skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

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:
; ; ; ; ;
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}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at https://doi.org/10.1103/PhysRevD.97.114508

Citation Metrics:
Cited by: 74 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Three-particle quantization condition in a finite volume: 1. The role of the three-particle force
journal, September 2017


The optical potential on the lattice
journal, June 2016


Quartet S wave neutron deuteron scattering in effective field theory
journal, May 2000


Benchmark calculations for elastic fermion-dimer scattering
journal, September 2012


Spectrum of Three-Body Bound States in a Finite Volume
journal, March 2015


Volume dependence of the energy spectrum in massive quantum field theories: I. Stable particle states
journal, June 1986


Erratum: Threshold expansion of the three-particle quantization condition [Phys. Rev. D 93 , 096006 (2016)]
journal, August 2017


Finite volume corrections to the binding energy of the X(3872)
journal, December 2015


Three-body unitarity in the finite volume
journal, December 2017


Relating the finite-volume spectrum and the two-and-three-particle S matrix for relativistic systems of identical scalar particles
journal, April 2017


The three-boson system with short-range interactions
journal, February 1999


Scattering phases for meson and baryon resonances on general moving-frame lattices
journal, November 2012


Topological phases for bound states moving in a finite volume
journal, November 2011


n -boson energies at finite volume and three-boson interactions
journal, October 2007


Renormalization of the Three-Body System with Short-Range Interactions
journal, January 1999


On the modification of the Efimov spectrum in a finite cubic box
journal, January 2010


Efimov physics in a finite volume
journal, March 2009


Scalar mesons moving in a finite volume and the role of partial wave mixing
journal, August 2012


Scattering processes and resonances from lattice QCD
journal, April 2018


Numerical approach for finite volume three-body interaction
journal, January 2018


Perturbative results for two- and three-particle threshold energies in finite volume
journal, January 2016


Three-particle quantization condition in a finite volume: 2. General formalism and the analysis of data
journal, October 2017


Applying the relativistic quantization condition to a three-particle bound state in a periodic box
journal, February 2017


The triton in a finite volume
journal, January 2011


Erratum: Spectrum of Three-Body Bound States in a Finite Volume [Phys. Rev. Lett. 114 , 091602 (2015)]
journal, August 2016


Relativistic, model-independent, three-particle quantization condition
journal, December 2014


A solvable three-body model in finite volume
journal, November 2017


Three particles in a finite volume
journal, May 2012


Three-particle scattering amplitudes from a finite volume formalism
journal, May 2013


Asymptotic behavior of Nambu-Bethe-Salpeter wave functions for multiparticles in quantum field theories
journal, July 2013


Threshold expansion of the three-particle quantization condition
journal, May 2016


Energy levels of three resonantly interacting particles
journal, August 1973


Three-body unitarity with isobars revisited
journal, September 2017


From deep inelastic scattering to heavy-flavor semileptonic decays: Total rates into multihadron final states from lattice QCD
journal, November 2017


Low-energy neutron-deuteron reactions with N 3 LO chiral forces
journal, November 2014


Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude
journal, December 2015


Volume dependence of N -body bound states
journal, April 2018


Resonance properties from the finite-volume energy spectrum
journal, August 2008


Volume dependence of the energy spectrum in massive quantum field theories: II. Scattering states
journal, June 1986


Three particles in a finite volume: The breakdown of spherical symmetry
journal, July 2012


Nuclear reactions from lattice QCD
journal, January 2015


Volume Dependence of N-Body Bound States
text, January 2018


Scattering phases for meson and baryon resonances on general moving-frame lattices
text, January 2012


Works referencing / citing this record:

Three-body spectrum in a finite volume: the role of cubic symmetry
text, January 2018


Energy levels of three resonantly interacting particles
journal, August 1973


Efimov physics in a finite volume
journal, March 2009


The triton in a finite volume
journal, January 2011


A solvable three-body model in finite volume
journal, November 2017


Volume dependence of N -body bound states
journal, April 2018


Nuclear reactions from lattice QCD
journal, January 2015


Resonance properties from the finite-volume energy spectrum
journal, August 2008


On the modification of the Efimov spectrum in a finite cubic box
journal, January 2010


Three particles in a finite volume
journal, May 2012


Three particles in a finite volume: The breakdown of spherical symmetry
journal, July 2012


Scalar mesons moving in a finite volume and the role of partial wave mixing
journal, August 2012


Low-energy neutron-deuteron reactions with N 3 LO chiral forces
journal, November 2014


Three-body unitarity with isobars revisited
journal, September 2017


Three-body unitarity in the finite volume
journal, December 2017


Lattice model of heavy-light three-body system
journal, February 2020


Opportunities for Lattice QCD in quark and lepton flavor physics
journal, November 2019


Hadrons and nuclei
journal, November 2019


Lattice QCD and neutrino-nucleus scattering
journal, November 2019


Phenomenology of relativistic $$\mathbf {3}\rightarrow \mathbf {3}$$ 3 → 3 reaction amplitudes within the isobar approximation
journal, January 2019