Three-body spectrum in a finite volume: The role of cubic symmetry
Abstract
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.
- Authors:
- 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); 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)
- OSTI Identifier:
- 1454362
- Alternate Identifier(s):
- OSTI ID: 1454728
- Report Number(s):
- JLAB-THY-18-2646; DOE/OR/-23177-4349
Journal ID: ISSN 2470-0010; PRVDAQ; 114508
- Grant/Contract Number:
- SC001658; AC05-06OR23177; TRR 110; SFB 1245; 11621131001; 05P15RDFN1; PHY-1452055; PHY-1415459; 93562; DI-2016-26
- Resource Type:
- Journal Article: Published Article
- Journal Name:
- Physical Review D
- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 97 Journal Issue: 11; Journal ID: ISSN 2470-0010
- Publisher:
- American Physical Society
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS
Citation Formats
Döring, M., Hammer, H. -W., Mai, M., Pang, J. -Y., Rusetsky, A., and Wu, J. Three-body spectrum in a finite volume: The role of cubic symmetry. United States: N. p., 2018.
Web. doi:10.1103/PhysRevD.97.114508.
Döring, M., Hammer, H. -W., Mai, M., Pang, J. -Y., Rusetsky, A., & Wu, J. Three-body spectrum in a finite volume: The role of cubic symmetry. United States. https://doi.org/10.1103/PhysRevD.97.114508
Döring, M., Hammer, H. -W., Mai, M., Pang, J. -Y., Rusetsky, A., and Wu, J. 2018.
"Three-body spectrum in a finite volume: The role of cubic symmetry". United States. https://doi.org/10.1103/PhysRevD.97.114508.
@article{osti_1454362,
title = {Three-body spectrum in a finite volume: The role of cubic symmetry},
author = {Döring, M. and Hammer, H. -W. and Mai, M. and Pang, J. -Y. and Rusetsky, A. and Wu, J.},
abstractNote = {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.},
doi = {10.1103/PhysRevD.97.114508},
url = {https://www.osti.gov/biblio/1454362},
journal = {Physical Review D},
issn = {2470-0010},
number = 11,
volume = 97,
place = {United States},
year = {Fri Jun 15 00:00:00 EDT 2018},
month = {Fri Jun 15 00:00:00 EDT 2018}
}
Web of Science
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Works referencing / citing this record:
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
Energy levels of three resonantly interacting particles
journal, August 1973
- Efimov, V.
- Nuclear Physics A, Vol. 210, Issue 1
Two-particle states on a torus and their relation to the scattering matrix
journal, May 1991
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journal, January 2011
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journal, November 2017
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journal, April 2018
- König, Sebastian; Lee, Dean
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Nuclear reactions from lattice QCD
journal, January 2015
- Briceño, Raúl A.; Davoudi, Zohreh; Luu, Thomas C.
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- Bernard, V.; Lage, M.; Meißner, U.-G.
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journal, May 2012
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Three particles in a finite volume: The breakdown of spherical symmetry
journal, July 2012
- Kreuzer, S.; Grießhammer, H. W.
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Scalar mesons moving in a finite volume and the role of partial wave mixing
journal, August 2012
- Döring, M.; Meißner, U. -G.; Oset, E.
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