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Title: Three-body unitarity in the finite volume

Abstract

We present the physical interpretation of lattice QCD simulations, performed in a small volume, requires an extrapolation to the infinite volume. A method is proposed to perform such an extrapolation for three interacting particles at energies above threshold. For this, a recently formulated relativistic $$3\to 3$$ amplitude based on the isobar formulation is adapted to the finite volume. The guiding principle is two- and three-body unitarity that imposes the imaginary parts of the amplitude in the infinite volume. In turn, these imaginary parts dictate the leading power-law finite-volume effects. It is demonstrated that finite-volume poles arising from the singular interaction, from the external two-body sub-amplitudes, and from the disconnected topology cancel exactly leaving only the genuine three-body eigenvalues. Lastly, the corresponding quantization condition is derived for the case of three identical scalar-isoscalar particles and its numerical implementation is demonstrated.

Authors:
 [1];  [2]
  1. George Washington Univ., Washington, DC (United States)
  2. George Washington Univ., Washington, DC (United States) ; Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
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) (SC-26)
OSTI Identifier:
1416327
Report Number(s):
JLAB-THY-17-2554; DOE/OR/23177-4221; arXiv:1709.08222
Journal ID: ISSN 1434-6001; PII: 12440; TRN: US1800924
Grant/Contract Number:  
AC05-06OR23177; SC001658
Resource Type:
Accepted Manuscript
Journal Name:
European Physical Journal. A
Additional Journal Information:
Journal Volume: 53; Journal Issue: 12; Journal ID: ISSN 1434-6001
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Mai, M., and Döring, M. Three-body unitarity in the finite volume. United States: N. p., 2017. Web. doi:10.1140/epja/i2017-12440-1.
Mai, M., & Döring, M. Three-body unitarity in the finite volume. United States. doi:10.1140/epja/i2017-12440-1.
Mai, M., and Döring, M. Mon . "Three-body unitarity in the finite volume". United States. doi:10.1140/epja/i2017-12440-1. https://www.osti.gov/servlets/purl/1416327.
@article{osti_1416327,
title = {Three-body unitarity in the finite volume},
author = {Mai, M. and Döring, M.},
abstractNote = {We present the physical interpretation of lattice QCD simulations, performed in a small volume, requires an extrapolation to the infinite volume. A method is proposed to perform such an extrapolation for three interacting particles at energies above threshold. For this, a recently formulated relativistic $3\to 3$ amplitude based on the isobar formulation is adapted to the finite volume. The guiding principle is two- and three-body unitarity that imposes the imaginary parts of the amplitude in the infinite volume. In turn, these imaginary parts dictate the leading power-law finite-volume effects. It is demonstrated that finite-volume poles arising from the singular interaction, from the external two-body sub-amplitudes, and from the disconnected topology cancel exactly leaving only the genuine three-body eigenvalues. Lastly, the corresponding quantization condition is derived for the case of three identical scalar-isoscalar particles and its numerical implementation is demonstrated.},
doi = {10.1140/epja/i2017-12440-1},
journal = {European Physical Journal. A},
number = 12,
volume = 53,
place = {United States},
year = {2017},
month = {12}
}

Journal Article:
Free Publicly Available Full Text
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Citation Metrics:
Cited by: 20 works
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Figures / Tables:

Figure 1 Figure 1: Red dashed line (green dotted line): Real (imaginary) part of the infinite-volume S-wave projection of the potential B0 from Eq. (6) with M = 138 MeV, λ = 3476 and β = 5000 MeV. In comparison, the finite-volume projection B A+111 from Eq. (10) for the transition frommore » shell 1 to shell 1 at L = 6 fm (blue dots).« less

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    Works referencing / citing this record:

    The impact of $K^{+}\Lambda$ K + Λ photoproduction on the resonance spectrum
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    The impact of $K^{+}\Lambda$ K + Λ photoproduction on the resonance spectrum
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