Relating the finitevolume spectrum and the twoandthreeparticle $S$ matrix for relativistic systems of identical scalar particles
Working in relativistic quantum field theory, we derive the quantization condition satisfied by coupled two and threeparticle systems of identical scalar particles confined to a cubic spatial volume with periodicity $L$. This gives the relation between the finitevolume spectrum and the infinitevolume $$\textbf 2 \to \textbf 2$$, $$\textbf 2 \to \textbf 3$$ 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 fourparticle threshold, and for which the twoparticle Kmatrix has no singularities below the threeparticle 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]}
 Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
 Johannes GutenbergUniv. Mainz, Mainz (Germany)
 Univ. of Washington, Seattle, WA (United States)
 Publication Date:
 Report Number(s):
 JLABTHY172400; arXiv:1701.07465; DOE/OR/231774058
Journal ID: ISSN 24700010; PRVDAQ; TRN: US1700533
 Grant/Contract Number:
 AC0506OR23177; SC0011637
 Type:
 Accepted Manuscript
 Journal Name:
 Physical Review D
 Additional Journal Information:
 Journal Volume: 95; Journal Issue: 7; Journal ID: ISSN 24700010
 Publisher:
 American Physical Society (APS)
 Research Org:
 Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; finite volume; relativistic scattering theory; lattice QCD
 OSTI Identifier:
 1353028
 Alternate Identifier(s):
 OSTI ID: 1352108
Briceño, Raúl A., Hansen, Maxwell T., and Sharpe, Stephen R.. Relating the finitevolume spectrum and the twoandthreeparticle S matrix for relativistic systems of identical scalar particles. United States: N. p.,
Web. doi:10.1103/PhysRevD.95.074510.
Briceño, Raúl A., Hansen, Maxwell T., & Sharpe, Stephen R.. Relating the finitevolume spectrum and the twoandthreeparticle 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.. 2017.
"Relating the finitevolume spectrum and the twoandthreeparticle 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 finitevolume spectrum and the twoandthreeparticle 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 threeparticle systems of identical scalar particles confined to a cubic spatial volume with periodicity $L$. This gives the relation between the finitevolume spectrum and the infinitevolume $\textbf 2 \to \textbf 2$, $\textbf 2 \to \textbf 3$ 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 fourparticle threshold, and for which the twoparticle Kmatrix has no singularities below the threeparticle 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 = {2017},
month = {4}
}