Three-body spectrum in a finite volume: The role of cubic symmetry

Döring, M.; Hammer, H. -W.; Mai, M.; Pang, J. -Y.; Rusetsky, A.; Wu, J.

doi:10.1103/PhysRevD.97.114508

Title: Three-body spectrum in a finite volume: The role of cubic symmetry

Journal Article · Fri Jun 15 00:00:00 EDT 2018 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.97.114508· OSTI ID:1454362

Döring, M.; Hammer, H. -W.; Mai, M.; Pang, J. -Y.; Rusetsky, A.; Wu, J.

The three-particle quantization condition is partially diagonalized in the center-of-mass frame by using cubic symmetry on the lattice. To this end, instead of spherical harmonics, the kernel of the Bethe-Salpeter equation for particle-dimer scattering is expanded in the basis functions of different irreducible representations of the octahedral group. Such a projection is of particular importance for the three-body problem in the finite volume due to the occurrence of three-body singularities above breakup. Additionally, we study the numerical solution and properties of such a projected quantization condition in a simple model. It is shown that, for large volumes, these solutions allow for an instructive interpretation of the energy eigenvalues in terms of bound and scattering states.

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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); National Science Foundation (NSF); National Natural Science Foundation of China (NSFC); German Research Foundation (DFG); German Federal Ministry of Education and Research (BMBF); Shota Rustaveli National Science Foundation (SRNSF)

Grant/Contract Number:: SC001658; AC05-06OR23177; TRR 110; SFB 1245; 11621131001; 05P15RDFN1; PHY-1452055; PHY-1415459; 93562; DI-2016-26

OSTI ID:: 1454362

Alternate ID(s):: OSTI ID: 1454728

Report Number(s):: JLAB-THY-18-2646; DOE/OR/-23177-4349; PRVDAQ; 114508

Journal Information:: Physical Review D, Journal Name: Physical Review D Vol. 97 Journal Issue: 11; ISSN 2470-0010

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 74 works

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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
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
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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
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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
Low-energy neutron-deuteron reactions with N 3 LO chiral forces Golak, J.; Skibiński, R.; Topolnicki, K. The European Physical Journal A, Vol. 50, Issue 11 https://doi.org/10.1140/epja/i2014-14177-7	journal	November 2014
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
Volume dependence of N -body bound states König, Sebastian; Lee, Dean Physics Letters B, Vol. 779 https://doi.org/10.1016/j.physletb.2018.01.060	journal	April 2018
Resonance properties from the finite-volume energy spectrum Bernard, V.; Lage, M.; Meißner, U.-G. Journal of High Energy Physics, Vol. 2008, Issue 08, Article No. 024 https://doi.org/10.1088/1126-6708/2008/08/024	journal	August 2008
Testing the threshold expansion for three-particle energies at fourth order in $ϕ^{4}$ theory Sharpe, Stephen R. Physical Review D, Vol. 96, Issue 5 https://doi.org/10.1103/PhysRevD.96.054515	journal	September 2017
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
Nuclear reactions from lattice QCD Briceño, Raúl A.; Davoudi, Zohreh; Luu, Thomas C. Journal of Physics G: Nuclear and Particle Physics, Vol. 42, Issue 2 https://doi.org/10.1088/0954-3899/42/2/023101	journal	January 2015
Volume Dependence of N-Body Bound States König, Sebastian; Lee, Dean GSI Helmholtzzentrum fuer Schwerionenforschung, GSI, Darmstadt https://doi.org/10.15120/gsi-2019-00697	text	January 2018
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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
Energy levels of three resonantly interacting particles Efimov, V. Nuclear Physics A, Vol. 210, Issue 1 https://doi.org/10.1016/0375-9474(73)90510-1	journal	August 1973
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
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
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
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
Volume dependence of N -body bound states König, Sebastian; Lee, Dean Physics Letters B, Vol. 779 https://doi.org/10.1016/j.physletb.2018.01.060	journal	April 2018
Nuclear reactions from lattice QCD Briceño, Raúl A.; Davoudi, Zohreh; Luu, Thomas C. Journal of Physics G: Nuclear and Particle Physics, Vol. 42, Issue 2 https://doi.org/10.1088/0954-3899/42/2/023101	journal	January 2015
Resonance properties from the finite-volume energy spectrum Bernard, V.; Lage, M.; Meißner, U.-G. Journal of High Energy Physics, Vol. 2008, Issue 08, Article No. 024 https://doi.org/10.1088/1126-6708/2008/08/024	journal	August 2008
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
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
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
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
Low-energy neutron-deuteron reactions with N 3 LO chiral forces Golak, J.; Skibiński, R.; Topolnicki, K. The European Physical Journal A, Vol. 50, Issue 11 https://doi.org/10.1140/epja/i2014-14177-7	journal	November 2014
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
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
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
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