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

Döring, Michael ; Hammer, Hans-Werner ; Mai, Maxim ; Pang, J.-Y. ; Rusetsky, Akaki ; Wu, J. (2022):
Three-body spectrum in a finite volume: The role of cubic symmetry. (Publisher's Version)
In: Physical Review D, 97 (11), American Physical Society, ISSN 2470-0010, e-ISSN 2470-0029,
DOI: 10.26083/tuprints-00012800,
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Item Type: Article
Origin: Secondary publication
Status: Publisher's Version
Title: Three-body spectrum in a finite volume: The role of cubic symmetry
Language: English
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 BetheSalpeter 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.

Journal or Publication Title: Physical Review D
Journal volume: 97
Issue Number: 11
Publisher: American Physical Society
Collation: 17 Seiten
Classification DDC: 500 Naturwissenschaften und Mathematik > 530 Physik
Divisions: 05 Department of Physics > Institute of Nuclear Physics
Date Deposited: 11 Mar 2022 13:13
Last Modified: 11 Mar 2022 13:14
DOI: 10.26083/tuprints-00012800
Corresponding Links:
URN: urn:nbn:de:tuda-tuprints-128003
Additional Information:

Supplements:

https://journals.aps.org/prd/supplemental/10.1103/PhysRevD.97.114508/Read_basis_functions.nb

https://journals.aps.org/prd/supplemental/10.1103/PhysRevD.97.114508/basisfunctions.wl

URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/12800
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