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

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

Publication Date:: Fri Jun 15 00:00:00 EDT 2018

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:: 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.

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                    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

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                    Döring, M., Hammer, H. -W., Mai, M., Pang, J. -Y., Rusetsky, A., and Wu, J. Fri .  
"Three-body spectrum in a finite volume: The role of cubic symmetry".  United States.  https://doi.org/10.1103/PhysRevD.97.114508.

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@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},

  journal      = {Physical Review D},

  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}

}

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