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Title: Equivalence of three-particle scattering formalisms

Abstract

In recent years, different on-shell 3→3 scattering formalisms have been proposed to be applied to both lattice QCD and infinite volume scattering processes. Here, we prove that the formulation in the infinite volume presented by Hansen and Sharpe in Phys. Rev. D92, 114509 (2015) and subsequently Briceno, Hansen, and Sharpe in Phys. Rev. D95, 074510 (2017) can be recovered from the B-matrix representation, derived on the basis of S-matrix unitarity, presented by Mai et al. in Eur. Phys. J. A53, 177 (2017) and Jackura et al. in Eur. Phys. J. C79, 56 (2019). Therefore, both formalisms in the infinite volume are equivalent and the physical content is identical. Additionally, the Faddeev equations are recovered in the non-relativistic limit of both representations.

Authors:
 [1];  [1];  [2]; ORCiD logo [3];  [4]; ORCiD logo [5];  [6];  [7]
  1. Indiana Univ., Bloomington, IN (United States)
  2. Univ. Nacional Autónoma de México, Ciudad de México (Mexico)
  3. Univ. Complutense de Madrid, Madrid (Spain)
  4. European Organization for Nuclear Research (CERN), Geneva (Switzerland)
  5. European Centre for Theoretical Studies in Nuclear Physics and Related areas (ECT*) and Fondazione Bruno Kessler, Villazzano, Trento (Italy); Istituto Nazionale di Fisica Nucleare (INFN), Genova (Italy)
  6. Univ. of Washington, Seattle, WA (United States)
  7. Indiana Univ., Bloomington, IN (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Publication Date:
Research Org.:
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Sponsoring Org.:
USDOE
Contributing Org.:
Joint Physics Analysis Center
OSTI Identifier:
1557359
Alternate Identifier(s):
OSTI ID: 1557621
Report Number(s):
JLAB-THY-19-2947; DOE/OR/23177-4683; arXiv:1905.12007
Journal ID: ISSN 2470-0010; PRVDAQ
Grant/Contract Number:  
SC0011637; AC05-06OR23177; FG02-87ER40365; PHY-1415459; IA101819; 251817; A1-S-21389
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 100; Journal Issue: 3; 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; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Citation Formats

Jackura, A. W., Dawid, S. M., Fernández-Ramírez, C., Mathieu, V., Mikhasenko, M., Pilloni, A., Sharpe, S. R., and Szczepaniak, A. P. Equivalence of three-particle scattering formalisms. United States: N. p., 2019. Web. doi:10.1103/PhysRevD.100.034508.
Jackura, A. W., Dawid, S. M., Fernández-Ramírez, C., Mathieu, V., Mikhasenko, M., Pilloni, A., Sharpe, S. R., & Szczepaniak, A. P. Equivalence of three-particle scattering formalisms. United States. doi:10.1103/PhysRevD.100.034508.
Jackura, A. W., Dawid, S. M., Fernández-Ramírez, C., Mathieu, V., Mikhasenko, M., Pilloni, A., Sharpe, S. R., and Szczepaniak, A. P. Tue . "Equivalence of three-particle scattering formalisms". United States. doi:10.1103/PhysRevD.100.034508.
@article{osti_1557359,
title = {Equivalence of three-particle scattering formalisms},
author = {Jackura, A. W. and Dawid, S. M. and Fernández-Ramírez, C. and Mathieu, V. and Mikhasenko, M. and Pilloni, A. and Sharpe, S. R. and Szczepaniak, A. P.},
abstractNote = {In recent years, different on-shell 3→3 scattering formalisms have been proposed to be applied to both lattice QCD and infinite volume scattering processes. Here, we prove that the formulation in the infinite volume presented by Hansen and Sharpe in Phys. Rev. D92, 114509 (2015) and subsequently Briceno, Hansen, and Sharpe in Phys. Rev. D95, 074510 (2017) can be recovered from the B-matrix representation, derived on the basis of S-matrix unitarity, presented by Mai et al. in Eur. Phys. J. A53, 177 (2017) and Jackura et al. in Eur. Phys. J. C79, 56 (2019). Therefore, both formalisms in the infinite volume are equivalent and the physical content is identical. Additionally, the Faddeev equations are recovered in the non-relativistic limit of both representations.},
doi = {10.1103/PhysRevD.100.034508},
journal = {Physical Review D},
number = 3,
volume = 100,
place = {United States},
year = {2019},
month = {8}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/PhysRevD.100.034508

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Works referenced in this record:

Three-particle quantization condition in a finite volume: 2. General formalism and the analysis of data
journal, October 2017

  • Hammer, Hans-Werner; Pang, Jin-Yi; Rusetsky, Akaki
  • Journal of High Energy Physics, Vol. 2017, Issue 10, 31 p.
  • DOI: 10.1007/JHEP10(2017)115

Three-particle quantization condition in a finite volume: 1. The role of the three-particle force
journal, September 2017

  • Hammer, Hans-Werner; Pang, Jin-Yi; Rusetsky, Akaki
  • Journal of High Energy Physics, Vol. 2017, Issue 9, 23 p.
  • DOI: 10.1007/JHEP09(2017)109