Three-body unitarity versus finite-volume π+π+π+ spectrum from lattice QCD

Mai, M.; Doring, M.; Culver, C.; Alexandru, A.

doi:10.1103/PhysRevD.101.054510

Title: Three-body unitarity versus finite-volume $π^{+} π^{+} π^{+}$ spectrum from lattice QCD

Journal Article · 20 March 2020 · Physical Review D

DOI: https://doi.org/10.1103/PhysRevD.101.054510 · OSTI ID:1605631

Mai, M. ^[1];

^[2]; Culver, C. ^[1]; Alexandru, A. ^[3]

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)
George Washington Univ., Washington, DC (United States); Univ. of Maryland, College Park, MD (United States)

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.

View Journal Article

Cite

Export

Save

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

Sponsoring Organization:: USDOE

Grant/Contract Number:: PHY-1452055; SC0016582; FG02-95ER40907

OSTI ID:: 1605631

Alternate ID(s):: OSTI ID: 1606196

Report Number(s):: JLAB-THY-20-3167; DOE-OR-23177-4949; PRVDAQ; TRN: US2104479

Journal Information:: Physical Review D, Vol. 101, Issue 5; ISSN 2470-0010

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 44 works

Citation information provided by
Web of Science

References (119)

Three-particle quantization condition in a finite volume: 1. The role of the three-particle force Hammer, Hans-Werner; Pang, Jin-Yi; Rusetsky, Akaki Journal of High Energy Physics, Vol. 2017, Issue 9, 23 p. https://doi.org/10.1007/JHEP09(2017)109	journal	September 2017
Quartet S wave neutron deuteron scattering in effective field theory Bedaque, Paulo F.; Grießhammer, Harald W. Nuclear Physics A, Vol. 671, Issue 1-4 https://doi.org/10.1016/S0375-9474(99)00691-0	journal	May 2000
Spectrum of Three-Body Bound States in a Finite Volume Meißner, Ulf-G.; Ríos, Guillermo; Rusetsky, Akaki Physical Review Letters, Vol. 114, Issue 9 https://doi.org/10.1103/PhysRevLett.114.091602	journal	March 2015
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
Erratum: Threshold expansion of the three-particle quantization condition [Phys. Rev. D 93 , 096006 (2016)] Hansen, Maxwell T.; Sharpe, Stephen R. Physical Review D, Vol. 96, Issue 3 https://doi.org/10.1103/PhysRevD.96.039901	journal	August 2017
From hadrons to quarks in neutron stars: a review Baym, Gordon; Hatsuda, Tetsuo; Kojo, Toru Reports on Progress in Physics, Vol. 81, Issue 5 https://doi.org/10.1088/1361-6633/aaae14	journal	March 2018
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
Relating the finite-volume spectrum and the two-and-three-particle S matrix for relativistic systems of identical scalar particles Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R. Physical Review D, Vol. 95, Issue 7 https://doi.org/10.1103/PhysRevD.95.074510	journal	April 2017
Inverse amplitude method and Adler zeros Gómez Nicola, A.; Peláez, J. R.; Ríos, G. Physical Review D, Vol. 77, Issue 5 https://doi.org/10.1103/PhysRevD.77.056006	journal	March 2008
Study of π π Scattering in the Isotopic-Spin-2 Channel Cohen, D.; Ferbel, T.; Slattery, P. Physical Review D, Vol. 7, Issue 3 https://doi.org/10.1103/PhysRevD.7.661	journal	February 1973
S - and D -wave phase shifts in isospin-2 π π scattering from lattice QCD Dudek, Jozef J.; Edwards, Robert G.; Thomas, Christopher E. Physical Review D, Vol. 86, Issue 3 https://doi.org/10.1103/PhysRevD.86.034031	journal	August 2012
Topological phases for bound states moving in a finite volume Bour, Shahin; König, Sebastian; Lee, Dean Physical Review D, Vol. 84, Issue 9 https://doi.org/10.1103/PhysRevD.84.091503	journal	November 2011
Signatures of few-body resonances in finite volume Klos, P.; König, S.; Hammer, H. -W. Physical Review C, Vol. 98, Issue 3 https://doi.org/10.1103/PhysRevC.98.034004	journal	September 2018
Chiral Perturbation Theory and Final-State Theorem Truong, Tran N. Physical Review Letters, Vol. 61, Issue 22 https://doi.org/10.1103/PhysRevLett.61.2526	journal	November 1988
On the modification of the Efimov spectrum in a finite cubic box Kreuzer, S.; Hammer, H. -W. The European Physical Journal A, Vol. 43, Issue 2 https://doi.org/10.1140/epja/i2010-10910-6	journal	January 2010
Strange and nonstrange quark mass dependence of elastic light resonances from SU(3) unitarized chiral perturbation theory to one loop Nebreda, J.; Peláez, J. R. Physical Review D, Vol. 81, Issue 5 https://doi.org/10.1103/PhysRevD.81.054035	journal	March 2010
U.S. nuclear physicists push for new neutrino experiment Cho, Adrian Science https://doi.org/10.1126/science.aad4725	journal	October 2015
Lattice calculation of I = 2 pion scattering length Sharpe, Stephen R.; Gupta, Rajan; Kilcup, Gregory W. Nuclear Physics B, Vol. 383, Issue 1-2 https://doi.org/10.1016/0550-3213(92)90681-Z	journal	September 1992
Numerical exploration of three relativistic particles in a finite volume including two-particle resonances and bound states Romero-López, Fernando; Sharpe, Stephen R.; Blanton, Tyler D. Journal of High Energy Physics, Vol. 2019, Issue 10 https://doi.org/10.1007/JHEP10(2019)007	journal	October 2019
Three-particle quantization condition in a finite volume: 2. General formalism and the analysis of data Hammer, Hans-Werner; Pang, Jin-Yi; Rusetsky, Akaki Journal of High Energy Physics, Vol. 2017, Issue 10, 31 p. https://doi.org/10.1007/JHEP10(2017)115	journal	October 2017
One spatial dimensional finite volume three-body interaction for a short-range potential Guo, Peng Physical Review D, Vol. 95, Issue 5 https://doi.org/10.1103/PhysRevD.95.054508	journal	March 2017
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
Analytic properties of the scattering amplitude and resonances parameters in a meson exchange model Döring, M.; Hanhart, C.; Huang, F. Nuclear Physics A, Vol. 829, Issue 3-4 https://doi.org/10.1016/j.nuclphysa.2009.08.010	journal	October 2009
I = 2 π π scattering phase shift with two flavors of O a improved dynamical quarks Yamazaki, T.; Aoki, S.; Fukugita, M. Physical Review D, Vol. 70, Issue 7 https://doi.org/10.1103/PhysRevD.70.074513	journal	October 2004
Erratum: Spectrum of Three-Body Bound States in a Finite Volume [Phys. Rev. Lett. 114 , 091602 (2015)] Meißner, Ulf-G.; Ríos, Guillermo; Rusetsky, Akaki Physical Review Letters, Vol. 117, Issue 6 https://doi.org/10.1103/PhysRevLett.117.069902	journal	August 2016
Relativistic, model-independent, three-particle quantization condition Hansen, Maxwell T.; Sharpe, Stephen R. Physical Review D, Vol. 90, Issue 11 https://doi.org/10.1103/PhysRevD.90.116003	journal	December 2014
A solvable three-body model in finite volume Guo, Peng; Gasparian, Vladimir Physics Letters B, Vol. 774 https://doi.org/10.1016/j.physletb.2017.10.009	journal	November 2017
Three particles in a finite volume Polejaeva, K.; Rusetsky, A. The European Physical Journal A, Vol. 48, Issue 5 https://doi.org/10.1140/epja/i2012-12067-8	journal	May 2012
Extended hadron and two-hadron operators of definite momentum for spectrum calculations in lattice QCD Morningstar, C.; Bulava, J.; Fahy, B. Physical Review D, Vol. 88, Issue 1 https://doi.org/10.1103/PhysRevD.88.014511	journal	July 2013
Three-particle scattering amplitudes from a finite volume formalism Briceño, Raúl A.; Davoudi, Zohreh Physical Review D, Vol. 87, Issue 9 https://doi.org/10.1103/PhysRevD.87.094507	journal	May 2013
Lattice QCD calculation of full pion scattering lengths Kuramashi, Y.; Fukugita, M.; Mino, H. Physical Review Letters, Vol. 71, Issue 15 https://doi.org/10.1103/PhysRevLett.71.2387	journal	October 1993
Chiral perturbation theory to one loop Gasser, J.; Leutwyler, H. Annals of Physics, Vol. 158, Issue 1 https://doi.org/10.1016/0003-4916(84)90242-2	journal	November 1984
Pion-nucleon scattering in the Roper channel from lattice QCD Lang, C. B.; Leskovec, L.; Padmanath, M. Universität Regensburg https://doi.org/10.5283/epub.38792	text	January 2017
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
Axial resonances a 1(1260), b 1(1235) and their decays from the lattice Lang, C. B.; Leskovec, Luka; Mohler, Daniel Journal of High Energy Physics, Vol. 2014, Issue 4 https://doi.org/10.1007/JHEP04(2014)162	journal	April 2014
A study of π−π− scattering from π−p interactions at 3.93 GeV/c Losty, M. J.; Chaloupka, V.; Ferrando, A. Nuclear Physics B, Vol. 69, Issue 1 https://doi.org/10.1016/0550-3213(74)90131-X	journal	January 1974
Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude Hansen, Maxwell T.; Sharpe, Stephen R. Physical Review D, Vol. 92, Issue 11 https://doi.org/10.1103/PhysRevD.92.114509	journal	December 2015
Meson-meson scattering within one-loop chiral perturbation theory and its unitarization Nicola, A. Gómez; Peláez, J. R. Physical Review D, Vol. 65, Issue 5 https://doi.org/10.1103/PhysRevD.65.054009	journal	January 2002
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
Pion-nucleon scattering in the Roper channel from lattice QCD Lang, C. B.; Leskovec, L.; Padmanath, M. Physical Review D, Vol. 95, Issue 1 https://doi.org/10.1103/PhysRevD.95.014510	journal	January 2017
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
Volume dependence of the energy spectrum in massive quantum field theories: II. Scattering states Lüscher, M. Communications in Mathematical Physics, Vol. 105, Issue 2 https://doi.org/10.1007/BF01211097	journal	June 1986
Three particles in a finite volume: The breakdown of spherical symmetry Kreuzer, S.; Grießhammer, H. W. The European Physical Journal A, Vol. 48, Issue 7 https://doi.org/10.1140/epja/i2012-12093-6	journal	July 2012
Dynamically-coupled partial-waves in ρπ isospin-2 scattering from lattice QCD Woss, Antoni J.; Thomas, Christopher E.; Dudek, Jozef J. Journal of High Energy Physics, Vol. 2018, Issue 7 https://doi.org/10.1007/JHEP07(2018)043	journal	July 2018
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
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
Multipion states in lattice QCD and the charged-pion condensate Detmold, William; Savage, Martin J.; Torok, Aaron Physical Review D, Vol. 78, Issue 1 https://doi.org/10.1103/PhysRevD.78.014507	journal	July 2008
Three-body scattering: ladders and resonances Mikhasenko, M.; Wunderlich, Y.; Jackura, A. Journal of High Energy Physics, Vol. 2019, Issue 8 https://doi.org/10.1007/JHEP08(2019)080	journal	August 2019
Finite volume corrections to the binding energy of the X(3872) Jansen, M.; Hammer, H. -W.; Jia, Yu Physical Review D, Vol. 92, Issue 11 https://doi.org/10.1103/PhysRevD.92.114031	journal	December 2015
Three-body unitarity in the finite volume Mai, M.; Döring, M. The European Physical Journal A, Vol. 53, Issue 12 https://doi.org/10.1140/epja/i2017-12440-1	journal	December 2017
Scattering in the π N negative parity channel in lattice QCD Lang, C. B.; Verduci, V. Physical Review D, Vol. 87, Issue 5 https://doi.org/10.1103/PhysRevD.87.054502	journal	March 2013
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
Pion scattering in the isospin I = 2 channel from elongated lattices Culver, C.; Mai, M.; Alexandru, A. Physical Review D, Vol. 100, Issue 3 https://doi.org/10.1103/PhysRevD.100.034509	journal	August 2019
Equivalence of three-particle scattering formalisms Jackura, A. W.; Dawid, S. M.; Fernández-Ramírez, C. Physical Review D, Vol. 100, Issue 3 https://doi.org/10.1103/PhysRevD.100.034508	journal	August 2019
Efimov physics in a finite volume Kreuzer, Simon; Hammer, H. -W. Physics Letters B, Vol. 673, Issue 4-5 https://doi.org/10.1016/j.physletb.2009.02.035	journal	March 2009
Scattering of unstable particles in a finite volume: The case of π ρ scattering and the a 1 ( 1260 ) resonance Roca, L.; Oset, E. Physical Review D, Vol. 85, Issue 5 https://doi.org/10.1103/PhysRevD.85.054507	journal	March 2012
Scalar mesons moving in a finite volume and the role of partial wave mixing Döring, M.; Meißner, U. -G.; Oset, E. The European Physical Journal A, Vol. 48, Issue 8 https://doi.org/10.1140/epja/i2012-12114-6	journal	August 2012
Scattering processes and resonances from lattice QCD Briceño, Raúl A.; Dudek, Jozef J.; Young, Ross D. Reviews of Modern Physics, Vol. 90, Issue 2 https://doi.org/10.1103/RevModPhys.90.025001	journal	April 2018
Numerical approach for finite volume three-body interaction Guo, Peng; Gasparian, Vladimir Physical Review D, Vol. 97, Issue 1 https://doi.org/10.1103/PhysRevD.97.014504	journal	January 2018
Lattice QCD and Three-Particle Decays of Resonances Hansen, Maxwell T.; Sharpe, Stephen R. Annual Review of Nuclear and Particle Science, Vol. 69, Issue 1 https://doi.org/10.1146/annurev-nucl-101918-023723	journal	October 2019
Chiral extrapolation of light resonances from one and two-loop unitarized chiral perturbation theory versus lattice results Peláez, J. R.; Ríos, G. Physical Review D, Vol. 82, Issue 11 https://doi.org/10.1103/PhysRevD.82.114002	journal	December 2010
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
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
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
Extraction of isoscalar π π phase shifts from lattice QCD Guo, D.; Alexandru, A.; Molina, R. Physical Review D, Vol. 98, Issue 1 https://doi.org/10.1103/PhysRevD.98.014507	journal	July 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
Elastic I = 3 / 2 p -wave nucleon-pion scattering amplitude and the Δ ( 1232 ) resonance from N f = 2 + 1 lattice QCD Andersen, Christian Walther; Bulava, John; Hörz, Ben Physical Review D, Vol. 97, Issue 1 https://doi.org/10.1103/PhysRevD.97.014506	journal	January 2018
Implementing the three-particle quantization condition including higher partial waves Blanton, Tyler D.; Romero-López, Fernando; Sharpe, Stephen R. Journal of High Energy Physics, Vol. 2019, Issue 3 https://doi.org/10.1007/JHEP03(2019)106	journal	March 2019
Observation of a J PC = 1 − + Exotic Resonance in Diffractive Dissociation of 190 GeV / c π − into π − π − π + Alekseev, M. G.; Alexakhin, V. Yu.; Alexandrov, Yu. Physical Review Letters, Vol. 104, Issue 24 https://doi.org/10.1103/PhysRevLett.104.241803	journal	June 2010
The triton in a finite volume Kreuzer, Simon; Hammer, H. -W. Physics Letters B, Vol. 694, Issue 4-5 https://doi.org/10.1016/j.physletb.2010.10.003	journal	January 2011
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 Hoogland, W.; Peters, S.; Grayer, G. Nuclear Physics B, Vol. 126, Issue 1 https://doi.org/10.1016/0550-3213(77)90154-7	journal	August 1977
Light nuclei and hypernuclei from quantum chromodynamics in the limit of SU(3) flavor symmetry Beane, S. R.; Chang, E.; Cohen, S. D. Physical Review D, Vol. 87, Issue 3 https://doi.org/10.1103/PhysRevD.87.034506	journal	February 2013
I = 2 pion scattering length from two-pion wave functions Aoki, S.; Fukugita, M.; Ishikawa, K-I. Physical Review D, Vol. 71, Issue 9 https://doi.org/10.1103/PhysRevD.71.094504	journal	May 2005
Rho resonance parameters from lattice QCD Guo, Dehua; Alexandru, Andrei; Molina, Raquel Physical Review D, Vol. 94, Issue 3 https://doi.org/10.1103/PhysRevD.94.034501	journal	August 2016
Extended partial-wave analysis of π N scattering data Arndt, R. A.; Briscoe, W. J.; Strakovsky, I. I. Physical Review C, Vol. 74, Issue 4 https://doi.org/10.1103/PhysRevC.74.045205	journal	October 2006
I = 2 pion scattering amplitude with Wilson fermions Gupta, Rajan; Patel, Apoorva; Sharpe, Stephen R. Physical Review D, Vol. 48, Issue 1 https://doi.org/10.1103/PhysRevD.48.388	journal	July 1993
Two-particle states on a torus and their relation to the scattering matrix Lüscher, Martin Nuclear Physics B, Vol. 354, Issue 2-3 https://doi.org/10.1016/0550-3213(91)90366-6	journal	May 1991
Inverse amplitude method in chiral perturbation theory Dobado, A.; Peláez, J. R. Physical Review D, Vol. 56, Issue 5 https://doi.org/10.1103/PhysRevD.56.3057	journal	September 1997
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
Three particles in a finite volume Polejaeva, Kathryn; Rusetsky, Akaki Proceedings of Sixth International Conference on Quarks and Nuclear Physics — PoS(QNP2012) https://doi.org/10.22323/1.157.0105	conference	October 2012
Energy of n identical bosons in a finite volume at O ( L − 7 ) Detmold, William; Savage, Martin J. Physical Review D, Vol. 77, Issue 5 https://doi.org/10.1103/PhysRevD.77.057502	journal	March 2008
Threshold expansion of the three-particle quantization condition Hansen, Maxwell T.; Sharpe, Stephen R. Physical Review D, Vol. 93, Issue 9 https://doi.org/10.1103/PhysRevD.93.096006	journal	May 2016
Three-body unitarity with isobars revisited Mai, M.; Hu, B.; Döring, M. The European Physical Journal A, Vol. 53, Issue 9 https://doi.org/10.1140/epja/i2017-12368-4	journal	September 2017
From deep inelastic scattering to heavy-flavor semileptonic decays: Total rates into multihadron final states from lattice QCD Hansen, Maxwell T.; Meyer, Harvey B.; Robaina, Daniel Physical Review D, Vol. 96, Issue 9 https://doi.org/10.1103/PhysRevD.96.094513	journal	November 2017
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
Extended hadron and two-hadron operators of definite momentum for spectrum calculations in lattice QCD Morningstar, Colin; Bulava, John; Fahy, Brendan Carnegie Mellon University https://doi.org/10.1184/r1/6506780.v1	text	January 2013
Cross-channel study of pion scattering from lattice QCD Mai, M.; Culver, C.; Alexandru, A. Physical Review D, Vol. 100, Issue 11 https://doi.org/10.1103/PhysRevD.100.114514	journal	December 2019
Multipion Systems in Lattice QCD and the Three-Pion Interaction Beane, Silas R.; Detmold, William; Luu, Thomas C. Physical Review Letters, Vol. 100, Issue 8 https://doi.org/10.1103/PhysRevLett.100.082004	journal	February 2008
Extended hadron and two-hadron operators of definite momentum for spectrum calculations in lattice QCD Morningstar, Colin; Bulava, John; Fahy, Brendan Carnegie Mellon University https://doi.org/10.1184/r1/6506780	text	January 2013
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
Multi-Pion States in Lattice QCD and the Charged-Pion Condensate Detmold, William; Savage, Martin J.; Torok, Aaron arXiv https://doi.org/10.48550/arxiv.0803.2728	text	January 2008
Efimov physics in a finite volume Kreuzer, Simon; Hammer, H. -W. arXiv https://doi.org/10.48550/arxiv.0811.0159	text	January 2008
On the modification of the Efimov spectrum in a finite cubic box Kreuzer, Simon; Hammer, H. -W. arXiv https://doi.org/10.48550/arxiv.0910.2191	text	January 2009
Strange and non-strange quark mass dependence of elastic light resonances from SU(3) Unitarized Chiral Perturbation Theory to one loop Nebreda, J.; Pelaez., J. R. arXiv https://doi.org/10.48550/arxiv.1001.5237	text	January 2010
The triton in a finite volume Kreuzer, Simon; Hammer, H. -W. arXiv https://doi.org/10.48550/arxiv.1008.4499	text	January 2010
Topological phases for bound states moving in a finite volume Bour, Shahin; König, Sebastian; Lee, Dean arXiv https://doi.org/10.48550/arxiv.1107.1272	text	January 2011
Three particles in a finite volume: The breakdown of spherical symmetry Kreuzer, Simon; Grießhammer, Harald W. arXiv https://doi.org/10.48550/arxiv.1205.0277	text	January 2012
Scalar mesons moving in a finite volume and the role of partial wave mixing Döring, M.; Meißner, U. -G.; Oset, E. arXiv https://doi.org/10.48550/arxiv.1205.4838	text	January 2012
Axial resonances a1(1260), b1(1235) and their decays from the lattice Lang, C. B.; Leskovec, Luka; Mohler, Daniel arXiv https://doi.org/10.48550/arxiv.1401.2088	text	January 2014
A relativistic, model-independent, three-particle quantization condition Hansen, Maxwell T.; Sharpe, Stephen R. arXiv https://doi.org/10.48550/arxiv.1408.5933	text	January 2014
Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude Hansen, Maxwell T.; Sharpe, Stephen R. arXiv https://doi.org/10.48550/arxiv.1504.04248	text	January 2015
Finite volume corrections to the binding energy of the X(3872) Jansen, M.; Hammer, H. -W.; Jia, Yu arXiv https://doi.org/10.48550/arxiv.1505.04099	text	January 2015
Rho resonance parameters from lattice QCD Guo, Dehua; Alexandru, Andrei; Molina, Raquel arXiv https://doi.org/10.48550/arxiv.1605.03993	text	January 2016
Relating the finite-volume spectrum and the two-and-three-particle $S$ matrix for relativistic systems of identical scalar particles Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R. arXiv https://doi.org/10.48550/arxiv.1701.07465	text	January 2017
Three-particle quantization condition in a finite volume: 1. The role of the three-particle force Hammer, H. -W.; Pang, J. -Y.; Rusetsky, A. arXiv https://doi.org/10.48550/arxiv.1706.07700	text	January 2017
Three particle quantization condition in a finite volume: 2. general formalism and the analysis of data Hammer, H. -W.; Pang, J. -Y.; Rusetsky, A. arXiv https://doi.org/10.48550/arxiv.1707.02176	text	January 2017
From hadrons to quarks in neutron stars: a review Baym, Gordon; Hatsuda, Tetsuo; Kojo, Toru arXiv https://doi.org/10.48550/arxiv.1707.04966	text	January 2017
Three-body Unitarity in the Finite Volume Mai, M.; Döring, M. arXiv https://doi.org/10.48550/arxiv.1709.08222	text	January 2017
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
Variational approach to $N$-body interactions in finite volume Guo, Peng; Döring, Michael; Szczepaniak, Adam P. arXiv https://doi.org/10.48550/arxiv.1810.01261	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
Lattice QCD and Three-particle Decays of Resonances Hansen, Maxwell T.; Sharpe, Stephen R. arXiv https://doi.org/10.48550/arxiv.1901.00483	text	January 2019
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
Three-body scattering: Ladders and Resonances Mikhasenko, M.; Wunderlich, Y.; Jackura, A. arXiv https://doi.org/10.48550/arxiv.1904.11894	text	January 2019
Extended Partial-Wave Analysis of piN Scattering Data Arndt, R. A.; Briscoe, W. J.; Strakovsky, I. I. arXiv https://doi.org/10.48550/arxiv.nucl-th/0605082	text	January 2006