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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

Abstract

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.

Authors:
 [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:
Research Org.:
Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1353028
Alternate Identifier(s):
OSTI ID: 1352108
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
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 95; Journal Issue: 7; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; finite volume; relativistic scattering theory; lattice QCD

Citation Formats

Briceño, Raúl A., Hansen, Maxwell T., and Sharpe, Stephen R. Relating the finite-volume spectrum and the two-and-three-particle S matrix for relativistic systems of identical scalar particles. United States: N. p., 2017. Web. doi:10.1103/PhysRevD.95.074510.
Briceño, Raúl A., Hansen, Maxwell T., & Sharpe, Stephen R. Relating the finite-volume spectrum and the two-and-three-particle S matrix for relativistic systems of identical scalar particles. United States. doi:10.1103/PhysRevD.95.074510.
Briceño, Raúl A., Hansen, Maxwell T., and Sharpe, Stephen R. Tue . "Relating the finite-volume spectrum and the two-and-three-particle S matrix for relativistic systems of identical scalar particles". United States. doi:10.1103/PhysRevD.95.074510. https://www.osti.gov/servlets/purl/1353028.
@article{osti_1353028,
title = {Relating the finite-volume spectrum and the two-and-three-particle S matrix for relativistic systems of identical scalar particles},
author = {Briceño, Raúl A. and Hansen, Maxwell T. and Sharpe, Stephen R.},
abstractNote = {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.},
doi = {10.1103/PhysRevD.95.074510},
journal = {Physical Review D},
number = 7,
volume = 95,
place = {United States},
year = {Tue Apr 18 00:00:00 EDT 2017},
month = {Tue Apr 18 00:00:00 EDT 2017}
}

Journal Article:
Free Publicly Available Full Text
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Cited by: 14works
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