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Title: Unitarity of the infinite-volume three-particle scattering amplitude arising from a finite-volume formalism

Abstract

Hansen and Sharpe [Phys. Rev. D 92, 114509 (2015)PRVDAQ1550-799810.1103/PhysRevD.92.114509] derived a relation between the scattering amplitude of three identical bosons, M3, and a real function referred to as the divergence-free K matrix and denoted Kdf,3. The result arose in the context of a relation between finite-volume energies and Kdf,3, derived to all orders in the perturbative expansion of a generic low-energy effective field theory. In this work we set aside the role of the finite volume and focus on the infinite-volume relation between Kdf,3 and M3. We show that, for any real choice of Kdf,3, M3 satisfies the three-particle unitarity constraint to all orders. Given that Kdf,3 is also free of a class of kinematic divergences, the function may provide a useful tool for parametrizing three-body scattering data. Applications include the phenomenological analysis of experimental data (where the connection to the finite volume is irrelevant) as well as calculations in lattice quantum chromodynamics (where the volume plays a key role).

Authors:
; ; ORCiD logo;
Publication Date:
Research Org.:
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Indiana Univ., Bloomington, IN (United States); Univ. of Washington, Seattle, WA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP); USDOE Office of Science (SC), High Energy Physics (HEP)
Contributing Org.:
Jefferson Lab, Indiana University
OSTI Identifier:
1562572
Alternate Identifier(s):
OSTI ID: 1567050; OSTI ID: 1595125; OSTI ID: 1669366
Report Number(s):
JLAB-THY-19-2945; DOE/OR/23177-4684; arXiv:1905.11188
Journal ID: ISSN 2470-0010; PRVDAQ; 054508
Grant/Contract Number:  
SC0011637; FG02-87ER40365; AC05-06OR23177; SC0019229; PHY-1415459
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Name: Physical Review D Journal Volume: 100 Journal Issue: 5; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
43 PARTICLE ACCELERATORS; Lattice QCD; Lattice field theory; Quantum field theory; Quantum field theory (low energy); Scattering amplitudes; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; lattice QCD, scattering

Citation Formats

Briceño, Raúl A., Hansen, Maxwell T., Sharpe, Stephen R., and Szczepaniak, Adam P. Unitarity of the infinite-volume three-particle scattering amplitude arising from a finite-volume formalism. United States: N. p., 2019. Web. doi:10.1103/PhysRevD.100.054508.
Briceño, Raúl A., Hansen, Maxwell T., Sharpe, Stephen R., & Szczepaniak, Adam P. Unitarity of the infinite-volume three-particle scattering amplitude arising from a finite-volume formalism. United States. doi:10.1103/PhysRevD.100.054508.
Briceño, Raúl A., Hansen, Maxwell T., Sharpe, Stephen R., and Szczepaniak, Adam P. Wed . "Unitarity of the infinite-volume three-particle scattering amplitude arising from a finite-volume formalism". United States. doi:10.1103/PhysRevD.100.054508.
@article{osti_1562572,
title = {Unitarity of the infinite-volume three-particle scattering amplitude arising from a finite-volume formalism},
author = {Briceño, Raúl A. and Hansen, Maxwell T. and Sharpe, Stephen R. and Szczepaniak, Adam P.},
abstractNote = {Hansen and Sharpe [Phys. Rev. D 92, 114509 (2015)PRVDAQ1550-799810.1103/PhysRevD.92.114509] derived a relation between the scattering amplitude of three identical bosons, M3, and a real function referred to as the divergence-free K matrix and denoted Kdf,3. The result arose in the context of a relation between finite-volume energies and Kdf,3, derived to all orders in the perturbative expansion of a generic low-energy effective field theory. In this work we set aside the role of the finite volume and focus on the infinite-volume relation between Kdf,3 and M3. We show that, for any real choice of Kdf,3, M3 satisfies the three-particle unitarity constraint to all orders. Given that Kdf,3 is also free of a class of kinematic divergences, the function may provide a useful tool for parametrizing three-body scattering data. Applications include the phenomenological analysis of experimental data (where the connection to the finite volume is irrelevant) as well as calculations in lattice quantum chromodynamics (where the volume plays a key role).},
doi = {10.1103/PhysRevD.100.054508},
journal = {Physical Review D},
number = 5,
volume = 100,
place = {United States},
year = {2019},
month = {9}
}

Journal Article:
Free Publicly Available Full Text
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DOI: 10.1103/PhysRevD.100.054508

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Cited by: 5 works
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