physical Review D, Vol. 92, Issue 7
Three particles in a finite volume: The breakdown of spherical symmetry
journal, July 2012
- Kreuzer, S.; Grießhammer, H. W.
- The European Physical Journal A, Vol. 48, Issue 7
Two particle states and the S -matrix elements in multi-channel scattering
journal, July 2005
- He, Song; Feng, Xu; Liu, Chuan
- Journal of High Energy Physics, Vol. 2005, Issue 07
Coupled-channel Dπ, Dη and D s K ¯ $$ {D}_s\overline{K} $$ scattering from lattice QCD
journal, October 2016
- Moir, Graham; Peardon, Michael; Ryan, Sinéad M.
- Journal of High Energy Physics, Vol. 2016, Issue 10
Isoscalar Scattering and the Meson Resonance from QCD
journal, January 2017
- Briceño, Raul A.; Dudek, Jozef J.; Edwards, Robert G.
- Physical Review Letters, Vol. 118, Issue 2
Coupled channel analysis of the meson decay in lattice QCD
journal, September 2011
- Lang, C. B.; Mohler, Daniel; Prelovsek, Sasa
- Physical Review D, Vol. 84, Issue 5
Efimov physics in a finite volume
journal, March 2009
- Kreuzer, Simon; Hammer, H. -W.
- Physics Letters B, Vol. 673, Issue 4-5
Scalar mesons moving in a finite volume and the role of partial wave mixing
journal, August 2012
- Döring, M.; Meißner, U. -G.; Oset, E.
- The European Physical Journal A, Vol. 48, Issue 8
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
Measurement of the beam asymmetry for and photoproduction on the proton at GeV
journal, April 2017
- Al Ghoul, H.; Anassontzis, E. G.; Austregesilo, A.
- Physical Review C, Vol. 95, Issue 4
Dynamical coupled-channel approaches on a momentum lattice
journal, December 2011
- Döring, M.; Haidenbauer, J.; Meißner, U. -G.
- The European Physical Journal A, Vol. 47, Issue 12
The triton in a finite volume
journal, January 2011
- Kreuzer, Simon; Hammer, H. -W.
- Physics Letters B, Vol. 694, Issue 4-5
Rho resonance parameters from lattice QCD
journal, August 2016
- Guo, Dehua; Alexandru, Andrei; Molina, Raquel
- Physical Review D, Vol. 94, Issue 3
Measurement of and Baryon Resonance Analysis
journal, July 2003
- Ripani, M.; Burkert, V. D.; Mokeev, V.
- Physical Review Letters, Vol. 91, Issue 2
Two-particle states on a torus and their relation to the scattering matrix
journal, May 1991
- Lüscher, Martin
- Nuclear Physics B, Vol. 354, Issue 2-3
Finite-volume Hamiltonian method for coupled-channels interactions in lattice QCD
journal, November 2014
- Wu, Jia-Jun; Lee, T. -S. H.; Thomas, A. W.
- Physical Review C, Vol. 90, Issue 5
Threshold expansion of the three-particle quantization condition
journal, May 2016
- Hansen, Maxwell T.; Sharpe, Stephen R.
- Physical Review D, Vol. 93, Issue 9
Three-body unitarity with isobars revisited
journal, September 2017
- Mai, M.; Hu, B.; Döring, M.
- The European Physical Journal A, Vol. 53, Issue 9
Charm Physics
journal, May 2009
- Asner, D. M.; Bigi, I. I.; Charles, J.
- International Journal of Modern Physics A, Vol. 24, Issue supp01
Resonance properties from the finite-volume energy spectrum
journal, August 2008
- Bernard, V.; Lage, M.; Meißner, U.-G.
- Journal of High Energy Physics, Vol. 2008, Issue 08, Article No. 024
Two-Flavor Simulations of and the Role of the Channel
journal, September 2016
- Hu, B.; Molina, R.; Döring, M.
- Physical Review Letters, Vol. 117, Issue 12
Unitarized Chiral Perturbation Theory in a finite volume: Scalar meson sector
journal, November 2011
- Döring, M.; Meißner, U. -G.; Oset, E.
- The European Physical Journal A, Vol. 47, Issue 11
Nuclear reactions from lattice QCD
journal, January 2015
- Briceño, Raúl A.; Davoudi, Zohreh; Luu, Thomas C.
- Journal of Physics G: Nuclear and Particle Physics, Vol. 42, Issue 2
Measurement of the beam asymmetry Σ for π0 and η photoproduction on the proton at Eγ=9 GeV
text, January 2017
- Al Ghoul, H.; Anassontzis, E. G.; Austregesilo, A.
- Figshare
Three particles in a finite volume
conference, October 2012
- Polejaeva, Kathryn; Rusetsky, Akaki
- Proceedings of Sixth International Conference on Quarks and Nuclear Physics — PoS(QNP2012)
Pion-nucleon scattering in the Roper channel from lattice QCD
text, January 2017
- Lang, C. B.; Leskovec, L.; Padmanath, M.
- Universität Regensburg
Multiple-channel generalization of Lellouch-Lüscher formula
conference, December 2012
- Hansen, Maxwell; Sharpe, Stephen R.
- Proceedings of The 30th International Symposium on Lattice Field Theory — PoS(Lattice 2012)
Model selection for pion photoproduction
conference, March 2018
- Molina Peralta, Raquel; Landay, Justin; Hu, Bin
- Proceedings of XVII International Conference on Hadron Spectroscopy and Structure — PoS(Hadron2017)
Isoscalar ππ Scattering and the σ Meson Resonance from QCD
text, January 2017
- Briceño, Ra; Dudek, Jj; Edwards, Rg
- Apollo - University of Cambridge Repository
Review of Particle Physics
text, January 2018
- Tanabashi, M.; Hagiwara, K.; Hikasa, K.
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
Review of Particle Physics
text, January 2012
- Beringer, J.; Arguin, J.; Barnett, R.
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
Resonance properties from the finite-volume energy spectrum
text, January 2008
- Bernard, Veronique; Lage, Michael; Meißner, Ulf-G.
- arXiv
Coupled channel analysis of the rho meson decay in lattice QCD
text, January 2011
- Lang, C. B.; Mohler, Daniel; Prelovsek, Sasa
- arXiv
Three particles in a finite volume: The breakdown of spherical symmetry
text, January 2012
- Kreuzer, Simon; Grießhammer, Harald W.
- arXiv
Scalar mesons moving in a finite volume and the role of partial wave mixing
text, January 2012
- Döring, M.; Meißner, U. -G.; Oset, E.
- arXiv
Axial resonances a1(1260), b1(1235) and their decays from the lattice
text, January 2014
- Lang, C. B.; Leskovec, Luka; Mohler, Daniel
- arXiv
Finite-volume Hamiltonian method for coupled channel interactions in lattice QCD
text, January 2014
- Wu, Jia-Jun; Lee, T. -S. H.; Thomas, A. W.
- arXiv
A relativistic, model-independent, three-particle quantization condition
text, January 2014
- Hansen, Maxwell T.; Sharpe, Stephen R.
- arXiv
Coupled channel approach to strangeness S = -2 baryon-bayron interactions in Lattice QCD
text, January 2015
- Sasaki, Kenji; Aoki, Sinya; Doi, Takumi
- arXiv
Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude
text, January 2015
- Hansen, Maxwell T.; Sharpe, Stephen R.
- arXiv
Finite volume corrections to the binding energy of the X(3872)
text, January 2015
- Jansen, M.; Hammer, H. -W.; Jia, Yu
- arXiv
Perturbative results for two and three particle threshold energies in finite volume
text, January 2015
- Hansen, Maxwell T.; Sharpe, Stephen R.
- arXiv
The $B\to K^*$ form factors on the lattice
text, January 2016
- Agadjanov, Andria; Bernard, Véronique; Meißner, Ulf-G.
- arXiv
Rho resonance parameters from lattice QCD
text, January 2016
- Guo, Dehua; Alexandru, Andrei; Molina, Raquel
- arXiv
Model Selection for Pion Photoproduction
text, January 2016
- Landay, J.; Döring, M.; Fernández-Ramírez, C.
- arXiv
Nucleon resonance structure in the finite volume of lattice QCD
text, January 2016
- Wu, Jia-Jun; Kamano, H.; Lee, T. -S. H.
- arXiv
Relating the finite-volume spectrum and the two-and-three-particle $S$ matrix for relativistic systems of identical scalar particles
text, January 2017
- Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R.
- arXiv
Three-particle quantization condition in a finite volume: 1. The role of the three-particle force
text, January 2017
- Hammer, H. -W.; Pang, J. -Y.; Rusetsky, A.
- arXiv
Three particle quantization condition in a finite volume: 2. general formalism and the analysis of data
text, January 2017
- Hammer, H. -W.; Pang, J. -Y.; Rusetsky, A.
- arXiv
Baryon mass splittings and strong CP violation in SU(3) Chiral Perturbation Theory
text, January 2015
- de Vries, Jordy; Mereghetti, Emanuele; Walker-Loud, Andre
- arXiv
Three particle quantization condition in a finite volume: 2. general formalism and the analysis of data
text, January 2017
- Hammer, H. -W.; Pang, J. -Y.; Rusetsky, A.
- arXiv
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journal, February 2020
- Guo, Peng; Döring, Michael
- Physical Review D, Vol. 101, Issue 3
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- Guo, Peng; Morris, Tyler
- Physical Review D, Vol. 99, Issue 1
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journal, June 2018
- Rönchen, D.; Döring, M.; Meißner, U. -G.
- The European Physical Journal A, Vol. 54, Issue 6
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journal, November 2019
- Lehner, Christoph; Meinel, Stefan; Blum, Tom
- The European Physical Journal A, Vol. 55, Issue 11
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- Detmold, William; Edwards, Robert G.; Dudek, Jozef J.
- The European Physical Journal A, Vol. 55, Issue 11
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- Romero-López, F.; Rusetsky, A.; Urbach, C.
- The European Physical Journal C, Vol. 78, Issue 10
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journal, October 2018
- Dax, Maximilian; Isken, Tobias; Kubis, Bastian
- The European Physical Journal C, Vol. 78, Issue 10
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journal, November 2018
- Colangelo, Gilberto; Lanz, Stefan; Leutwyler, Heinrich
- The European Physical Journal C, Vol. 78, Issue 11
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journal, January 2019
- Jackura, A.; Fernández-Ramírez, C.; Mathieu, V.
- The European Physical Journal C, Vol. 79, Issue 1
Variational approach to -body interactions in finite volume
journal, November 2018
- Guo, Peng; Döring, Michael; Szczepaniak, Adam P.
- Physical Review D, Vol. 98, Issue 9
Three-body spectrum in a finite volume: the role of cubic symmetry
text, January 2018
- Döring, M.; Hammer, H. -W.; Mai, M.
- GSI Helmholtzzentrum fuer Schwerionenforschung, GSI, Darmstadt
Dynamically-coupled partial-waves in ρπ isospin-2 scattering from lattice QCD
text, January 2018
- Woss, Antoni; Thomas, Christopher; Dudek, Jj
- Apollo - University of Cambridge Repository
Three-particle bound states in a finite volume: unequal masses and higher partial waves
text, January 2017
- Meng, Yu; Liu, Chuan; Meißner, Ulf-G.
- arXiv
Three-body spectrum in a finite volume: the role of cubic symmetry
text, January 2018
- Döring, M.; Hammer, H. -W.; Mai, M.
- arXiv
Numerical study of the relativistic three-body quantization condition in the isotropic approximation
text, January 2018
- Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R.
- arXiv
Signatures of few-body resonances in finite volume
text, January 2018
- Klos, P.; König, S.; Hammer, H. -W.
- arXiv
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text, January 2018
- Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R.
- arXiv
Energy shift of the three-particle system in a finite volume
text, January 2019
- Pang, Jin-Yi; Wu, Jia-Jun; Hammer, H. -W.
- arXiv
Scattering amplitudes from finite-volume spectral functions
text, January 2019
- Bulava, John; Hansen, Maxwell T.
- arXiv
Opportunities for lattice QCD in quark and lepton flavor physics
text, January 2019
- Lehner, Christoph; Meinel, Stefan; Blum, Tom
- arXiv
Three-body scattering: Ladders and Resonances
text, January 2019
- Mikhasenko, M.; Wunderlich, Y.; Jackura, A.
- arXiv
Three-body unitarity versus finite-volume $π^+π^+π^+$ spectrum from lattice QCD
text, January 2019
- Mai, M.; Döring, M.; Culver, C.
- arXiv
Consistency checks for two-body finite-volume matrix elements: I. Conserved currents and bound states
text, January 2019
- Briceño, Raúl A.; Hansen, Maxwell T.; Jackura, Andrew W.
- arXiv
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