Numerical study of the relativistic three-body quantization condition in the isotropic approximation
Abstract
We present numerical results showing how our recently proposed relativistic three-particle quantization condition can be used in practice. Using the isotropic (generalized s-wave) approximation, and keeping only the leading terms in the effective range expansion, we show how the quantization condition can be solved numerically in a straightforward manner. In addition, we show how the integral equations that relate the intermediate three-particle infinite-volume scattering quantity, Kdf,3, to the physical scattering amplitude can be solved at and below threshold. We test our methods by reproducing known analytic results for the 1/L expansion of the threshold state, the volume dependence of three-particle bound-state energies, and the Bethe-Salpeter wavefunctions for these bound states. We also find that certain values of Kdf,3 lead to unphysical finite-volume energies, and give a preliminary analysis of these artifacts.
- Authors:
- Publication Date:
- Research Org.:
- Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Univ. of Washington, Seattle, WA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP); USDOE Office of Science (SC), High Energy Physics (HEP)
- OSTI Identifier:
- 1459751
- Alternate Identifier(s):
- OSTI ID: 1460364; OSTI ID: 1595810
- Report Number(s):
- JLAB-THY-18-2657; DOE/OR/23177-4359; arXiv:1803.04169; CERN-TH-2018-046
Journal ID: ISSN 2470-0010; PRVDAQ; 014506
- Grant/Contract Number:
- SC0011637; AC05-06OR23177
- Resource Type:
- Published Article
- Journal Name:
- Physical Review D
- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 98 Journal Issue: 1; Journal ID: ISSN 2470-0010
- Publisher:
- American Physical Society
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Citation Formats
Briceño, Raúl A., Hansen, Maxwell T., and Sharpe, Stephen R. Numerical study of the relativistic three-body quantization condition in the isotropic approximation. United States: N. p., 2018.
Web. doi:10.1103/PhysRevD.98.014506.
Briceño, Raúl A., Hansen, Maxwell T., & Sharpe, Stephen R. Numerical study of the relativistic three-body quantization condition in the isotropic approximation. United States. doi:https://doi.org/10.1103/PhysRevD.98.014506
Briceño, Raúl A., Hansen, Maxwell T., and Sharpe, Stephen R. Wed .
"Numerical study of the relativistic three-body quantization condition in the isotropic approximation". United States. doi:https://doi.org/10.1103/PhysRevD.98.014506.
@article{osti_1459751,
title = {Numerical study of the relativistic three-body quantization condition in the isotropic approximation},
author = {Briceño, Raúl A. and Hansen, Maxwell T. and Sharpe, Stephen R.},
abstractNote = {We present numerical results showing how our recently proposed relativistic three-particle quantization condition can be used in practice. Using the isotropic (generalized s-wave) approximation, and keeping only the leading terms in the effective range expansion, we show how the quantization condition can be solved numerically in a straightforward manner. In addition, we show how the integral equations that relate the intermediate three-particle infinite-volume scattering quantity, Kdf,3, to the physical scattering amplitude can be solved at and below threshold. We test our methods by reproducing known analytic results for the 1/L expansion of the threshold state, the volume dependence of three-particle bound-state energies, and the Bethe-Salpeter wavefunctions for these bound states. We also find that certain values of Kdf,3 lead to unphysical finite-volume energies, and give a preliminary analysis of these artifacts.},
doi = {10.1103/PhysRevD.98.014506},
journal = {Physical Review D},
number = 1,
volume = 98,
place = {United States},
year = {2018},
month = {7}
}
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DOI: https://doi.org/10.1103/PhysRevD.98.014506
DOI: https://doi.org/10.1103/PhysRevD.98.014506
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Works referencing / citing this record:
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