Three-body unitarity in the finite volume

Mai, M.; Döring, M.

doi:10.1140/epja/i2017-12440-1

Title: Three-body unitarity in the finite volume

Journal Article · Mon Dec 18 04:00:00 UTC 2017 · European Physical Journal. A

DOI: https://doi.org/10.1140/epja/i2017-12440-1 · OSTI ID:1416327

Mai, M. ^[1]; Döring, M. ^[2]

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)

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.

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Research Organization:: Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)

Grant/Contract Number:: AC05-06OR23177

OSTI ID:: 1416327

Report Number(s):: JLAB-THY--17-2554; DOE/OR/23177-4221; arXiv:1709.08222; PII: 12440

Journal Information:: European Physical Journal. A, Journal Name: European Physical Journal. A Journal Issue: 12 Vol. 53; ISSN 1434-6001

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

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Scattering amplitudes from finite-volume spectral functions Bulava, John; Hansen, Maxwell T. Physical Review D, Vol. 100, Issue 3 https://doi.org/10.1103/physrevd.100.034521	journal	August 2019
b 1 resonance in coupled π ω , π ϕ scattering from lattice QCD Woss, Antoni J.; Thomas, Christopher E.; Dudek, Jozef J. Physical Review D, Vol. 100, Issue 5 https://doi.org/10.1103/physrevd.100.054506	journal	September 2019
Unitarity of the infinite-volume three-particle scattering amplitude arising from a finite-volume formalism Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R. Physical Review D, Vol. 100, Issue 5 https://doi.org/10.1103/physrevd.100.054508	journal	September 2019
Consistency checks for two-body finite-volume matrix elements: Conserved currents and bound states Briceño, Raúl A.; Hansen, Maxwell T.; Jackura, Andrew W. Physical Review D, Vol. 100, Issue 11 https://doi.org/10.1103/physrevd.100.114505	journal	December 2019
Long-range electroweak amplitudes of single hadrons from Euclidean finite-volume correlation functions Briceño, Raúl A.; Davoudi, Zohreh; Hansen, Maxwell T. Physical Review D, Vol. 101, Issue 1 https://doi.org/10.1103/physrevd.101.014509	journal	January 2020
Lattice model of heavy-light three-body system Guo, Peng; Döring, Michael Physical Review D, Vol. 101, Issue 3 https://doi.org/10.1103/physrevd.101.034501	journal	February 2020
Three-body unitarity versus finite-volume π + π + π + spectrum from lattice QCD Mai, M.; Döring, M.; Culver, C. Physical Review D, Vol. 101, Issue 5 https://doi.org/10.1103/physrevd.101.054510	journal	March 2020
Three-body spectrum in a finite volume: The role of cubic symmetry Döring, M.; Hammer, H. -W.; Mai, M. Physical Review D, Vol. 97, Issue 11 https://doi.org/10.1103/physrevd.97.114508	journal	June 2018
Numerical study of the relativistic three-body quantization condition in the isotropic approximation Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R. Physical Review D, Vol. 98, Issue 1 https://doi.org/10.1103/physrevd.98.014506	journal	July 2018
Three-particle bound states in a finite volume: Unequal masses and higher partial waves Meng, Yu; Liu, Chuan; Meißner, Ulf-G. Physical Review D, Vol. 98, Issue 1 https://doi.org/10.1103/physrevd.98.014508	journal	July 2018
Variational approach to N -body interactions in finite volume Guo, Peng; Döring, Michael; Szczepaniak, Adam P. Physical Review D, Vol. 98, Issue 9 https://doi.org/10.1103/physrevd.98.094502	journal	November 2018
Pole position of the a 1 ( 1260 ) from τ -decay Mikhasenko, M.; Pilloni, A.; Jackura, A. Physical Review D, Vol. 98, Issue 9 https://doi.org/10.1103/physrevd.98.096021	journal	November 2018
Multiple-particle interaction in ( 1 + 1 )-dimensional lattice model Guo, Peng; Morris, Tyler Physical Review D, Vol. 99, Issue 1 https://doi.org/10.1103/physrevd.99.014501	journal	January 2019
Three-particle systems with resonant subprocesses in a finite volume Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R. Physical Review D, Vol. 99, Issue 1 https://doi.org/10.1103/physrevd.99.014516	journal	January 2019
Towards the minimal spectrum of excited baryons Landay, J.; Mai, M.; Döring, M. Physical Review D, Vol. 99, Issue 1 https://doi.org/10.1103/physrevd.99.016001	journal	January 2019
Energy shift of the three-particle system in a finite volume Pang, Jin-Yi; Wu, Jia-Jun; Hammer, Hans-Werner Physical Review D, Vol. 99, Issue 7 https://doi.org/10.1103/physrevd.99.074513	journal	April 2019
Finite-Volume Spectrum of π + π + and π + π + π + Systems Mai, M.; Döring, M. Physical Review Letters, Vol. 122, Issue 6 https://doi.org/10.1103/physrevlett.122.062503	journal	February 2019
Two- and Three-Pion Finite-Volume Spectra at Maximal Isospin from Lattice QCD Hörz, Ben; Hanlon, Andrew Physical Review Letters, Vol. 123, Issue 14 https://doi.org/10.1103/physrevlett.123.142002	journal	October 2019
I = 3 Three-Pion Scattering Amplitude from Lattice QCD Blanton, Tyler D.; Romero-López, Fernando; Sharpe, Stephen R. Physical Review Letters, Vol. 124, Issue 3 https://doi.org/10.1103/physrevlett.124.032001	journal	January 2020
The impact of $K^{+}\Lambda$ K + Λ photoproduction on the resonance spectrum Rönchen, D.; Döring, M.; Meißner, U. -G. The European Physical Journal A, Vol. 54, Issue 6 https://doi.org/10.1140/epja/i2018-12541-3	journal	June 2018
Opportunities for Lattice QCD in quark and lepton flavor physics Lehner, Christoph; Meinel, Stefan; Blum, Tom The European Physical Journal A, Vol. 55, Issue 11 https://doi.org/10.1140/epja/i2019-12891-2	journal	November 2019
Hadrons and nuclei Detmold, William; Edwards, Robert G.; Dudek, Jozef J. The European Physical Journal A, Vol. 55, Issue 11 https://doi.org/10.1140/epja/i2019-12902-4	journal	November 2019
Two- and three-body interactions in $$\varphi ^4$$ φ 4 theory from lattice simulations Romero-López, F.; Rusetsky, A.; Urbach, C. The European Physical Journal C, Vol. 78, Issue 10 https://doi.org/10.1140/epjc/s10052-018-6325-8	journal	October 2018
Quark-mass dependence in $$\omega \rightarrow 3\pi $$ ω → 3 π decays Dax, Maximilian; Isken, Tobias; Kubis, Bastian The European Physical Journal C, Vol. 78, Issue 10 https://doi.org/10.1140/epjc/s10052-018-6346-3	journal	October 2018
Dispersive analysis of $$\eta \rightarrow 3 \pi $$ η → 3 π Colangelo, Gilberto; Lanz, Stefan; Leutwyler, Heinrich The European Physical Journal C, Vol. 78, Issue 11 https://doi.org/10.1140/epjc/s10052-018-6377-9	journal	November 2018
Phenomenology of relativistic $$\mathbf {3}\rightarrow \mathbf {3}$$ 3 → 3 reaction amplitudes within the isobar approximation Jackura, A.; Fernández-Ramírez, C.; Mathieu, V. The European Physical Journal C, Vol. 79, Issue 1 https://doi.org/10.1140/epjc/s10052-019-6566-1	journal	January 2019
Three-body spectrum in a finite volume: the role of cubic symmetry Döring, M.; Hammer, H. -W.; Mai, M. GSI Helmholtzzentrum fuer Schwerionenforschung, GSI, Darmstadt https://doi.org/10.15120/gsi-2019-00687	text	January 2018
Dynamically-coupled partial-waves in ρπ isospin-2 scattering from lattice QCD Woss, Antoni; Thomas, Christopher; Dudek, Jj Apollo - University of Cambridge Repository https://doi.org/10.17863/cam.26944	text	January 2018
Three-particle bound states in a finite volume: unequal masses and higher partial waves Meng, Yu; Liu, Chuan; Meißner, Ulf-G. arXiv https://doi.org/10.48550/arxiv.1712.08464	text	January 2017
Three-body spectrum in a finite volume: the role of cubic symmetry Döring, M.; Hammer, H. -W.; Mai, M. arXiv https://doi.org/10.48550/arxiv.1802.03362	text	January 2018
Numerical study of the relativistic three-body quantization condition in the isotropic approximation Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R. arXiv https://doi.org/10.48550/arxiv.1803.04169	text	January 2018
Signatures of few-body resonances in finite volume Klos, P.; König, S.; Hammer, H. -W. arXiv https://doi.org/10.48550/arxiv.1805.02029	text	January 2018
Three-particle systems with resonant subprocesses in a finite volume Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R. arXiv https://doi.org/10.48550/arxiv.1810.01429	text	January 2018
Energy shift of the three-particle system in a finite volume Pang, Jin-Yi; Wu, Jia-Jun; Hammer, H. -W. arXiv https://doi.org/10.48550/arxiv.1902.01111	text	January 2019
Scattering amplitudes from finite-volume spectral functions Bulava, John; Hansen, Maxwell T. arXiv https://doi.org/10.48550/arxiv.1903.11735	text	January 2019
Opportunities for lattice QCD in quark and lepton flavor physics Lehner, Christoph; Meinel, Stefan; Blum, Tom arXiv https://doi.org/10.48550/arxiv.1904.09479	text	January 2019
Three-body scattering: Ladders and Resonances Mikhasenko, M.; Wunderlich, Y.; Jackura, A. arXiv https://doi.org/10.48550/arxiv.1904.11894	text	January 2019
Three-body unitarity versus finite-volume $π^+π^+π^+$ spectrum from lattice QCD Mai, M.; Döring, M.; Culver, C. arXiv https://doi.org/10.48550/arxiv.1909.05749	text	January 2019
Consistency checks for two-body finite-volume matrix elements: I. Conserved currents and bound states Briceño, Raúl A.; Hansen, Maxwell T.; Jackura, Andrew W. arXiv https://doi.org/10.48550/arxiv.1909.10357	text	January 2019

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