Numerical exploration of three relativistic particles in a finite volume including twoparticle resonances and bound states
Abstract
In this work, we use an extension of the quantization condition, given in ref. [1], to numerically explore the finitevolume spectrum of three relativistic particles, in the case that twoparticle subsets are either resonant or bound. The original form of the relativistic threeparticle quantization condition was derived under a technical assumption on the two particle K matrix that required the absence of twoparticle bound states or narrow two particle resonances. Here we describe how this restriction can be lifted in a simple way using the freedom in the definition of the Kmatrixlike quantity that enters the quantization condition. With this in hand, we extend previous numerical studies of the quantization condition to explore the finitevolume signature for a variety of two and threeparticle interactions. We determine the spectrum for parameters such that the system contains both dimers (twoparticle bound states) and one or more trimers (in which all three particles are bound), and also for cases where the twoparticle subchannel is resonant. We also show how the quantization condition provides a tool for determining infinitevolume dimer particle scattering amplitudes for energies below the dimer breakup. We illustrate this for a series of examples, including one that parallels physical deuteronnucleon scattering.more »
 Authors:

 CSICUniv. de Valéncia, Paterna (Spain)
 Univ. of Washington, Seattle, WA (United States). Dept. of Physics
 Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Old Dominion Univ., Norfolk, VA (United States). Dept. of Physics
 European Organization for Nuclear Research (CERN), Geneva (Switzerland)
 Publication Date:
 Research Org.:
 Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (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); European Union (EU); Australian Research Council (ARC); Kyoto University (Japan)
 OSTI Identifier:
 1574401
 Alternate Identifier(s):
 OSTI ID: 1595142
 Report Number(s):
 JLABTHY193011; DOE/OR/231774759; arXiv:1908.02411
Journal ID: ISSN 10298479; TRN: US2001288
 Grant/Contract Number:
 AC0506OR23177; SC0011637; SC0019229; DP190102215
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2019; Journal Issue: 10; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Lattice QCD; Scattering Amplitudes
Citation Formats
RomeroLópez, Fernando, Sharpe, Stephen R., Blanton, Tyler D., Briceño, Raúl A., and Hansen, Maxwell T. Numerical exploration of three relativistic particles in a finite volume including twoparticle resonances and bound states. United States: N. p., 2019.
Web. doi:10.1007/JHEP10(2019)007.
RomeroLópez, Fernando, Sharpe, Stephen R., Blanton, Tyler D., Briceño, Raúl A., & Hansen, Maxwell T. Numerical exploration of three relativistic particles in a finite volume including twoparticle resonances and bound states. United States. https://doi.org/10.1007/JHEP10(2019)007
RomeroLópez, Fernando, Sharpe, Stephen R., Blanton, Tyler D., Briceño, Raúl A., and Hansen, Maxwell T. Thu .
"Numerical exploration of three relativistic particles in a finite volume including twoparticle resonances and bound states". United States. https://doi.org/10.1007/JHEP10(2019)007. https://www.osti.gov/servlets/purl/1574401.
@article{osti_1574401,
title = {Numerical exploration of three relativistic particles in a finite volume including twoparticle resonances and bound states},
author = {RomeroLópez, Fernando and Sharpe, Stephen R. and Blanton, Tyler D. and Briceño, Raúl A. and Hansen, Maxwell T.},
abstractNote = {In this work, we use an extension of the quantization condition, given in ref. [1], to numerically explore the finitevolume spectrum of three relativistic particles, in the case that twoparticle subsets are either resonant or bound. The original form of the relativistic threeparticle quantization condition was derived under a technical assumption on the two particle K matrix that required the absence of twoparticle bound states or narrow two particle resonances. Here we describe how this restriction can be lifted in a simple way using the freedom in the definition of the Kmatrixlike quantity that enters the quantization condition. With this in hand, we extend previous numerical studies of the quantization condition to explore the finitevolume signature for a variety of two and threeparticle interactions. We determine the spectrum for parameters such that the system contains both dimers (twoparticle bound states) and one or more trimers (in which all three particles are bound), and also for cases where the twoparticle subchannel is resonant. We also show how the quantization condition provides a tool for determining infinitevolume dimer particle scattering amplitudes for energies below the dimer breakup. We illustrate this for a series of examples, including one that parallels physical deuteronnucleon scattering. All calculations presented here are restricted to the case of three identical scalar particles.},
doi = {10.1007/JHEP10(2019)007},
journal = {Journal of High Energy Physics (Online)},
number = 10,
volume = 2019,
place = {United States},
year = {2019},
month = {10}
}
Web of Science
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