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Title: Relating the finite-volume spectrum and the two-and-three-particle S matrix for relativistic systems of identical scalar particles

Working in relativistic quantum field theory, we derive the quantization condition satisfied by coupled two- and three-particle systems of identical scalar particles confined to a cubic spatial volume with periodicity $L$. This gives the relation between the finite-volume spectrum and the infinite-volume $$\textbf 2 \to \textbf 2$$, $$\textbf 2 \to \textbf 3$$ and $$\textbf 3 \to \textbf 3$$ scattering amplitudes for such theories. The result holds for relativistic systems composed of scalar particles with nonzero mass $m$, whose center of mass energy lies below the four-particle threshold, and for which the two-particle K-matrix has no singularities below the three-particle threshold. Finally, the quantization condition is exact up to corrections of the order $$\mathcal{O}(e^{-mL})$$ and holds for any choice of total momenta satisfying the boundary conditions.
 [1] ;  [2] ;  [3]
  1. Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
  2. Johannes Gutenberg-Univ. Mainz, Mainz (Germany)
  3. Univ. of Washington, Seattle, WA (United States)
Publication Date:
Report Number(s):
JLAB-THY-17-2400; arXiv:1701.07465; DOE/OR/23177-4058
Journal ID: ISSN 2470-0010; PRVDAQ; TRN: US1700533
Grant/Contract Number:
AC05-06OR23177; SC0011637
Accepted Manuscript
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 95; Journal Issue: 7; Journal ID: ISSN 2470-0010
American Physical Society (APS)
Research Org:
Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)
Sponsoring Org:
Country of Publication:
United States
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; finite volume; relativistic scattering theory; lattice QCD
OSTI Identifier:
Alternate Identifier(s):
OSTI ID: 1352108