Threebody 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 threebody unitarity that imposes the imaginary parts of the amplitude in the infinite volume. In turn, these imaginary parts dictate the leading powerlaw finitevolume effects. It is demonstrated that finitevolume poles arising from the singular interaction, from the external twobody subamplitudes, and from the disconnected topology cancel exactly leaving only the genuine threebody eigenvalues. Lastly, the corresponding quantization condition is derived for the case of three identical scalarisoscalar particles and its numerical implementation is demonstrated.
 Authors:
 George Washington Univ., Washington, DC (United States)
 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) (SC26)
 OSTI Identifier:
 1416327
 Report Number(s):
 JLABTHY172554; DOE/OR/231774221; arXiv:1709.08222
Journal ID: ISSN 14346001; PII: 12440
 Grant/Contract Number:
 AC0506OR23177; SC001658
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 European Physical Journal. A
 Additional Journal Information:
 Journal Volume: 53; Journal Issue: 12; Journal ID: ISSN 14346001
 Publisher:
 Springer
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Citation Formats
Mai, M., and Döring, M. Threebody unitarity in the finite volume. United States: N. p., 2017.
Web. doi:10.1140/epja/i2017124401.
Mai, M., & Döring, M. Threebody unitarity in the finite volume. United States. doi:10.1140/epja/i2017124401.
Mai, M., and Döring, M. 2017.
"Threebody unitarity in the finite volume". United States.
doi:10.1140/epja/i2017124401.
@article{osti_1416327,
title = {Threebody 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 threebody unitarity that imposes the imaginary parts of the amplitude in the infinite volume. In turn, these imaginary parts dictate the leading powerlaw finitevolume effects. It is demonstrated that finitevolume poles arising from the singular interaction, from the external twobody subamplitudes, and from the disconnected topology cancel exactly leaving only the genuine threebody eigenvalues. Lastly, the corresponding quantization condition is derived for the case of three identical scalarisoscalar particles and its numerical implementation is demonstrated.},
doi = {10.1140/epja/i2017124401},
journal = {European Physical Journal. A},
number = 12,
volume = 53,
place = {United States},
year = 2017,
month =
}

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