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Title: Numerical exploration of three relativistic particles in a finite volume including two-particle resonances and bound states

Abstract

In this work, we use an extension of the quantization condition, given in Ref. [1], to numerically explore the finite-volume spectrum of three relativistic particles, in the case that two-particle subsets are either resonant or bound. The original form of the relativistic three-particle quantization condition was derived under a technical assumption on the two-particle K matrix that required the absence of two-particle 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 K-matrix-like quantity that enters the quantization condition. With this in hand, we extend previous numerical studies of the quantization condition to explore the finite-volume signature for a variety of two- and three-particle interactions. We determine the spectrum for parameters such that the system contains both dimers (two-particle bound states) and one or more trimers (in which all three particles are bound), and also for cases where the two-particle subchannel is resonant. We also show how the quantization condition provides a tool for determining infinite-volume dimer-particle scattering amplitudes for energies below the dimer breakup. We illustrate this for a series of examples, including one that parallels physical deuteron-nucleon scattering. All calculations presentedmore » here are restricted to the case of three identical scalar particles.« less

Authors:
ORCiD logo [1];  [2];  [2];  [3];  [4]
  1. CSIC-Univ. de Valéncia, Paterna (Spain)
  2. Univ. of Washington, Seattle, WA (United States). Dept. of Physics
  3. Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Old Dominion Univ., Norfolk, VA (United States). Dept. of Physics
  4. 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):
JLAB-THY-19-3011; DOE/OR/-23177-4759; arXiv:1908.02411
Journal ID: ISSN 1029-8479; TRN: US2001288
Grant/Contract Number:  
AC05-06OR23177; 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 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Lattice QCD; Scattering Amplitudes

Citation Formats

Romero-López, 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 two-particle resonances and bound states. United States: N. p., 2019. Web. doi:10.1007/JHEP10(2019)007.
Romero-López, Fernando, Sharpe, Stephen R., Blanton, Tyler D., Briceño, Raúl A., & Hansen, Maxwell T. Numerical exploration of three relativistic particles in a finite volume including two-particle resonances and bound states. United States. https://doi.org/10.1007/JHEP10(2019)007
Romero-López, 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 two-particle 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 two-particle resonances and bound states},
author = {Romero-López, 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 finite-volume spectrum of three relativistic particles, in the case that two-particle subsets are either resonant or bound. The original form of the relativistic three-particle quantization condition was derived under a technical assumption on the two-particle K matrix that required the absence of two-particle 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 K-matrix-like quantity that enters the quantization condition. With this in hand, we extend previous numerical studies of the quantization condition to explore the finite-volume signature for a variety of two- and three-particle interactions. We determine the spectrum for parameters such that the system contains both dimers (two-particle bound states) and one or more trimers (in which all three particles are bound), and also for cases where the two-particle subchannel is resonant. We also show how the quantization condition provides a tool for determining infinite-volume dimer-particle scattering amplitudes for energies below the dimer breakup. We illustrate this for a series of examples, including one that parallels physical deuteron-nucleon 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}
}

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Works referencing / citing this record:

Opportunities for Lattice QCD in quark and lepton flavor physics
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I = 3 Three-Pion Scattering Amplitude from Lattice QCD
journal, January 2020


Three-body unitarity versus finite-volume π + π + π + spectrum from lattice QCD
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