Helicity operators for mesons in flight on the lattice

Edwards, Robert G.; Dudek, Jozef J.

doi:10.1103/PhysRevD.85.014507

Title: Helicity operators for mesons in flight on the lattice

Abstract

Motivated by the desire to construct meson-meson operators of definite relative momentum in order to study resonances in lattice QCD, we present a set of single-meson interpolating fields at non-zero momentum that respect the reduced symmetry of a cubic lattice in a finite cubic volume. These operators follow from the subduction of operators of definite helicity into irreducible representations of the appropriate little groups. We show their effectiveness in explicit computations where we find that the spectrum of states interpolated by these operators is close to diagonal in helicity, admitting a description in terms of single-meson states of identified J^PC. Lastly, the variationally determined optimal superpositions of the operators for each state give rapid relaxation in Euclidean time to that state, ideal for the construction of meson-meson operators and for the evaluation of matrix elements at finite momentum.

Authors:

Christopher E. Thomas; Edwards, Robert G. ^[1]; Dudek, Jozef J. ^[2]

Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Old Dominion Univ., Norfolk, VA (United States)

Publication Date:: Fri Jan 20 00:00:00 EST 2012

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)

OSTI Identifier:: 1033505

Alternate Identifier(s):: OSTI ID: 1099006

Report Number(s):: JLAB-THY-11-1368; DOE/OR/23177-1619; arXiv:1107.1930
Journal ID: ISSN 1550-7998; TRN: US1200337

Grant/Contract Number:: AC05-06OR23177

Resource Type:: Accepted Manuscript

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

Additional Journal Information:: Journal Volume: 85; 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; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CONSTRUCTION; CUBIC LATTICES; EVALUATION; HELICITY; IRREDUCIBLE REPRESENTATIONS; MATRIX ELEMENTS; MESONS; QUANTUM CHROMODYNAMICS; RELAXATION; SYMMETRY

Citation Formats


                    Christopher E. Thomas, Edwards, Robert G., and Dudek, Jozef J. Helicity operators for mesons in flight on the lattice.  United States: N. p., 2012. 
Web.  doi:10.1103/PhysRevD.85.014507.

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                    Christopher E. Thomas, Edwards, Robert G., & Dudek, Jozef J. Helicity operators for mesons in flight on the lattice.  United States.  https://doi.org/10.1103/PhysRevD.85.014507

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                    Christopher E. Thomas, Edwards, Robert G., and Dudek, Jozef J. Fri .  
"Helicity operators for mesons in flight on the lattice".  United States.  https://doi.org/10.1103/PhysRevD.85.014507.  https://www.osti.gov/servlets/purl/1033505.

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@article{osti_1033505,

  title        = {Helicity operators for mesons in flight on the lattice},

  author       = {Christopher E. Thomas and Edwards, Robert G. and Dudek, Jozef J.},

  abstractNote = {Motivated by the desire to construct meson-meson operators of definite relative momentum in order to study resonances in lattice QCD, we present a set of single-meson interpolating fields at non-zero momentum that respect the reduced symmetry of a cubic lattice in a finite cubic volume. These operators follow from the subduction of operators of definite helicity into irreducible representations of the appropriate little groups. We show their effectiveness in explicit computations where we find that the spectrum of states interpolated by these operators is close to diagonal in helicity, admitting a description in terms of single-meson states of identified JPC. Lastly, the variationally determined optimal superpositions of the operators for each state give rapid relaxation in Euclidean time to that state, ideal for the construction of meson-meson operators and for the evaluation of matrix elements at finite momentum.},

  doi          = {10.1103/PhysRevD.85.014507},

  journal      = {Physical Review. D, Particles, Fields, Gravitation and Cosmology},

  number       = ,

  volume       = 85,

  place        = {United States},

  year         = {Fri Jan 20 00:00:00 EST 2012},

  month        = {Fri Jan 20 00:00:00 EST 2012}

}

Copy to clipboard

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Nucleon, $Δ$ , and $Ω$ excited state spectra in $N_{f} = 2 + 1$ lattice QCD
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Phase shift of isospin-2 $π π$ scattering from lattice QCD
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Dudek, Jozef J.; Edwards, Robert G.; Peardon, Michael J.
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Isoscalar meson spectroscopy from lattice QCD
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Novel quark-field creation operator construction for hadronic physics in lattice QCD
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Peardon, Michael; Bulava, John; Foley, Justin
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Tuning for Three-flavors of Anisotropic Clover Fermions with Stout-link Smearing
text, January 2008

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Exotic and excited-state radiative transitions in charmonium from lattice QCD
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Solving Lattice QCD systems of equations using mixed precision solvers on GPUs
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Works referencing / citing this record:

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

Gockeler, M.; Horsley, R.; Lage, M.
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/phppubdb-23062

Rho Resonance, Timelike Pion Form Factor, and Implications for Lattice Studies of the Hadronic Vacuum Polarisation
text, January 2019

Erben, Felix; Green, Jeremy R.; Mohler, Daniel
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2020-00201

Extended hadron and two-hadron operators of definite momentum for spectrum calculations in lattice QCD
text, January 2013

Morningstar, Colin; Bulava, John; Fahy, Brendan
Carnegie Mellon University
DOI: 10.1184/r1/6506780.v1

Rho resonance, timelike pion form factor, and implications for lattice studies of the hadronic vacuum polarization
text, January 2020

Erben, Felix; Green, Jeremy; Mohler, Daniel
Deutsches Elektronen-Synchrotron, DESY, Hamburg
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Rho resonance, timelike pion form factor, and implications for lattice studies of the hadronic vacuum polarization
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Erben, Felix; Green, Jeremy R.; Mohler, Daniel
Physical Review D, Vol. 101, Issue 5
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Extended hadron and two-hadron operators of definite momentum for spectrum calculations in lattice QCD
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Morningstar, Colin; Bulava, John; Fahy, Brendan
Carnegie Mellon University
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Isoscalar ππ Scattering and the σ Meson Resonance from QCD
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Briceño, Ra; Dudek, Jj; Edwards, Rg
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Toward the excited isoscalar meson spectrum from lattice QCD
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Dudek, Jozef J.; Edwards, Robert G.; Guo, Peng
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The Search for Beauty-fully Bound Tetraquarks Using Lattice Non-Relativistic QCD
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Hughes, Ciaran; Eichten, Estia; Davies, Christine T. H.
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Rho resonance, timelike pion form factor, and implications for lattice studies of the hadronic vacuum polarisation
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Erben, Felix; Green, Jeremy R.; Mohler, Daniel
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Title: Helicity operators for mesons in flight on the lattice

Abstract

Citation Formats

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

Exotic and excited-state radiative transitions in charmonium from lattice QCD journal, May 2009

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

Tuning for three flavors of anisotropic clover fermions with stout-link smearing journal, September 2008

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

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

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

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Angular momentum on the lattice: The case of nonzero linear momentum journal, January 2006

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

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

Nucleon, Δ , and Ω excited state spectra in N f = 2 + 1 lattice QCD journal, July 2010

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

Isoscalar meson spectroscopy from lattice QCD journal, June 2011

Adjoint sources in lattice gauge theory journal, September 1985

How to calculate the elastic scattering matrix in two-dimensional quantum field theories by numerical simulation journal, July 1990

Elementary Particle Theory journal, August 1972

The Chroma Software System for Lattice QCD journal, March 2005

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

On the General Theory of Collisions for Particles with Spin journal, April 2000

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

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Tuning for Three-flavors of Anisotropic Clover Fermions with Stout-link Smearing text, January 2008

Exotic and excited-state radiative transitions in charmonium from lattice QCD text, January 2009

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

The Chroma Software System for Lattice QCD text, January 2004

Resonance Scattering Phase Shifts on a Non-Rest Frame Lattice text, January 1995

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

Rho Resonance, Timelike Pion Form Factor, and Implications for Lattice Studies of the Hadronic Vacuum Polarisation text, January 2019

Extended hadron and two-hadron operators of definite momentum for spectrum calculations in lattice QCD text, January 2013

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

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

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Rho resonance, timelike pion form factor, and implications for lattice studies of the hadronic vacuum polarisation text, January 2019

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

Exotic and excited-state radiative transitions in charmonium from lattice QCD
journal, May 2009

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

Tuning for three flavors of anisotropic clover fermions with stout-link smearing
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First results from $2 + 1$ dynamical quark flavors on an anisotropic lattice: Light-hadron spectroscopy and setting the strange-quark mass
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Resonance scattering phase shifts on a non-rest-frame lattice
journal, September 1995

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

On the general theory of collisions for particles with spin
journal, August 1959

Charmonium excited state spectrum in lattice QCD
journal, February 2008

Angular momentum on the lattice: The case of nonzero linear momentum
journal, January 2006

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

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

Nucleon, $Δ$ , and $Ω$ excited state spectra in $N_{f} = 2 + 1$ lattice QCD
journal, July 2010

Phase shift of isospin-2 $π π$ scattering from lattice QCD
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Adjoint sources in lattice gauge theory
journal, September 1985

How to calculate the elastic scattering matrix in two-dimensional quantum field theories by numerical simulation
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Elementary Particle Theory
journal, August 1972

The Chroma Software System for Lattice QCD
journal, March 2005

Solving lattice QCD systems of equations using mixed precision solvers on GPUs
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On the General Theory of Collisions for Particles with Spin
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Novel quark-field creation operator construction for hadronic physics in lattice QCD
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Tuning for Three-flavors of Anisotropic Clover Fermions with Stout-link Smearing
text, January 2008

Exotic and excited-state radiative transitions in charmonium from lattice QCD
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Resonance Scattering Phase Shifts on a Non-Rest Frame Lattice
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Rho Resonance, Timelike Pion Form Factor, and Implications for Lattice Studies of the Hadronic Vacuum Polarisation
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