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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:
Journal Article: 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.
@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 = {Mon Dec 18 00:00:00 EST 2017},
month = {Mon Dec 18 00:00:00 EST 2017}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on December 18, 2018
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