I = 3 Three-Pion Scattering Amplitude from Lattice QCD

Blanton, Tyler D.; Romero-López, Fernando; Sharpe, Stephen R.

doi:10.1103/PhysRevLett.124.032001

Title: $I = 3$ Three-Pion Scattering Amplitude from Lattice QCD

Abstract

We analyze the spectrum of two- and three-pion states of maximal isospin obtained recently for isosymmetric QCD with pion mass $M \approx 200 MeV$ in Hörz and Hanlon, [Phys. Rev. Lett. 123, 142002 (2019)]. Using the relativistic three-particle quantization condition, we find $~ 2 σ$ evidence for a nonzero value for the contact part of the $3 π^{+}$ ( $I = 3$ ) scattering amplitude. We also compare our results to leading-order chiral perturbation theory. We find good agreement at threshold and some tension in the energy dependent part of the $3 π^{+}$ scattering amplitude. We also find that the $2 π^{+}$ ( $I = 2$ ) spectrum is fit well by an $s$ -wave phase shift that incorporates the expected Adler zero.

Authors:

;

Publication Date:: Wed Jan 22 00:00:00 EST 2020

Research Org.:: Univ. of Washington, Seattle, WA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:: 1593187

Alternate Identifier(s):: OSTI ID: 1595803; OSTI ID: 1774009

Grant/Contract Number:: SC0011637

Resource Type:: Published Article

Journal Name:: Physical Review Letters

Additional Journal Information:: Journal Name: Physical Review Letters Journal Volume: 124 Journal Issue: 3; Journal ID: ISSN 0031-9007

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Blanton, Tyler D., Romero-López, Fernando, and Sharpe, Stephen R. I = 3 Three-Pion Scattering Amplitude from Lattice QCD.  United States: N. p., 2020. 
Web.  doi:10.1103/PhysRevLett.124.032001.

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                    Blanton, Tyler D., Romero-López, Fernando, & Sharpe, Stephen R. I = 3 Three-Pion Scattering Amplitude from Lattice QCD.  United States.  https://doi.org/10.1103/PhysRevLett.124.032001

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                    Blanton, Tyler D., Romero-López, Fernando, and Sharpe, Stephen R. Wed .  
"I = 3 Three-Pion Scattering Amplitude from Lattice QCD".  United States.  https://doi.org/10.1103/PhysRevLett.124.032001.

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@article{osti_1593187,

  title        = {I = 3 Three-Pion Scattering Amplitude from Lattice QCD},

  author       = {Blanton, Tyler D. and Romero-López, Fernando and Sharpe, Stephen R.},

  abstractNote = {We analyze the spectrum of two- and three-pion states of maximal isospin obtained recently for isosymmetric QCD with pion mass M≈200MeV in Hörz and Hanlon, [Phys. Rev. Lett. 123, 142002 (2019)]. Using the relativistic three-particle quantization condition, we find ~2σ evidence for a nonzero value for the contact part of the 3π+ (I=3) scattering amplitude. We also compare our results to leading-order chiral perturbation theory. We find good agreement at threshold and some tension in the energy dependent part of the 3π+ scattering amplitude. We also find that the 2π+ (I=2) spectrum is fit well by an s-wave phase shift that incorporates the expected Adler zero.},

  doi          = {10.1103/PhysRevLett.124.032001},

  journal      = {Physical Review Letters},

  number       = 3,

  volume       = 124,

  place        = {United States},

  year         = {Wed Jan 22 00:00:00 EST 2020},

  month        = {Wed Jan 22 00:00:00 EST 2020}

}

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Title: I = 3 Three-Pion Scattering Amplitude from Lattice QCD

Abstract

Citation Formats

Scalar mesons in a finite volume journal, January 2011

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

Energy shift of the three-particle system in a finite volume journal, April 2019

Erratum: Threshold expansion of the three-particle quantization condition [Phys. Rev. D 93 , 096006 (2016)] journal, August 2017

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

Multiple-channel generalization of Lellouch-Lüscher formula journal, July 2012

Relating the finite-volume spectrum and the two-and-three-particle S matrix for relativistic systems of identical scalar particles journal, April 2017

S - and D -wave phase shifts in isospin-2 π π scattering from lattice QCD journal, August 2012

Signatures of few-body resonances in finite volume journal, September 2018

n -boson energies at finite volume and three-boson interactions journal, October 2007

Extracting scattering phase shifts in higher partial waves from lattice QCD calculations journal, June 2011

A method to measure the antikaon–nucleon scattering length in lattice QCD journal, November 2009

Moving multichannel systems in a finite volume with application to proton-proton fusion journal, November 2013

Three-pion contribution to hadronic vacuum polarization journal, August 2019

Global parameterization of $$\pi \pi $$ππ scattering up to 2 $${\mathrm {\,GeV}}$$GeV journal, December 2019

Evidence for a P 11 Pion-Nucleon Resonance at 556 MeV journal, March 1964

Numerical exploration of three relativistic particles in a finite volume including two-particle resonances and bound states journal, October 2019

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

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

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

Relativistic, model-independent, three-particle quantization condition journal, December 2014

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

Three particles in a finite volume journal, May 2012

A solvable three-body model in finite volume journal, November 2017

Coupled π π , K K ¯ scattering in P -wave and the ρ resonance from lattice QCD journal, November 2015

Chiral perturbation theory to one loop journal, November 1984

b 1 resonance in coupled π ω , π ϕ scattering from lattice QCD journal, September 2019

Heavy-quark QCD exotica journal, March 2017

Two-particle multichannel systems in a finite volume with arbitrary spin journal, April 2014

Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude journal, December 2015

Isospin-0 π π s-wave scattering length from twisted mass lattice QCD journal, September 2017

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

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

Three particles in a finite volume: The breakdown of spherical symmetry journal, July 2012

Three-particle systems with resonant subprocesses in a finite volume journal, January 2019

Consistency Conditions on the Strong Interactions Implied by a Partially Conserved Axial-Vector Current journal, February 1965

Multipion states in lattice QCD and the charged-pion condensate journal, July 2008

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

Hadron-Hadron Interactions from N f = 2 + 1 + 1 lattice QCD: Isospin-1 K K scattering length journal, August 2017

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

Scattering phases for meson and baryon resonances on general moving-frame lattices journal, November 2012

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

I = 1 and I = 2 π – π scattering phase shifts from N f = 2 + 1 lattice QCD journal, September 2016

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

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

Pion Scattering Lengths journal, September 1966

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

Scalar mesons moving in a finite volume and the role of partial wave mixing journal, August 2012

Scattering processes and resonances from lattice QCD journal, April 2018

Vector particle scattering on the lattice journal, July 2018

Lattice QCD and Three-Particle Decays of Resonances journal, October 2019

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

Two- and Three-Pion Finite-Volume Spectra at Maximal Isospin from Lattice QCD journal, October 2019

Extraction of isoscalar π π phase shifts from 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

Numerical study of the relativistic three-body quantization condition in the isotropic approximation journal, July 2018

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

An a 0 resonance in strongly coupled π η , K K ¯ scattering from lattice QCD journal, May 2016

I = 2 π π S -wave scattering phase shift from lattice QCD journal, February 2012

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

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

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

Threshold expansion of the three-particle quantization condition journal, May 2016

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

Phenomenological Lagrangians journal, April 1979

Cross-channel study of pion scattering from lattice QCD journal, December 2019

Setting the scale for the CLS 2 + 1 flavor ensembles journal, April 2017

Simulation of QCD with N f = 2 + 1 flavors of non-perturbatively improved Wilson fermions journal, February 2015

Title: $I = 3$ Three-Pion Scattering Amplitude from Lattice QCD

Scalar mesons in a finite volume
journal, January 2011

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

Energy shift of the three-particle system in a finite volume
journal, April 2019

Erratum: Threshold expansion of the three-particle quantization condition [Phys. Rev. D 93 , 096006 (2016)]
journal, August 2017

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

Multiple-channel generalization of Lellouch-Lüscher formula
journal, July 2012

Relating the finite-volume spectrum and the two-and-three-particle $S$ matrix for relativistic systems of identical scalar particles
journal, April 2017

$S$ - and $D$ -wave phase shifts in isospin-2 $π π$ scattering from lattice QCD
journal, August 2012

Signatures of few-body resonances in finite volume
journal, September 2018

$n$ -boson energies at finite volume and three-boson interactions
journal, October 2007

Extracting scattering phase shifts in higher partial waves from lattice QCD calculations
journal, June 2011

A method to measure the antikaon–nucleon scattering length in lattice QCD
journal, November 2009

Moving multichannel systems in a finite volume with application to proton-proton fusion
journal, November 2013

Three-pion contribution to hadronic vacuum polarization
journal, August 2019

Global parameterization of $$\pi \pi $$ππ scattering up to 2 $${\mathrm {\,GeV}}$$GeV
journal, December 2019

Evidence for a $P_{11}$ Pion-Nucleon Resonance at 556 MeV
journal, March 1964

Numerical exploration of three relativistic particles in a finite volume including two-particle resonances and bound states
journal, October 2019

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

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

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

Relativistic, model-independent, three-particle quantization condition
journal, December 2014

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

Three particles in a finite volume
journal, May 2012

A solvable three-body model in finite volume
journal, November 2017

Coupled $π π$ , $K \bar{K}$ scattering in $P$ -wave and the $ρ$ resonance from lattice QCD
journal, November 2015

Chiral perturbation theory to one loop
journal, November 1984

$b_{1}$ resonance in coupled $π ω$ , $π ϕ$ scattering from lattice QCD
journal, September 2019

Heavy-quark QCD exotica
journal, March 2017

Two-particle multichannel systems in a finite volume with arbitrary spin
journal, April 2014

Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude
journal, December 2015

Isospin-0 $π π$ s-wave scattering length from twisted mass lattice QCD
journal, September 2017

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

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

Three particles in a finite volume: The breakdown of spherical symmetry
journal, July 2012

Three-particle systems with resonant subprocesses in a finite volume
journal, January 2019

Consistency Conditions on the Strong Interactions Implied by a Partially Conserved Axial-Vector Current
journal, February 1965

Multipion states in lattice QCD and the charged-pion condensate
journal, July 2008

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

Hadron-Hadron Interactions from N f = 2 + 1 + 1 lattice QCD: Isospin-1 K K scattering length
journal, August 2017

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

Scattering phases for meson and baryon resonances on general moving-frame lattices
journal, November 2012

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

I = 1 and I = 2 π – π scattering phase shifts from N f = 2 + 1 lattice QCD
journal, September 2016

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

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

Pion Scattering Lengths
journal, September 1966

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

Scalar mesons moving in a finite volume and the role of partial wave mixing
journal, August 2012

Scattering processes and resonances from lattice QCD
journal, April 2018

Vector particle scattering on the lattice
journal, July 2018

Lattice QCD and Three-Particle Decays of Resonances
journal, October 2019

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

Two- and Three-Pion Finite-Volume Spectra at Maximal Isospin from Lattice QCD
journal, October 2019

Extraction of isoscalar $π π$ phase shifts from 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

Numerical study of the relativistic three-body quantization condition in the isotropic approximation
journal, July 2018

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

An $a_{0}$ resonance in strongly coupled $π η$ , $K \bar{K}$ scattering from lattice QCD
journal, May 2016

$I = 2$ $π π$ $S$ -wave scattering phase shift from lattice QCD
journal, February 2012

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

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

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

Threshold expansion of the three-particle quantization condition
journal, May 2016

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

Phenomenological Lagrangians
journal, April 1979

Cross-channel study of pion scattering from lattice QCD
journal, December 2019

Setting the scale for the CLS $2 + 1$ flavor ensembles
journal, April 2017

Simulation of QCD with N f = 2 + 1 flavors of non-perturbatively improved Wilson fermions
journal, February 2015