Computing the hadronic vacuum polarization function by analytic continuation

Feng, Xu; Hashimoto, Shoji; Hotzel, Grit; Jansen, Karl; Petschlies, Marcus; Renner, Dru B.

doi:10.1103/PhysRevD.88.034505

Title: Computing the hadronic vacuum polarization function by analytic continuation

Abstract

We propose a method to compute the hadronic vacuum polarization function on the lattice at continuous values of photon momenta bridging between the spacelike and timelike regions. We provide two independent demonstrations to show that this method leads to the desired hadronic vacuum polarization function in Minkowski spacetime. We present with the example of the leading-order QCD correction to the muon anomalous magnetic moment that this approach can provide a valuable alternative method for calculations of physical quantities where the hadronic vacuum polarization function enters.

Authors:

Feng, Xu ^[1]; Hashimoto, Shoji ^[2]; Hotzel, Grit ^[3]; Jansen, Karl ^[4]; Petschlies, Marcus ^[5]; Renner, Dru B. ^[6]

High Energy Accelerator Research Organization (KEK), Tsukuba (Japan)
High Energy Accelerator Research Organization (KEK), Tsukuba (Japan); The Graduate Univ. for Advanced Studies (Sokendai), Tsukuba (Japan)
Humboldt Univ. zu Berlin, Berlin (Germany)
Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Univ. of Cyprus, Nicosia (Cyprus)
The Cyprus Institute, Nicosia (Cyprus)
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Publication Date:: Thu Aug 29 00:00:00 EDT 2013

Research Org.:: Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1091780

Report Number(s):: KEK-CP-286; DESY-13-085; JLAB-THY-13-1736; SFB/CPP-13-30; HU-EP-13/24; DOE/OR/23177-2562; arXiv:1305.5878
Journal ID: ISSN 1550-7998; PRVDAQ; TRN: US1600823

Grant/Contract Number:: AC05-06OR23177

Resource Type:: Accepted Manuscript

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

Additional Journal Information:: Journal Volume: 88; Journal Issue: 3; 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; hadronic vacuum polarization; muon g-2; lattice QCD

Citation Formats


                    Feng, Xu, Hashimoto, Shoji, Hotzel, Grit, Jansen, Karl, Petschlies, Marcus, and Renner, Dru B. Computing the hadronic vacuum polarization function by analytic continuation.  United States: N. p., 2013. 
Web.  doi:10.1103/PhysRevD.88.034505.

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                    Feng, Xu, Hashimoto, Shoji, Hotzel, Grit, Jansen, Karl, Petschlies, Marcus, & Renner, Dru B. Computing the hadronic vacuum polarization function by analytic continuation.  United States.  https://doi.org/10.1103/PhysRevD.88.034505

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                    Feng, Xu, Hashimoto, Shoji, Hotzel, Grit, Jansen, Karl, Petschlies, Marcus, and Renner, Dru B. Thu .  
"Computing the hadronic vacuum polarization function by analytic continuation".  United States.  https://doi.org/10.1103/PhysRevD.88.034505.  https://www.osti.gov/servlets/purl/1091780.

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@article{osti_1091780,

  title        = {Computing the hadronic vacuum polarization function by analytic continuation},

  author       = {Feng, Xu and Hashimoto, Shoji and Hotzel, Grit and Jansen, Karl and Petschlies, Marcus and Renner, Dru B.},

  abstractNote = {We propose a method to compute the hadronic vacuum polarization function on the lattice at continuous values of photon momenta bridging between the spacelike and timelike regions. We provide two independent demonstrations to show that this method leads to the desired hadronic vacuum polarization function in Minkowski spacetime. We present with the example of the leading-order QCD correction to the muon anomalous magnetic moment that this approach can provide a valuable alternative method for calculations of physical quantities where the hadronic vacuum polarization function enters.},

  doi          = {10.1103/PhysRevD.88.034505},

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

  number       = 3,

  volume       = 88,

  place        = {United States},

  year         = {Thu Aug 29 00:00:00 EDT 2013},

  month        = {Thu Aug 29 00:00:00 EDT 2013}

}

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Works referenced in this record:

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Electroweak effective couplings for future precision experiments
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Hoecker, Andreas
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Two-flavor QCD correction to lepton magnetic moments at leading-order in the electromagnetic coupling
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Feng, Xu; Petschlies, Marcus; Jansen, Karl
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Model-independent parametrization of the hadronic vacuum polarization and g-2 for the muon on the lattice
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Aubin, Christopher; Blum, Thomas; Golterman, Maarten
arXiv
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Two-photon decay of the neutral pion in lattice QCD
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Feng, Xu; Aoki, Sinya; Fukaya, Hidenori
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Lattice calculation of the lowest order hadronic contribution to the muon anomalous magnetic moment
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Works referencing / citing this record:

Lattice Calculations and the Muon Anomalous Magnetic Moment
journal, May 2017

Marinković, Marina Krstić
Few-Body Systems, Vol. 58, Issue 4
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Muon g – 2 theory: The hadronic part
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QCD and strongly coupled gauge theories: challenges and perspectives
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Burger, Florian; Jansen, Karl; Petschlies, Marcus
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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
Deutsches Elektronen-Synchrotron, DESY, Hamburg
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Leading-order hadronic contributions to the electron and tau anomalous magnetic moments
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Burger, Florian; Jansen, Karl; Petschlies, Marcus
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; Mohler, Daniel
Deutsches Elektronen-Synchrotron, DESY, Hamburg
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The hadronic vacuum polarization contribution to the muon g − 2 from lattice QCD
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Della Morte, Michele; Francis, Anthony; Gülpers, Vera
ETH Zurich
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Erben, Felix; Green, Jeremy R.; Mohler, Daniel
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Title: Computing the hadronic vacuum polarization function by analytic continuation

Abstract

Citation Formats

The muon g−2 journal, June 2009

The hadronic contribution to the muon anomalous magnetic moment and to the running electromagnetic fine structure constant at — overview and latest results journal, September 2011

Vector correlators in lattice QCD: Methods and applications journal, November 2011

Towards a precise lattice determination of the leading hadronic contribution to (g − 2) μ journal, March 2012

Lattice Calculation of the Lowest-Order Hadronic Contribution to the Muon Anomalous Magnetic Moment journal, July 2003

Vacuum polarization and hadronic contribution to muon g−2 from lattice QCD journal, June 2004

Calculating the hadronic vacuum polarization and leading hadronic contribution to the muon anomalous magnetic moment with improved staggered quarks journal, June 2007

Two-Flavor QCD Correction to Lepton Magnetic Moments at Leading Order in the Electromagnetic Coupling journal, August 2011

Lattice determination of the hadronic contribution to the muon g − 2 using dynamical domain wall fermions journal, April 2012

Model-independent parametrization of the hadronic vacuum polarization and g -2 for the muon on the lattice journal, September 2012

On the extraction of zero momentum form factors on the lattice journal, December 2012

Studying Hadronic Structure of the Photon in Lattice QCD journal, January 2001

High-precision charm-quark mass and QCD coupling from current-current correlators in lattice and continuum QCD journal, September 2008

Heavy quark masses from sum rules in four-loop approximation journal, August 2007

Precise charm- and bottom-quark masses: Theoretical and experimental uncertainties journal, February 2012

Two-Photon Decay of the Neutral Pion in Lattice QCD journal, November 2012

Two-Photon Decays of Charmonia from Lattice QCD journal, October 2006

Light meson physics from maximally twisted mass lattice QCD journal, August 2010

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

Lattice QCD and the Timelike Pion Form Factor journal, August 2011

Electroweak effective couplings for future precision experiments journal, October 2011

Lattice calculation of the lowest-order hadronic contribution to the muon anomalous magnetic moment journal, March 2005

Studying Hadronic Structure of the Photon in Lattice QCD text, January 2001

High-Precision Charm-Quark Mass and QCD Coupling from Current-Current Correlators in Lattice and Continuum QCD text, January 2008

Precise Charm- and Bottom-Quark Masses: Theoretical and Experimental Uncertainties text, January 2010

The Hadronic Contribution to the Muon Anomalous Magnetic Moment and to the Running Electromagnetic Fine Structure Constant at MZ - Overview and Latest Results text, January 2010

Two-flavor QCD correction to lepton magnetic moments at leading-order in the electromagnetic coupling text, January 2011

Model-independent parametrization of the hadronic vacuum polarization and g-2 for the muon on the lattice text, January 2012

Two-photon decay of the neutral pion in lattice QCD text, January 2012

Weak transition matrix elements from finite-volume correlation functions text, January 2000

Lattice calculation of the lowest order hadronic contribution to the muon anomalous magnetic moment text, January 2002

Calculating the hadronic vacuum polarization and leading hadronic contribution to the muon anomalous magnetic moment with improved staggered quarks text, January 2006

Lattice Calculations and the Muon Anomalous Magnetic Moment journal, May 2017

Leading-order hadronic contribution to the electron and muon g − 2 journal, January 2016

Muon g – 2 theory: The hadronic part journal, January 2018

QCD and strongly coupled gauge theories: challenges and perspectives journal, October 2014

Muon $$g-2$$ g - 2 estimates: can one trust effective Lagrangians and global fits? journal, December 2015

Leading-order hadronic contributions to the electron and tau anomalous magnetic moments journal, August 2016

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

Leading-order hadronic contributions to the electron and tau anomalous magnetic moments text, January 2016

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

The hadronic vacuum polarization contribution to the muon g − 2 from lattice QCD text, January 2017

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

QCD and Strongly Coupled Gauge Theories: Challenges and Perspectives text, January 2014

Leading-order hadronic contribution to the electron and muon $g − 2$ text, January 2016

Strange and charm quark contributions to the anomalous magnetic moment of the muon text, January 2014

Calculation of the hadronic vacuum polarization disconnected contribution to the muon anomalous magnetic moment text, January 2015

Connected and leading disconnected hadronic light-by-light contribution to the muon anomalous magnetic moment with physical pion mass text, January 2016

Lattice calculations and the muon anomalous magnetic moment preprint, January 2017

Calculation of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment text, January 2018

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

The muon g−2
journal, June 2009

The hadronic contribution to the muon anomalous magnetic moment and to the running electromagnetic fine structure constant at — overview and latest results
journal, September 2011

Vector correlators in lattice QCD: Methods and applications
journal, November 2011

Towards a precise lattice determination of the leading hadronic contribution to (g − 2) μ
journal, March 2012

Lattice Calculation of the Lowest-Order Hadronic Contribution to the Muon Anomalous Magnetic Moment
journal, July 2003

Vacuum polarization and hadronic contribution to muon g−2 from lattice QCD
journal, June 2004

Calculating the hadronic vacuum polarization and leading hadronic contribution to the muon anomalous magnetic moment with improved staggered quarks
journal, June 2007

Two-Flavor QCD Correction to Lepton Magnetic Moments at Leading Order in the Electromagnetic Coupling
journal, August 2011

Lattice determination of the hadronic contribution to the muon $g - 2$ using dynamical domain wall fermions
journal, April 2012

Model-independent parametrization of the hadronic vacuum polarization and $g$ -2 for the muon on the lattice
journal, September 2012

On the extraction of zero momentum form factors on the lattice
journal, December 2012

Studying Hadronic Structure of the Photon in Lattice QCD
journal, January 2001

High-precision charm-quark mass and QCD coupling from current-current correlators in lattice and continuum QCD
journal, September 2008

Heavy quark masses from sum rules in four-loop approximation
journal, August 2007

Precise charm- and bottom-quark masses: Theoretical and experimental uncertainties
journal, February 2012

Two-Photon Decay of the Neutral Pion in Lattice QCD
journal, November 2012

Two-Photon Decays of Charmonia from Lattice QCD
journal, October 2006

Light meson physics from maximally twisted mass lattice QCD
journal, August 2010

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

Lattice QCD and the Timelike Pion Form Factor
journal, August 2011

Electroweak effective couplings for future precision experiments
journal, October 2011

Lattice calculation of the lowest-order hadronic contribution to the muon anomalous magnetic moment
journal, March 2005

Studying Hadronic Structure of the Photon in Lattice QCD
text, January 2001

High-Precision Charm-Quark Mass and QCD Coupling from Current-Current Correlators in Lattice and Continuum QCD
text, January 2008

Precise Charm- and Bottom-Quark Masses: Theoretical and Experimental Uncertainties
text, January 2010

The Hadronic Contribution to the Muon Anomalous Magnetic Moment and to the Running Electromagnetic Fine Structure Constant at MZ - Overview and Latest Results
text, January 2010

Two-flavor QCD correction to lepton magnetic moments at leading-order in the electromagnetic coupling
text, January 2011

Model-independent parametrization of the hadronic vacuum polarization and g-2 for the muon on the lattice
text, January 2012

Two-photon decay of the neutral pion in lattice QCD
text, January 2012

Weak transition matrix elements from finite-volume correlation functions
text, January 2000

Lattice calculation of the lowest order hadronic contribution to the muon anomalous magnetic moment
text, January 2002

Calculating the hadronic vacuum polarization and leading hadronic contribution to the muon anomalous magnetic moment with improved staggered quarks
text, January 2006

Lattice Calculations and the Muon Anomalous Magnetic Moment
journal, May 2017

Leading-order hadronic contribution to the electron and muon g − 2
journal, January 2016

Muon g – 2 theory: The hadronic part
journal, January 2018

QCD and strongly coupled gauge theories: challenges and perspectives
journal, October 2014

Muon $$g-2$$ g - 2 estimates: can one trust effective Lagrangians and global fits?
journal, December 2015

Leading-order hadronic contributions to the electron and tau anomalous magnetic moments
journal, August 2016

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

Leading-order hadronic contributions to the electron and tau anomalous magnetic moments
text, January 2016

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

The hadronic vacuum polarization contribution to the muon g − 2 from lattice QCD
text, January 2017

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

QCD and Strongly Coupled Gauge Theories: Challenges and Perspectives
text, January 2014

Leading-order hadronic contribution to the electron and muon $g − 2$
text, January 2016

Strange and charm quark contributions to the anomalous magnetic moment of the muon
text, January 2014

Calculation of the hadronic vacuum polarization disconnected contribution to the muon anomalous magnetic moment
text, January 2015

Connected and leading disconnected hadronic light-by-light contribution to the muon anomalous magnetic moment with physical pion mass
text, January 2016

Lattice calculations and the muon anomalous magnetic moment
preprint, January 2017

Calculation of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment
text, January 2018

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