Three-body unitarity versus finite-volume spectrum from lattice QCD
Abstract
Strong three-body interactions above threshold govern the dynamics of many exotics and conventional excited mesons and baryons. Three-body finite-volume energies calculated from lattice QCD promise an ab initio understanding of these systems. We calculate the three-π+ spectrum unraveling the three-body dynamics that is tightly intertwined with the S-matrix principle of three-body unitarity and compare it with recent lattice QCD results. For this purpose, we develop a formalism for three-body systems in moving frames and apply it numerically.
- Authors:
- Publication Date:
- Research Org.:
- Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1605631
- Alternate Identifier(s):
- OSTI ID: 1606196
- Report Number(s):
- JLAB-THY-20-3167; DOE-OR-23177-4949
Journal ID: ISSN 2470-0010; PRVDAQ; 054510
- Grant/Contract Number:
- SC0016582; FG02-95ER40907; PHY-1452055
- Resource Type:
- Published Article
- Journal Name:
- Physical Review D
- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 101 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; Chiral perturbation theory; Few-body systems; Lattice QCD; Chiral symmetry
Citation Formats
Mai, M., Döring, M., Culver, C., and Alexandru, A. Three-body unitarity versus finite-volume π + π + π + spectrum from lattice QCD. United States: N. p., 2020.
Web. doi:10.1103/PhysRevD.101.054510.
Mai, M., Döring, M., Culver, C., & Alexandru, A. Three-body unitarity versus finite-volume π + π + π + spectrum from lattice QCD. United States. https://doi.org/10.1103/PhysRevD.101.054510
Mai, M., Döring, M., Culver, C., and Alexandru, A. Fri .
"Three-body unitarity versus finite-volume π + π + π + spectrum from lattice QCD". United States. https://doi.org/10.1103/PhysRevD.101.054510.
@article{osti_1605631,
title = {Three-body unitarity versus finite-volume π + π + π + spectrum from lattice QCD},
author = {Mai, M. and Döring, M. and Culver, C. and Alexandru, A.},
abstractNote = {Strong three-body interactions above threshold govern the dynamics of many exotics and conventional excited mesons and baryons. Three-body finite-volume energies calculated from lattice QCD promise an ab initio understanding of these systems. We calculate the three-π+ spectrum unraveling the three-body dynamics that is tightly intertwined with the S-matrix principle of three-body unitarity and compare it with recent lattice QCD results. For this purpose, we develop a formalism for three-body systems in moving frames and apply it numerically.},
doi = {10.1103/PhysRevD.101.054510},
journal = {Physical Review D},
number = 5,
volume = 101,
place = {United States},
year = {2020},
month = {3}
}
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https://doi.org/10.1103/PhysRevD.101.054510
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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.
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
Determination of SU(2) chiral perturbation theory low energy constants from a precise description of pion-pion scattering threshold parameters
journal, September 2013
- Nebreda, J.; Peláez, J. R.; Ríos, G.
- Physical Review D, Vol. 88, Issue 5
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
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
Erratum: Threshold expansion of the three-particle quantization condition [Phys. Rev. D 93 , 096006 (2016)]
journal, August 2017
- Hansen, Maxwell T.; Sharpe, Stephen R.
- Physical Review D, Vol. 96, Issue 3
Relativistic Three-Body Theory with Applications to Scattering
journal, October 1968
- Aaron, R.; Amado, R. D.; Young, J. E.
- Physical Review, Vol. 174, Issue 5
From hadrons to quarks in neutron stars: a review
journal, March 2018
- Baym, Gordon; Hatsuda, Tetsuo; Kojo, Toru
- Reports on Progress in Physics, Vol. 81, Issue 5
Finite-Volume Spectrum of and Systems
journal, February 2019
- Mai, M.; Döring, M.
- Physical Review Letters, Vol. 122, Issue 6
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
Inverse amplitude method and Adler zeros
journal, March 2008
- Gómez Nicola, A.; Peláez, J. R.; Ríos, G.
- Physical Review D, Vol. 77, Issue 5
Study of Scattering in the Isotopic-Spin-2 Channel
journal, February 1973
- Cohen, D.; Ferbel, T.; Slattery, P.
- Physical Review D, Vol. 7, Issue 3
- and -wave phase shifts in isospin-2 scattering from lattice QCD
journal, August 2012
- Dudek, Jozef J.; Edwards, Robert G.; Thomas, Christopher E.
- Physical Review D, Vol. 86, Issue 3
Topological phases for bound states moving in a finite volume
journal, November 2011
- Bour, Shahin; König, Sebastian; Lee, Dean
- Physical Review D, Vol. 84, Issue 9
Signatures of few-body resonances in finite volume
journal, September 2018
- Klos, P.; König, S.; Hammer, H. -W.
- Physical Review C, Vol. 98, Issue 3
Chiral Perturbation Theory and Final-State Theorem
journal, November 1988
- Truong, Tran N.
- Physical Review Letters, Vol. 61, Issue 22
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
Strange and nonstrange quark mass dependence of elastic light resonances from SU(3) unitarized chiral perturbation theory to one loop
journal, March 2010
- Nebreda, J.; Peláez, J. R.
- Physical Review D, Vol. 81, Issue 5
Lattice calculation of I = 2 pion scattering length
journal, September 1992
- Sharpe, Stephen R.; Gupta, Rajan; Kilcup, Gregory W.
- Nuclear Physics B, Vol. 383, Issue 1-2
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
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.
One spatial dimensional finite volume three-body interaction for a short-range potential
journal, March 2017
- Guo, Peng
- Physical Review D, Vol. 95, Issue 5
Scattering amplitudes from finite-volume spectral functions
journal, August 2019
- Bulava, John; Hansen, Maxwell T.
- Physical Review D, Vol. 100, 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
scattering phase shift with two flavors of improved dynamical quarks
journal, October 2004
- Yamazaki, T.; Aoki, S.; Fukugita, M.
- Physical Review D, Vol. 70, Issue 7
Erratum: Spectrum of Three-Body Bound States in a Finite Volume [Phys. Rev. Lett. 114 , 091602 (2015)]
journal, August 2016
- Meißner, Ulf-G.; Ríos, Guillermo; Rusetsky, Akaki
- Physical Review Letters, Vol. 117, Issue 6
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
Extended hadron and two-hadron operators of definite momentum for spectrum calculations in lattice QCD
journal, July 2013
- Morningstar, C.; Bulava, J.; Fahy, B.
- Physical Review D, Vol. 88, Issue 1
Three-particle scattering amplitudes from a finite volume formalism
journal, May 2013
- Briceño, Raúl A.; Davoudi, Zohreh
- Physical Review D, Vol. 87, Issue 9
Lattice QCD calculation of full pion scattering lengths
journal, October 1993
- Kuramashi, Y.; Fukugita, M.; Mino, H.
- Physical Review Letters, Vol. 71, Issue 15
Chiral perturbation theory to one loop
journal, November 1984
- Gasser, J.; Leutwyler, H.
- Annals of Physics, Vol. 158, Issue 1
resonance in coupled , scattering from lattice QCD
journal, September 2019
- Woss, Antoni J.; Thomas, Christopher E.; Dudek, Jozef J.
- Physical Review D, Vol. 100, Issue 5
Axial resonances a 1(1260), b 1(1235) and their decays from the lattice
journal, April 2014
- Lang, C. B.; Leskovec, Luka; Mohler, Daniel
- Journal of High Energy Physics, Vol. 2014, Issue 4
A study of π−π− scattering from π−p interactions at 3.93 GeV/c
journal, January 1974
- Losty, M. J.; Chaloupka, V.; Ferrando, A.
- Nuclear Physics B, Vol. 69, Issue 1
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
Meson-meson scattering within one-loop chiral perturbation theory and its unitarization
journal, January 2002
- Nicola, A. Gómez; Peláez, J. R.
- Physical Review D, Vol. 65, Issue 5
Unitarity of the infinite-volume three-particle scattering amplitude arising from a finite-volume formalism
journal, September 2019
- Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R.
- Physical Review D, Vol. 100, Issue 5
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
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
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
Dynamically-coupled partial-waves in ρπ isospin-2 scattering from lattice QCD
journal, July 2018
- Woss, Antoni J.; Thomas, Christopher E.; Dudek, Jozef J.
- Journal of High Energy Physics, Vol. 2018, Issue 7
Three-Pion Scattering Amplitude from Lattice QCD
journal, January 2020
- Blanton, Tyler D.; Romero-López, Fernando; Sharpe, Stephen R.
- Physical Review Letters, Vol. 124, Issue 3
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
The optical potential on the lattice
journal, June 2016
- Agadjanov, Dimitri; Döring, Michael; Mai, Maxim
- Journal of High Energy Physics, Vol. 2016, Issue 6
Multipion states in lattice QCD and the charged-pion condensate
journal, July 2008
- Detmold, William; Savage, Martin J.; Torok, Aaron
- Physical Review D, Vol. 78, Issue 1
Benchmark calculations for elastic fermion-dimer scattering
journal, September 2012
- Bour, Shahin; Hammer, H. -W.; Lee, Dean
- Physical Review C, Vol. 86, Issue 3
Three-body scattering: ladders and resonances
journal, August 2019
- Mikhasenko, M.; Wunderlich, Y.; Jackura, A.
- Journal of High Energy Physics, Vol. 2019, Issue 8
Finite volume corrections to the binding energy of the X(3872)
journal, December 2015
- Jansen, M.; Hammer, H. -W.; Jia, Yu
- Physical Review D, Vol. 92, Issue 11
Three-body unitarity in the finite volume
journal, December 2017
- Mai, M.; Döring, M.
- The European Physical Journal A, Vol. 53, Issue 12
Scattering in the negative parity channel in lattice QCD
journal, March 2013
- Lang, C. B.; Verduci, V.
- Physical Review D, Vol. 87, Issue 5
Multiple-particle interaction in ( )-dimensional lattice model
journal, January 2019
- Guo, Peng; Morris, Tyler
- Physical Review D, Vol. 99, 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
Pion scattering in the isospin channel from elongated lattices
journal, August 2019
- Culver, C.; Mai, M.; Alexandru, A.
- Physical Review D, Vol. 100, Issue 3
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
Efimov physics in a finite volume
journal, March 2009
- Kreuzer, Simon; Hammer, H. -W.
- Physics Letters B, Vol. 673, Issue 4-5
Scattering of unstable particles in a finite volume: The case of scattering and the resonance
journal, March 2012
- Roca, L.; Oset, E.
- Physical Review D, Vol. 85, Issue 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
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
Numerical approach for finite volume three-body interaction
journal, January 2018
- Guo, Peng; Gasparian, Vladimir
- Physical Review D, Vol. 97, Issue 1
Lattice QCD and Three-Particle Decays of Resonances
journal, October 2019
- Hansen, Maxwell T.; Sharpe, Stephen R.
- Annual Review of Nuclear and Particle Science, Vol. 69, Issue 1
Chiral extrapolation of light resonances from one and two-loop unitarized chiral perturbation theory versus lattice results
journal, December 2010
- Peláez, J. R.; Ríos, G.
- Physical Review D, Vol. 82, Issue 11
Two- and Three-Pion Finite-Volume Spectra at Maximal Isospin from Lattice QCD
journal, October 2019
- Hörz, Ben; Hanlon, Andrew
- Physical Review Letters, Vol. 123, Issue 14
Two- and three-body interactions in $$\varphi ^4$$ φ 4 theory from lattice simulations
journal, October 2018
- Romero-López, F.; Rusetsky, A.; Urbach, C.
- The European Physical Journal C, Vol. 78, Issue 10
Three-particle bound states in a finite volume: Unequal masses and higher partial waves
journal, July 2018
- Meng, Yu; Liu, Chuan; Meißner, Ulf-G.
- Physical Review D, Vol. 98, Issue 1
Extraction of isoscalar phase shifts from lattice QCD
journal, July 2018
- Guo, D.; Alexandru, A.; Molina, R.
- Physical Review D, Vol. 98, Issue 1
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
Elastic -wave nucleon-pion scattering amplitude and the resonance from lattice QCD
journal, January 2018
- Andersen, Christian Walther; Bulava, John; Hörz, Ben
- Physical Review D, Vol. 97, Issue 1
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
Observation of a Exotic Resonance in Diffractive Dissociation of into
journal, June 2010
- Alekseev, M. G.; Alexakhin, V. Yu.; Alexandrov, Yu.
- Physical Review Letters, Vol. 104, Issue 24
The triton in a finite volume
journal, January 2011
- Kreuzer, Simon; Hammer, H. -W.
- Physics Letters B, Vol. 694, Issue 4-5
Measurement and analysis of the π+π+ system produced at small momentum transfer in the reaction π+p→π+π+n at 12.5 GeV
journal, August 1977
- Hoogland, W.; Peters, S.; Grayer, G.
- Nuclear Physics B, Vol. 126, Issue 1
Light nuclei and hypernuclei from quantum chromodynamics in the limit of SU(3) flavor symmetry
journal, February 2013
- Beane, S. R.; Chang, E.; Cohen, S. D.
- Physical Review D, Vol. 87, Issue 3
pion scattering length from two-pion wave functions
journal, May 2005
- Aoki, S.; Fukugita, M.; Ishikawa, K-I.
- Physical Review D, Vol. 71, Issue 9
Rho resonance parameters from lattice QCD
journal, August 2016
- Guo, Dehua; Alexandru, Andrei; Molina, Raquel
- Physical Review D, Vol. 94, Issue 3
Extended partial-wave analysis of scattering data
journal, October 2006
- Arndt, R. A.; Briscoe, W. J.; Strakovsky, I. I.
- Physical Review C, Vol. 74, Issue 4
pion scattering amplitude with Wilson fermions
journal, July 1993
- Gupta, Rajan; Patel, Apoorva; Sharpe, Stephen R.
- Physical Review D, Vol. 48, Issue 1
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
Inverse amplitude method in chiral perturbation theory
journal, September 1997
- Dobado, A.; Peláez, J. R.
- Physical Review D, Vol. 56, Issue 5
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
Energy of identical bosons in a finite volume at
journal, March 2008
- Detmold, William; Savage, Martin J.
- Physical Review D, Vol. 77, 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
From deep inelastic scattering to heavy-flavor semileptonic decays: Total rates into multihadron final states from lattice QCD
journal, November 2017
- Hansen, Maxwell T.; Meyer, Harvey B.; Robaina, Daniel
- Physical Review D, Vol. 96, Issue 9
Search for low-lying lattice QCD eigenstates in the Roper regime
journal, April 2017
- Kiratidis, Adrian L.; Kamleh, Waseem; Leinweber, Derek B.
- Physical Review D, Vol. 95, Issue 7
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
Cross-channel study of pion scattering from lattice QCD
journal, December 2019
- Mai, M.; Culver, C.; Alexandru, A.
- Physical Review D, Vol. 100, Issue 11
Multipion Systems in Lattice QCD and the Three-Pion Interaction
journal, February 2008
- Beane, Silas R.; Detmold, William; Luu, Thomas C.
- Physical Review Letters, Vol. 100, Issue 8
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