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

Romero-López, Fernando; Sharpe, Stephen R.; Blanton, Tyler D.; Briceño, Raúl A.; Hansen, Maxwell T.

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.  https://doi.org/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.  https://doi.org/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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Works referenced in this record:

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Works referencing / citing this record:

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

$I = 3$ 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
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Three-body unitarity versus finite-volume $π^{+} π^{+} π^{+}$ spectrum from lattice QCD
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Mai, M.; Döring, M.; Culver, C.
Physical Review D, Vol. 101, Issue 5
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Lattice model of heavy-light three-body system
journal, February 2020

Guo, Peng; Döring, Michael
Physical Review D, Vol. 101, Issue 3
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Opportunities for lattice QCD in quark and lepton flavor physics
text, January 2019

Lehner, Christoph; Meinel, Stefan; Blum, Tom
arXiv
DOI: 10.48550/arxiv.1904.09479

Three-body unitarity versus finite-volume $π^+π^+π^+$ spectrum from lattice QCD
text, January 2019

Mai, M.; Döring, M.; Culver, C.
arXiv
DOI: 10.48550/arxiv.1909.05749

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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

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

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

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

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

Dynamically-coupled partial-waves in ρπ isospin-2 scattering from lattice QCD text, January 2018

Determination of proton-deuteron scattering lengths journal, December 1999

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

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

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

Isoscalar ππ Scattering and the σ Meson Resonance from QCD text, January 2017

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

Determination of s- and p-wave I = 1/2 Kπ scattering amplitudes in Nf = 2 + 1 lattice QCD journal, July 2018

Elastic I = 3 / 2 p -wave nucleon-pion scattering amplitude and the Δ ( 1232 ) resonance from N f = 2 + 1 lattice QCD journal, January 2018

Extraction of isoscalar π π phase shifts from lattice QCD journal, July 2018

The I = 1 pion–pion scattering amplitude and timelike pion form factor from Nf = 2 + 1 lattice QCD journal, February 2019

Resonances in Coupled π K − η K Scattering from Quantum Chromodynamics journal, October 2014

Hadron-Hadron interactions from N f = 2 + 1 + 1 lattice QCD: I = 3 / 2 π K scattering length journal, December 2018

Hadron-hadron interactions from N f = 2 + 1 + 1 lattice QCD: isospin-2 ππ scattering length journal, September 2015

Pion scattering in the isospin I = 2 channel from elongated lattices journal, August 2019

Volume dependence of the energy spectrum in massive quantum field theories: II. Scattering states journal, June 1986

Two-particle states on a torus and their relation to the scattering matrix journal, May 1991

Resonance scattering phase shifts on a non-rest-frame lattice journal, September 1995

Finite-volume effects for two-hadron states in moving frames journal, October 2005

Two particle states and the S -matrix elements in multi-channel scattering journal, July 2005

Tetraquark operators in lattice QCD and exotic flavour states in the charm sector journal, November 2017

Two- and three-body interactions in $$\varphi ^4$$ φ 4 theory from lattice simulations journal, October 2018

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

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

Three-body spectrum in a finite volume: The role of cubic symmetry journal, June 2018

Three-body unitarity in the finite volume journal, December 2017

Finite-Volume Spectrum of π + π + and π + π + π + Systems journal, February 2019

Three-body unitarity with isobars revisited journal, September 2017

Spectrum of Three-Body Bound States in a Finite Volume journal, March 2015

Volume dependence of the energy spectrum in massive quantum field theories: I. Stable particle states journal, June 1986

A framework for exploring the interactions and decays of hyperons with lattice QCD journal, January 2005

Isoscalar π π , K K ¯ , η η scattering and the σ , f 0 , f 2 mesons from QCD journal, March 2018

The three-boson system with short-range interactions journal, February 1999

Three-body scattering: Ladders and Resonances text, January 2019

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

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 journal, March 2020

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

Opportunities for lattice QCD in quark and lepton flavor physics text, January 2019

Three-body unitarity versus finite-volume $π^+π^+π^+$ spectrum from lattice QCD text, January 2019

Scalar mesons in a finite volume
journal, January 2011

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

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

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

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

Dynamically-coupled partial-waves in ρπ isospin-2 scattering from lattice QCD
text, January 2018

Determination of proton-deuteron scattering lengths
journal, December 1999

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

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

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

Isoscalar ππ Scattering and the σ Meson Resonance from QCD
text, January 2017

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

Determination of s- and p-wave I = 1/2 Kπ scattering amplitudes in Nf = 2 + 1 lattice QCD
journal, July 2018

Elastic $I = 3 / 2$ $p$ -wave nucleon-pion scattering amplitude and the $Δ (1232)$ resonance from $N_{f} = 2 + 1$ lattice QCD
journal, January 2018

Extraction of isoscalar $π π$ phase shifts from lattice QCD
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The I = 1 pion–pion scattering amplitude and timelike pion form factor from Nf = 2 + 1 lattice QCD
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journal, October 2014

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Pion scattering in the isospin $I = 2$ channel from elongated lattices
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Volume dependence of the energy spectrum in massive quantum field theories: II. Scattering states
journal, June 1986

Two-particle states on a torus and their relation to the scattering matrix
journal, May 1991

Resonance scattering phase shifts on a non-rest-frame lattice
journal, September 1995

Finite-volume effects for two-hadron states in moving frames
journal, October 2005

Two particle states and the S -matrix elements in multi-channel scattering
journal, July 2005

Tetraquark operators in lattice QCD and exotic flavour states in the charm sector
journal, November 2017

Two- and three-body interactions in $$\varphi ^4$$ φ 4 theory from lattice simulations
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journal, October 2017

Three-body spectrum in a finite volume: The role of cubic symmetry
journal, June 2018

Three-body unitarity in the finite volume
journal, December 2017

Finite-Volume Spectrum of $π^{+} π^{+}$ and $π^{+} π^{+} π^{+}$ Systems
journal, February 2019

Three-body unitarity with isobars revisited
journal, September 2017

Spectrum of Three-Body Bound States in a Finite Volume
journal, March 2015

Volume dependence of the energy spectrum in massive quantum field theories: I. Stable particle states
journal, June 1986

A framework for exploring the interactions and decays of hyperons with lattice QCD
journal, January 2005

Isoscalar $π π, K \bar{K}, η η$ scattering and the $σ, f_{0}, f_{2}$ mesons from QCD
journal, March 2018

The three-boson system with short-range interactions
journal, February 1999

Three-body scattering: Ladders and Resonances
text, January 2019

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

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

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

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

Opportunities for lattice QCD in quark and lepton flavor physics
text, January 2019

Three-body unitarity versus finite-volume $π^+π^+π^+$ spectrum from lattice QCD
text, January 2019