Extracting scattering phase shifts in higher partial waves from lattice QCD calculations

Luu, Thomas; Savage, Martin J.

doi:10.1103/PhysRevD.83.114508

Title: Extracting scattering phase shifts in higher partial waves from lattice QCD calculations

Abstract

Lüscher’s method is routinely used to determine meson-meson, meson-baryon, and baryon-baryon s-wave scattering amplitudes below inelastic thresholds from lattice QCD calculations—presently at unphysical light-quark masses. In this work we review the formalism and develop the requisite expressions to extract phase shifts describing meson-meson scattering in partial waves with angular momentum l≤6 and l=9. The implications of the underlying cubic symmetry, and strategies for extracting the phase shifts from lattice QCD calculations, are presented, along with a discussion of the signal-to-noise problem that afflicts the higher partial waves.

Authors:: Luu, Thomas; Savage, Martin J.

Publication Date:: Wed Jun 01 00:00:00 EDT 2011

Research Org.:: Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1068270

Report Number(s):: LLNL-JRNL-472171
Journal ID: ISSN 1550-7998; PRVDAQ

DOE Contract Number:: W-7405-ENG-48

Resource Type:: Journal Article

Journal Name:: Physical Review. D, Particles, Fields, Gravitation and Cosmology

Additional Journal Information:: Journal Volume: 83; Journal Issue: 11; Journal ID: ISSN 1550-7998

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Luu, Thomas, and Savage, Martin J. Extracting scattering phase shifts in higher partial waves from lattice QCD calculations.  United States: N. p., 2011. 
        Web.  doi:10.1103/PhysRevD.83.114508.

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                    Luu, Thomas, & Savage, Martin J. Extracting scattering phase shifts in higher partial waves from lattice QCD calculations.  United States.  https://doi.org/10.1103/PhysRevD.83.114508

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                    Luu, Thomas, and Savage, Martin J. 2011.  
        "Extracting scattering phase shifts in higher partial waves from lattice QCD calculations".  United States.  https://doi.org/10.1103/PhysRevD.83.114508.  https://www.osti.gov/servlets/purl/1068270.

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@article{osti_1068270,

  title        = {Extracting scattering phase shifts in higher partial waves from lattice QCD calculations},

  author       = {Luu, Thomas and Savage, Martin J.},

  abstractNote = {Lüscher’s method is routinely used to determine meson-meson, meson-baryon, and baryon-baryon s-wave scattering amplitudes below inelastic thresholds from lattice QCD calculations—presently at unphysical light-quark masses. In this work we review the formalism and develop the requisite expressions to extract phase shifts describing meson-meson scattering in partial waves with angular momentum l≤6 and l=9. The implications of the underlying cubic symmetry, and strategies for extracting the phase shifts from lattice QCD calculations, are presented, along with a discussion of the signal-to-noise problem that afflicts the higher partial waves.},

  doi          = {10.1103/PhysRevD.83.114508},

  url          = {https://www.osti.gov/biblio/1068270},
  journal      = {Physical Review. D, Particles, Fields, Gravitation and Cosmology},

  issn         = {1550-7998},

  number       = 11,

  volume       = 83,

  place        = {United States},

  year         = {Wed Jun 01 00:00:00 EDT 2011},

  month        = {Wed Jun 01 00:00:00 EDT 2011}

}

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Title: Extracting scattering phase shifts in higher partial waves from lattice QCD calculations

Abstract

Citation Formats

I = 2 pion scattering phase shift with Wilson fermions journal, January 2003

Clebsch-Gordan construction of lattice interpolated fields for excited baryons journal, October 2005

Finite volume corrections to π π scattering journal, April 2006

Lattice calculations for A = 3 , 4, 6, 12 nuclei using chiral effective field theory journal, July 2010

I = 2 pion scattering length from two-pion wave function journal, March 2004

Pion scattering on the lattice with chirally improved fermions journal, March 2005

I = 2 pion scattering length with Wilson Fermions journal, April 2000

Nucleon-Nucleon Scattering from Fully Dynamical Lattice QCD journal, July 2006

Lattice calculation of I = 2 pion scattering length journal, September 1992

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

I = 2 π π scattering phase shift with two flavors of O a improved dynamical quarks journal, October 2004

Calculating the I=2 pion scattering length using tadpole improved clover Wilson action on coarse anisotropic lattices journal, March 2002

Two Particle States in a box and the S-Matrix in Multi-Channel Scattering journal, February 2006

Lattice study of K π scattering in I = 3 / 2 and 1 / 2 channels journal, October 2009

Evidence for a Bound H Dibaryon from Lattice QCD journal, April 2011

Pion-pion scattering amplitude. III. Improving the analysis with forward dispersion relations and Roy equations journal, March 2008

Effective theory for trapped few-fermion systems journal, December 2007

I = 2 π π scattering from fully-dynamical mixed-action lattice QCD journal, March 2006

Lattice QCD calculation of full pion scattering lengths journal, October 1993

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

Exploratory Study of Nucleon-Nucleon Scattering Lengths in Lattice QCD journal, October 1994

Nucleon-nucleon scattering in a harmonic potential journal, September 2010

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

I = 2 pion scattering length and phase shift with Wilson fermions journal, March 2002

Precise determination of the I = 2 π π scattering length from mixed-action lattice QCD journal, January 2008

Meson-baryon scattering lengths from mixed-action lattice QCD journal, April 2010

Nuclear physics from lattice QCD journal, January 2011

The nuclear force from Monte Carlo simulations of lattice quantum chromodynamics journal, October 2008

More on volume dependence of spectral weight functions journal, September 2010

π K scattering in full QCD with domain-wall valence quarks journal, December 2006

Efimov physics in a finite volume journal, March 2009

Hyperon–nucleon scattering from fully-dynamical lattice QCD journal, October 2007

I = 2 pion scattering phase shift with Wilson fermions journal, May 2003

Pion Scattering Length from Two-Pion Wave Function journal, March 2005

Electroweak matrix elements in the two-nucleon sector from lattice QCD journal, October 2004

Two nucleons on a lattice journal, April 2004

The triton in a finite volume journal, January 2011

I = 2 pion scattering length from two-pion wave functions journal, May 2005

I = 2 pion scattering amplitude with Wilson fermions journal, July 1993

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

High statistics analysis using anisotropic clover lattices: III. Baryon-baryon interactions journal, March 2010

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

Representations of the rotation reflection symmetry group of the four-dimensional cubic lattice journal, November 1983

K + K + scattering length from lattice QCD journal, May 2008

Multiparticle states and the hadron spectrum on the lattice journal, September 2006

Hadron scattering lengths in lattice QCD journal, September 1995

I=2 pion scattering length with the parametrized fixed point action journal, March 2004

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

Exploring the π + -π + Interaction in Lattice QCD journal, November 2000

I = 2 pion scattering length with the Wilson fermion journal, October 2002

Theoretical Foundation of the Nuclear Force in QCD and Its Applications to Central and Tensor Forces in Quenched Lattice QCD Simulations journal, January 2010

$I = 2$ pion scattering phase shift with Wilson fermions
journal, January 2003

Clebsch-Gordan construction of lattice interpolated fields for excited baryons
journal, October 2005

Finite volume corrections to $π π$ scattering
journal, April 2006

Lattice calculations for A = 3 , 4, 6, 12 nuclei using chiral effective field theory
journal, July 2010

I = 2 pion scattering length from two-pion wave function
journal, March 2004

Pion scattering on the lattice with chirally improved fermions
journal, March 2005

I = 2 pion scattering length with Wilson Fermions
journal, April 2000

Nucleon-Nucleon Scattering from Fully Dynamical Lattice QCD
journal, July 2006

Lattice calculation of I = 2 pion scattering length
journal, September 1992

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

$I = 2 π π$ scattering phase shift with two flavors of $O (a)$ improved dynamical quarks
journal, October 2004

Calculating the I=2 pion scattering length using tadpole improved clover Wilson action on coarse anisotropic lattices
journal, March 2002

Two Particle States in a box and the S-Matrix in Multi-Channel Scattering
journal, February 2006

Lattice study of $K π$ scattering in $I = 3 / 2$ and $1 / 2$ channels
journal, October 2009

Evidence for a Bound $H$ Dibaryon from Lattice QCD
journal, April 2011

Pion-pion scattering amplitude. III. Improving the analysis with forward dispersion relations and Roy equations
journal, March 2008

Effective theory for trapped few-fermion systems
journal, December 2007

$I = 2$ $π π$ scattering from fully-dynamical mixed-action lattice QCD
journal, March 2006

Lattice QCD calculation of full pion scattering lengths
journal, October 1993

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

Exploratory Study of Nucleon-Nucleon Scattering Lengths in Lattice QCD
journal, October 1994

Nucleon-nucleon scattering in a harmonic potential
journal, September 2010

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

I = 2 pion scattering length and phase shift with Wilson fermions
journal, March 2002

Precise determination of the $I = 2$ $π π$ scattering length from mixed-action lattice QCD
journal, January 2008

Meson-baryon scattering lengths from mixed-action lattice QCD
journal, April 2010

Nuclear physics from lattice QCD
journal, January 2011

The nuclear force from Monte Carlo simulations of lattice quantum chromodynamics
journal, October 2008

More on volume dependence of spectral weight functions
journal, September 2010

$π K$ scattering in full QCD with domain-wall valence quarks
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Efimov physics in a finite volume
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Hyperon–nucleon scattering from fully-dynamical lattice QCD
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I = 2 pion scattering phase shift with Wilson fermions
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Pion Scattering Length from Two-Pion Wave Function
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Electroweak matrix elements in the two-nucleon sector from lattice QCD
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Two nucleons on a lattice
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The triton in a finite volume
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$I = 2$ pion scattering length from two-pion wave functions
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$I = 2$ pion scattering amplitude with Wilson fermions
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Two-particle states on a torus and their relation to the scattering matrix
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High statistics analysis using anisotropic clover lattices: III. Baryon-baryon interactions
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Phase shift of isospin-2 $π π$ scattering from lattice QCD
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Representations of the rotation reflection symmetry group of the four-dimensional cubic lattice
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$K^{+} K^{+}$ scattering length from lattice QCD
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Multiparticle states and the hadron spectrum on the lattice
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Hadron scattering lengths in lattice QCD
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I=2 pion scattering length with the parametrized fixed point action
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Finite-volume effects for two-hadron states in moving frames
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Exploring the π + -π + Interaction in Lattice QCD
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$I = 2$ pion scattering length with the Wilson fermion
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Theoretical Foundation of the Nuclear Force in QCD and Its Applications to Central and Tensor Forces in Quenched Lattice QCD Simulations
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