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

Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R.

doi:10.1103/PhysRevD.95.074510

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

Journal Article · Tue Apr 18 00:00:00 EDT 2017 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.95.074510· OSTI ID:1353028

Briceño, Raúl A. ^[1]; Hansen, Maxwell T. ^[2]; Sharpe, Stephen R. ^[3]

Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Johannes Gutenberg-Univ. Mainz, Mainz (Germany)
Univ. of Washington, Seattle, WA (United States)

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.

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Research Organization:: Univ. of Washington, Seattle, WA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: AC05-06OR23177; SC0011637

OSTI ID:: 1353028

Alternate ID(s):: OSTI ID: 1352108; OSTI ID: 1595489

Report Number(s):: JLAB-THY-17-2400; arXiv:1701.07465; DOE/OR/23177-4058; PRVDAQ; TRN: US1700533

Journal Information:: Physical Review D, Vol. 95, Issue 7; ISSN 2470-0010

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 123 works

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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