Isoscalar ππ Scattering and the σ Meson Resonance from QCD

Briceño, Raul A.; Dudek, Jozef J.; Edwards, Robert G.; Wilson, David J.

doi:10.1103/PhysRevLett.118.022002

Title: Isoscalar $π π$ Scattering and the $σ$ Meson Resonance from QCD

Abstract

Here, we present for the first time a determination of the energy dependence of the isoscalar ππ elastic scattering phase-shift within a first-principles numerical lattice approach to QCD. We also compute the hadronic correlation functions including all required quark propagation diagrams. From these the discrete spectrum of states in the finite volume defined by the lattice boundary is extracted. From the volume dependence of the spectrum we obtain the S-wave phase-shift up to the K$$\bar{K}$$ threshold. Calculations are performed at two values of the u, d quark mass corresponding to m_π = 236, 391 MeV and the resulting amplitudes are described in terms of a σ meson which evolves from a bound-state below ππ threshold at the heavier quark mass, to a broad resonance at the lighter quark mass.

Authors:

Briceño, Raul A. ^[1]; Dudek, Jozef J. ^[2]; Edwards, Robert G. ^[1]; Wilson, David J. ^[3]

Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); College of William and Mary, Williamsburg, VA (United States). Dept. of Physics
Univ. of Cambridge (United Kingdom). Dept. of Applied Mathematics and Theoretical Physics

Publication Date:: Mon Jan 09 00:00:00 EST 2017

Research Org.:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP)

Contributing Org.:: for the Hadron Spectrum Collaboration

OSTI Identifier:: 1340904

Alternate Identifier(s):: OSTI ID: 1338659

Report Number(s):: JLAB-THY-16-2287; DOE/OR/23177-3844; arXiv:1607.05900
Journal ID: ISSN 0031-9007; PRLTAO; TRN: US1701023

Grant/Contract Number:: AC05-00OR22725; AC02-05CH11231; AC05-06OR23177; SC0006765; OCI-0725070; ACI-1238993; RG74916

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review Letters

Additional Journal Information:: Journal Volume: 118; Journal Issue: 2; 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


                    Briceño, Raul A., Dudek, Jozef J., Edwards, Robert G., and Wilson, David J. Isoscalar ππ Scattering and the σ Meson Resonance from QCD.  United States: N. p., 2017. 
Web.  doi:10.1103/PhysRevLett.118.022002.

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                    Briceño, Raul A., Dudek, Jozef J., Edwards, Robert G., & Wilson, David J. Isoscalar ππ Scattering and the σ Meson Resonance from QCD.  United States.  https://doi.org/10.1103/PhysRevLett.118.022002

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                    Briceño, Raul A., Dudek, Jozef J., Edwards, Robert G., and Wilson, David J. Mon .  
"Isoscalar ππ Scattering and the σ Meson Resonance from QCD".  United States.  https://doi.org/10.1103/PhysRevLett.118.022002.  https://www.osti.gov/servlets/purl/1340904.

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@article{osti_1340904,

  title        = {Isoscalar ππ Scattering and the σ Meson Resonance from QCD},

  author       = {Briceño, Raul A. and Dudek, Jozef J. and Edwards, Robert G. and Wilson, David J.},

  abstractNote = {Here, we present for the first time a determination of the energy dependence of the isoscalar ππ elastic scattering phase-shift within a first-principles numerical lattice approach to QCD. We also compute the hadronic correlation functions including all required quark propagation diagrams. From these the discrete spectrum of states in the finite volume defined by the lattice boundary is extracted. From the volume dependence of the spectrum we obtain the S-wave phase-shift up to the K$\bar{K}$ threshold. Calculations are performed at two values of the u, d quark mass corresponding to mπ = 236, 391 MeV and the resulting amplitudes are described in terms of a σ meson which evolves from a bound-state below ππ threshold at the heavier quark mass, to a broad resonance at the lighter quark mass.},

  doi          = {10.1103/PhysRevLett.118.022002},

  journal      = {Physical Review Letters},

  number       = 2,

  volume       = 118,

  place        = {United States},

  year         = {Mon Jan 09 00:00:00 EST 2017},

  month        = {Mon Jan 09 00:00:00 EST 2017}

}

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Title: Isoscalar ππ Scattering and the σ Meson Resonance from QCD

Abstract

Citation Formats

Helicity operators for mesons in flight on the lattice journal, January 2012

Rummukainen-Gottlieb formula on a two-particle system with different masses journal, January 2012

Coupled-channel scattering on a torus journal, July 2013

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

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

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Review of Particle Physics journal, August 2014

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

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Strange and nonstrange quark mass dependence of elastic light resonances from SU(3) unitarized chiral perturbation theory to one loop journal, March 2010

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

Adaptive Multigrid Algorithm for the Lattice Wilson-Dirac Operator journal, November 2010

Weak Transition Matrix Elements¶from Finite-Volume Correlation Functions journal, May 2001

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ρ and K * resonances on the lattice at nearly physical quark masses and N f = 2 journal, March 2016

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

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

High statistics study of the reaction π−p→π−π+n: Apparatus, method of analysis, and general features of results at 17 GeV/c journal, June 1974

Charmonium excited state spectrum in lattice QCD journal, February 2008

Resonance parameters of the ρ meson from lattice QCD journal, May 2011

Lattice QCD calculation of the ρ meson decay width journal, November 2007

Scattering phase shifts for two particles of different mass and nonzero total momentum in lattice QCD journal, June 2012

Lattice QCD study of the s -wave π π scattering lengths in the I = 0 and 2 channels journal, April 2013

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Precise Determination of the f 0 ( 600 ) and f 0 ( 980 ) Pole Parameters from a Dispersive Data Analysis journal, August 2011

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Multichannel 0 → 2 and 1 → 2 transition amplitudes for arbitrary spin particles in a finite volume journal, October 2015

π π Partial-Wave Analysis from Reactions π + p → π + π − Δ + + and π + p → K + K − Δ + + at 7.1 GeV/ c journal, March 1973

Standard Model Prediction for Direct C P Violation in K → π π Decay journal, November 2015

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

Nonperturbative Approach to Effective Chiral Lagrangians and Meson Interactions journal, April 1998

Aharonov–Bohm effect and nucleon–nucleon phase shifts on the lattice journal, July 2004

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

Quark-Mass Dependence of the ρ and σ Mesons from Dispersion Relations and Chiral Perturbation Theory journal, April 2008

Matrix elements of unstable states journal, September 2012

Erratum: Energy dependence of the ρ resonance in π π elastic scattering from lattice QCD [Phys. Rev. D 87 , 034505 (2013)] journal, November 2014

Erratum: Meson-meson interactions in a nonperturbative chiral approach [Phys. Rev. D 59 , 074001 (1999)] journal, May 2007

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

Mass and Width of the Lowest Resonance in QCD journal, April 2006

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

Meson-meson interactions in a nonperturbative chiral approach journal, February 1999

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

Resonances in coupled π K , η K scattering from lattice QCD journal, March 2015

ππ Phase-shift analysis from 600 to 1900 MeV journal, November 1973

On the generalized eigenvalue method for energies and matrix elements in lattice field theory journal, April 2009

Lattice QCD study of four-quark components of the isosinglet scalar mesons: Significance of disconnected diagrams journal, May 2015

Lattice study of light scalar tetraquarks with I = 0 , 2 , 1 / 2 , 3 / 2 : Are σ and κ tetraquarks? journal, November 2010

Energy dependence of the ρ resonance in π π elastic scattering from lattice QCD journal, February 2013

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

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Phase shift of isospin-2 π π scattering from lattice QCD journal, April 2011

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ππ phase-shift analysis below the threshold journal, September 1974

The Chroma Software System for Lattice QCD journal, March 2005

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Scattering phases for meson and baryon resonances on general moving-frame lattices text, January 2012

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

Novel quark-field creation operator construction for hadronic physics in lattice QCD text, January 2009

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Title: Isoscalar $π π$ Scattering and the $σ$ Meson Resonance from QCD

Helicity operators for mesons in flight on the lattice
journal, January 2012

Rummukainen-Gottlieb formula on a two-particle system with different masses
journal, January 2012

Coupled-channel scattering on a torus
journal, July 2013

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

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

Partial twisting for scalar mesons
journal, January 2014

Solving lattice QCD systems of equations using mixed precision solvers on GPUs
journal, September 2010

Review of Particle Physics
journal, August 2014

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

Toward the excited isoscalar meson spectrum from lattice QCD
journal, November 2013

Strange and nonstrange quark mass dependence of elastic light resonances from SU(3) unitarized chiral perturbation theory to one loop
journal, March 2010

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

Adaptive Multigrid Algorithm for the Lattice Wilson-Dirac Operator
journal, November 2010

Weak Transition Matrix Elements¶from Finite-Volume Correlation Functions
journal, May 2001

Insight into the scalar mesons from a lattice calculation
journal, July 2000

$ρ$ and $K^{*}$ resonances on the lattice at nearly physical quark masses and $N_{f} = 2$
journal, March 2016

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

Relativistic, model-independent, multichannel $2 \to 2$ transition amplitudes in a finite volume
journal, July 2016

Highly Excited and Exotic Meson Spectrum from Dynamical Lattice QCD
journal, December 2009

Novel quark-field creation operator construction for hadronic physics in lattice QCD
journal, September 2009

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

High statistics study of the reaction π−p→π−π+n: Apparatus, method of analysis, and general features of results at 17 GeV/c
journal, June 1974

Charmonium excited state spectrum in lattice QCD
journal, February 2008

Resonance parameters of the $ρ$ meson from lattice QCD
journal, May 2011

Lattice QCD calculation of the $ρ$ meson decay width
journal, November 2007

Scattering phase shifts for two particles of different mass and nonzero total momentum in lattice QCD
journal, June 2012

Lattice QCD study of the $s$ -wave $π π$ scattering lengths in the $I = 0$ and 2 channels
journal, April 2013

First results from $2 + 1$ dynamical quark flavors on an anisotropic lattice: Light-hadron spectroscopy and setting the strange-quark mass
journal, February 2009

Precise Determination of the $f_{0} (600)$ and $f_{0} (980)$ Pole Parameters from a Dispersive Data Analysis
journal, August 2011

Toward the excited meson spectrum of dynamical QCD
journal, August 2010

Multichannel $1 \to 2$ transition amplitudes in a finite volume
journal, February 2015

Multichannel $0 \to 2$ and $1 \to 2$ transition amplitudes for arbitrary spin particles in a finite volume
journal, October 2015

$π π$ Partial-Wave Analysis from Reactions $π^{+} p \to π^{+} π^{-} Δ^{+ +}$ and $π^{+} p \to K^{+} K^{-} Δ^{+ +}$ at 7.1 GeV/ c
journal, March 1973

Standard Model Prediction for Direct $C P$ Violation in $K \to π π$ Decay
journal, November 2015

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

Nonperturbative Approach to Effective Chiral Lagrangians and Meson Interactions
journal, April 1998

Aharonov–Bohm effect and nucleon–nucleon phase shifts on the lattice
journal, July 2004

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

Quark-Mass Dependence of the $ρ$ and $σ$ Mesons from Dispersion Relations and Chiral Perturbation Theory
journal, April 2008

Matrix elements of unstable states
journal, September 2012

Erratum: Energy dependence of the $ρ$ resonance in $π π$ elastic scattering from lattice QCD [Phys. Rev. D 87 , 034505 (2013)]
journal, November 2014

Erratum: Meson-meson interactions in a nonperturbative chiral approach [Phys. Rev. D 59 , 074001 (1999)]
journal, May 2007

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

Mass and Width of the Lowest Resonance in QCD
journal, April 2006

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

Meson-meson interactions in a nonperturbative chiral approach
journal, February 1999

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

Resonances in coupled $π K, η K$ scattering from lattice QCD
journal, March 2015

ππ Phase-shift analysis from 600 to 1900 MeV
journal, November 1973

On the generalized eigenvalue method for energies and matrix elements in lattice field theory
journal, April 2009

Lattice QCD study of four-quark components of the isosinglet scalar mesons: Significance of disconnected diagrams
journal, May 2015

Lattice study of light scalar tetraquarks with $I = 0, 2, 1 / 2, 3 / 2$ : Are $σ$ and $κ$ tetraquarks?
journal, November 2010

Energy dependence of the $ρ$ resonance in $π π$ elastic scattering from lattice QCD
journal, February 2013

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

Inverse amplitude method in chiral perturbation theory
journal, September 1997

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

Phase shift of isospin-2 $π π$ scattering from lattice QCD
journal, April 2011

Adjoint sources in lattice gauge theory
journal, September 1985

$ρ$ meson decay in $2 + 1$ flavor lattice QCD
journal, November 2011

Resonant $π^{+} γ \to π^{+} π^{0}$ Amplitude from Quantum Chromodynamics
journal, December 2015

$π π \to π γ^{}$ amplitude and the resonant $ρ \to π γ^{}$ transition from lattice QCD
journal, June 2016

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

Isoscalar meson spectroscopy from lattice QCD
journal, June 2011

Exact integral equation for pion-pion scattering involving only physical region partial waves
journal, September 1971

Unitarized Chiral Perturbation Theory in a finite volume: Scalar meson sector
journal, November 2011

ππ phase-shift analysis below the threshold
journal, September 1974

The Chroma Software System for Lattice QCD
journal, March 2005

Chiral symmetry amplitudes in the S-wave isoscalar and isovector channels and the σ, f0(980), a0(980) scalar mesons
journal, July 1997

Scattering phases for meson and baryon resonances on general moving-frame lattices
text, January 2012

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

Novel quark-field creation operator construction for hadronic physics in lattice QCD
text, January 2009

Review of Particle Physics
text, January 2008

Multiple-channel generalization of Lellouch-Lüscher formula
conference, December 2012

Review of Particle Physics
text, January 2018

Novel quark-field creation operator construction for hadronic physics in lattice QCD
text, January 2009

Review of Particle Physics
text, January 2012

On the generalized eigenvalue method for energies and matrix elements in lattice field theory
text, January 2009

Solving Lattice QCD systems of equations using mixed precision solvers on GPUs
text, January 2009