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This content will become publicly available on December 18, 2018

Title: Three-body unitarity in the finite volume

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:
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
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
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)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
OSTI Identifier:
1416327