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Title: Efficient solution of the multichannel Lüscher determinant condition through eigenvalue decomposition

Abstract

We present a method for efficiently finding solutions of Lüscher’s quantization condition, the equation which relates two-particle scattering amplitudes to the discrete spectrum of states in a periodic spatial volume of finite extent such as that present in lattice QCD. The approach proposed is based on an eigenvalue decomposition in the space of coupled-channels and partial-waves, which proves to have several desirable and simplifying features that are of great benefit when considering problems beyond simple elastic scattering of spinless particles. We illustrate the method with a toy model of vector-vector scattering featuring a high density of solutions, and with an application to explicit lattice QCD energy level data describing $J^P=1^-$ and $1^+$ scattering in several coupled channels.

Authors:
ORCiD logo; ORCiD logo; ORCiD logo
Publication Date:
Research Org.:
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Nuclear Physics (NP); Science and Technology Facilities Council (STFC) (United Kingdom)
Contributing Org.:
for the Hadron Spectrum Collaboration
OSTI Identifier:
1633699
Alternate Identifier(s):
OSTI ID: 1633980
Report Number(s):
JLAB-THY-20-3133; DOE/OR/23177-4898; arXiv:2001.08474
Journal ID: ISSN 2470-0010; PRVDAQ; 114505
Grant/Contract Number:  
ST/P000681/1; ST/P002307/1; ST/R002452/1; ST/R00689X/1; SC0018416; AC05-06OR23177; AC05-00OR22725; AC02-05CH11231
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Name: Physical Review D Journal Volume: 101 Journal Issue: 11; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Lattice QCD; Quantum chromodynamics; Particles & Fields

Citation Formats

Woss, Antoni J., Wilson, David J., and Dudek, Jozef J. Efficient solution of the multichannel Lüscher determinant condition through eigenvalue decomposition. United States: N. p., 2020. Web. doi:10.1103/PhysRevD.101.114505.
Woss, Antoni J., Wilson, David J., & Dudek, Jozef J. Efficient solution of the multichannel Lüscher determinant condition through eigenvalue decomposition. United States. doi:https://doi.org/10.1103/PhysRevD.101.114505
Woss, Antoni J., Wilson, David J., and Dudek, Jozef J. Mon . "Efficient solution of the multichannel Lüscher determinant condition through eigenvalue decomposition". United States. doi:https://doi.org/10.1103/PhysRevD.101.114505.
@article{osti_1633699,
title = {Efficient solution of the multichannel Lüscher determinant condition through eigenvalue decomposition},
author = {Woss, Antoni J. and Wilson, David J. and Dudek, Jozef J.},
abstractNote = {We present a method for efficiently finding solutions of Lüscher’s quantization condition, the equation which relates two-particle scattering amplitudes to the discrete spectrum of states in a periodic spatial volume of finite extent such as that present in lattice QCD. The approach proposed is based on an eigenvalue decomposition in the space of coupled-channels and partial-waves, which proves to have several desirable and simplifying features that are of great benefit when considering problems beyond simple elastic scattering of spinless particles. We illustrate the method with a toy model of vector-vector scattering featuring a high density of solutions, and with an application to explicit lattice QCD energy level data describing $J^P=1^-$ and $1^+$ scattering in several coupled channels.},
doi = {10.1103/PhysRevD.101.114505},
journal = {Physical Review D},
number = 11,
volume = 101,
place = {United States},
year = {2020},
month = {6}
}

Journal Article:
Free Publicly Available Full Text
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DOI: https://doi.org/10.1103/PhysRevD.101.114505

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