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

doi:10.1007/JHEP10(2019)007

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 »« less

Authors:

^[1]; Sharpe, Stephen R. ^[2]; Blanton, Tyler D. ^[2]; Briceño, Raúl A. ^[3]; Hansen, Maxwell T. ^[4]

CSIC-Univ. 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:: 2019-10-03

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.

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                    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.  doi:10.1007/JHEP10(2019)007.

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                    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.  doi:10.1007/JHEP10(2019)007.  https://www.osti.gov/servlets/purl/1574401.

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@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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DOI: 10.1007/JHEP10(2019)007

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Works referenced in this record:

Scalar mesons in a finite volume
journal, January 2011

Bernard, V.; Lage, M.; Meißner, U. -G.
Journal of High Energy Physics, Vol. 2011, Issue 1
DOI: 10.1007/JHEP01(2011)019

Determination of proton-deuteron scattering lengths
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Black, T. C.; Karwowski, H. J.; Ludwig, E. J.
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Implementing the three-particle quantization condition including higher partial waves
journal, March 2019

Blanton, Tyler D.; Romero-López, Fernando; Sharpe, Stephen R.
Journal of High Energy Physics, Vol. 2019, Issue 3
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Doublet coulomb-nuclear scattering length and other parameters of the effective-range function for proton-deuteron scattering from an analysis of present-day data
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Orlov, Yu. V.; Orevkov, Yu. P.
Physics of Atomic Nuclei, Vol. 69, Issue 5
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Three-body scattering: ladders and resonances
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Mikhasenko, M.; Wunderlich, Y.; Jackura, A.
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Isoscalar $π π$ Scattering and the $σ$ Meson Resonance from QCD
journal, January 2017

Briceño, Raul A.; Dudek, Jozef J.; Edwards, Robert G.
Physical Review Letters, Vol. 118, Issue 2
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Energy levels arising from resonant two-body forces in a three-body system
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Efimov, V.
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Scattering processes and resonances from lattice QCD
journal, April 2018

Briceño, Raúl A.; Dudek, Jozef J.; Young, Ross D.
Reviews of Modern Physics, Vol. 90, Issue 2
DOI: 10.1103/RevModPhys.90.025001

Analysis of experimental data on doublet neutron-deuteron scattering at energies below the deuteron-breakup threshold on the basis of the pole approximation of the effective-range function
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Babenko, V. A.; Petrov, N. M.
Physics of Atomic Nuclei, Vol. 71, Issue 1
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Dynamically-coupled partial-waves in ρπ isospin-2 scattering from lattice QCD
journal, July 2018

Woss, Antoni J.; Thomas, Christopher E.; Dudek, Jozef J.
Journal of High Energy Physics, Vol. 2018, Issue 7
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Consistency of the low-energy three-nucleon observables and the separable interaction model
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Works referencing / citing this record:

Lattice model of heavy-light three-body system
journal, February 2020

Guo, Peng; Döring, Michael
Physical Review D, Vol. 101, Issue 3
DOI: 10.1103/physrevd.101.034501

Three-body unitarity versus finite-volume $π^{+} π^{+} π^{+}$ spectrum from lattice QCD
journal, March 2020

Mai, M.; Döring, M.; Culver, C.
Physical Review D, Vol. 101, Issue 5
DOI: 10.1103/physrevd.101.054510

$I = 3$ Three-Pion Scattering Amplitude from Lattice QCD
journal, January 2020

Blanton, Tyler D.; Romero-López, Fernando; Sharpe, Stephen R.
Physical Review Letters, Vol. 124, Issue 3
DOI: 10.1103/physrevlett.124.032001

Opportunities for Lattice QCD in quark and lepton flavor physics
journal, November 2019

Lehner, Christoph; Meinel, Stefan; Blum, Tom
The European Physical Journal A, Vol. 55, Issue 11
DOI: 10.1140/epja/i2019-12891-2

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

Abstract

Citation Formats

Scalar mesons in a finite volume journal, January 2011

Determination of proton-deuteron scattering lengths journal, December 1999

Implementing the three-particle quantization condition including higher partial waves journal, March 2019

Doublet coulomb-nuclear scattering length and other parameters of the effective-range function for proton-deuteron scattering from an analysis of present-day data journal, May 2006

Three-body scattering: ladders and resonances journal, August 2019

Isoscalar π π Scattering and the σ Meson Resonance from QCD journal, January 2017

Energy levels arising from resonant two-body forces in a three-body system journal, December 1970

The neutron-deuteron scattering lengths journal, September 1971

Scattering processes and resonances from lattice QCD journal, April 2018

Analysis of experimental data on doublet neutron-deuteron scattering at energies below the deuteron-breakup threshold on the basis of the pole approximation of the effective-range function journal, January 2008

Dynamically-coupled partial-waves in ρπ isospin-2 scattering from lattice QCD journal, July 2018

Consistency of the low-energy three-nucleon observables and the separable interaction model journal, January 1968

Lattice model of heavy-light three-body system journal, February 2020

Three-body unitarity versus finite-volume π + π + π + spectrum from lattice QCD journal, March 2020

I = 3 Three-Pion Scattering Amplitude from Lattice QCD journal, January 2020

Opportunities for Lattice QCD in quark and lepton flavor physics journal, November 2019

Scalar mesons in a finite volume
journal, January 2011

Determination of proton-deuteron scattering lengths
journal, December 1999

Implementing the three-particle quantization condition including higher partial waves
journal, March 2019

Doublet coulomb-nuclear scattering length and other parameters of the effective-range function for proton-deuteron scattering from an analysis of present-day data
journal, May 2006

Three-body scattering: ladders and resonances
journal, August 2019

Isoscalar $π π$ Scattering and the $σ$ Meson Resonance from QCD
journal, January 2017

Energy levels arising from resonant two-body forces in a three-body system
journal, December 1970

The neutron-deuteron scattering lengths
journal, September 1971

Scattering processes and resonances from lattice QCD
journal, April 2018

Analysis of experimental data on doublet neutron-deuteron scattering at energies below the deuteron-breakup threshold on the basis of the pole approximation of the effective-range function
journal, January 2008

Dynamically-coupled partial-waves in ρπ isospin-2 scattering from lattice QCD
journal, July 2018

Consistency of the low-energy three-nucleon observables and the separable interaction model
journal, January 1968

Lattice model of heavy-light three-body system
journal, February 2020

Three-body unitarity versus finite-volume $π^{+} π^{+} π^{+}$ spectrum from lattice QCD
journal, March 2020

$I = 3$ Three-Pion Scattering Amplitude from Lattice QCD
journal, January 2020

Opportunities for Lattice QCD in quark and lepton flavor physics
journal, November 2019