Pion-Pole Contribution to Hadronic Light-By-Light Scattering in the Anomalous Magnetic Moment of the Muon

Hoferichter, Martin; Hoid, Bai-Long; Kubis, Bastian; Leupold, Stefan; Schneider, Sebastian P.

doi:10.1103/PhysRevLett.121.112002

Title: Pion-Pole Contribution to Hadronic Light-By-Light Scattering in the Anomalous Magnetic Moment of the Muon

Abstract

Here, the π⁰ pole constitutes the lowest-lying singularity of the hadronic light-by-light (HLBL) tensor, and thus, it provides the leading contribution in a dispersive approach to HLBL scattering in the anomalous magnetic moment of the muon (g–2)_μ. It is unambiguously defined in terms of the doubly virtual pion transition form factor, which in principle, can be accessed in its entirety by experiment. We demonstrate that, in the absence of a direct measurement, the full spacelike doubly virtual form factor can be reconstructed very accurately based on existing data for e⁺e^– → 3π, e⁺e^– → e⁺e^–π⁰, and the π⁰ → γγ decay width. We derive a representation that incorporates all the low-lying singularities of the form factor, matches correctly onto the asymptotic behavior expected from perturbative QCD, and is suitable for the evaluation of the (g–2)_μ loop integral. The resulting value, a^π⁰-poleμ = 62.6^+3.0–_2.5 × 10^–11, for the first time, represents a complete data-driven determination of the pion-pole contribution with fully controlled uncertainty estimates. In particular, we show that already improved singly virtual measurements alone would allow one to further reduce the uncertainty in a^π⁰-pole_μ.

Authors:: Hoferichter, Martin; Hoid, Bai-Long; Kubis, Bastian; Leupold, Stefan; Schneider, Sebastian P.

Publication Date:: Wed Sep 12 00:00:00 EDT 2018

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

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

OSTI Identifier:: 1469750

Alternate Identifier(s):: OSTI ID: 1502087

Grant/Contract Number:: FG02-00ER41132

Resource Type:: Published Article

Journal Name:: Physical Review Letters

Additional Journal Information:: Journal Name: Physical Review Letters Journal Volume: 121 Journal Issue: 11; Journal ID: ISSN 0031-9007

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Hoferichter, Martin, Hoid, Bai-Long, Kubis, Bastian, Leupold, Stefan, and Schneider, Sebastian P. Pion-Pole Contribution to Hadronic Light-By-Light Scattering in the Anomalous Magnetic Moment of the Muon.  United States: N. p., 2018. 
Web.  doi:10.1103/PhysRevLett.121.112002.

Copy to clipboard


                    Hoferichter, Martin, Hoid, Bai-Long, Kubis, Bastian, Leupold, Stefan, & Schneider, Sebastian P. Pion-Pole Contribution to Hadronic Light-By-Light Scattering in the Anomalous Magnetic Moment of the Muon.  United States.  https://doi.org/10.1103/PhysRevLett.121.112002

Copy to clipboard


                    Hoferichter, Martin, Hoid, Bai-Long, Kubis, Bastian, Leupold, Stefan, and Schneider, Sebastian P. Wed .  
"Pion-Pole Contribution to Hadronic Light-By-Light Scattering in the Anomalous Magnetic Moment of the Muon".  United States.  https://doi.org/10.1103/PhysRevLett.121.112002.

Copy to clipboard


                    
@article{osti_1469750,

  title        = {Pion-Pole Contribution to Hadronic Light-By-Light Scattering in the Anomalous Magnetic Moment of the Muon},

  author       = {Hoferichter, Martin and Hoid, Bai-Long and Kubis, Bastian and Leupold, Stefan and Schneider, Sebastian P.},

  abstractNote = {Here, the π0 pole constitutes the lowest-lying singularity of the hadronic light-by-light (HLBL) tensor, and thus, it provides the leading contribution in a dispersive approach to HLBL scattering in the anomalous magnetic moment of the muon (g–2)μ. It is unambiguously defined in terms of the doubly virtual pion transition form factor, which in principle, can be accessed in its entirety by experiment. We demonstrate that, in the absence of a direct measurement, the full spacelike doubly virtual form factor can be reconstructed very accurately based on existing data for e+e– → 3π, e+e– → e+e–π0, and the π0 → γγ decay width. We derive a representation that incorporates all the low-lying singularities of the form factor, matches correctly onto the asymptotic behavior expected from perturbative QCD, and is suitable for the evaluation of the (g–2)μ loop integral. The resulting value, aπ0-poleμ = 62.6+3.0–2.5 × 10–11, for the first time, represents a complete data-driven determination of the pion-pole contribution with fully controlled uncertainty estimates. In particular, we show that already improved singly virtual measurements alone would allow one to further reduce the uncertainty in aπ0-poleμ.},

  doi          = {10.1103/PhysRevLett.121.112002},

  journal      = {Physical Review Letters},

  number       = 11,

  volume       = 121,

  place        = {United States},

  year         = {Wed Sep 12 00:00:00 EDT 2018},

  month        = {Wed Sep 12 00:00:00 EDT 2018}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Publisher's Version of Record
https://doi.org/10.1103/PhysRevLett.121.112002

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 72 works

Citation information provided by
Web of Science

Figures / Tables:

FIG. 1. : Diagrammatic representation of (a) HVP, (b) HLBL, and (c) the $π$⁰ pole in HLBL. Solid, dashed, and wiggly lines denote muons, pions, and photons, respectively, and the shortdashed line indicates that the pion is to be taken on shell.

All figures and tables (4 total)

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

High-precision calculation of the 4-loop contribution to the electron g -2 in QED
journal, September 2017

Laporta, Stefano
Physics Letters B, Vol. 772
DOI: 10.1016/j.physletb.2017.06.056

Study of the $e^{+} e^{-} \to π^{+} π^{-} π^{0}$ process using initial state radiation with BABAR
journal, October 2004

Aubert, B.; Barate, R.; Boutigny, D.
Physical Review D, Vol. 70, Issue 7
DOI: 10.1103/PhysRevD.70.072004

Review of Particle Physics
journal, October 2016

Olive, K. A.
Chinese Physics C, Vol. 40, Issue 10
DOI: 10.1088/1674-1137/40/10/100001

Four-point functions and the permutation group $S_{4}$
journal, September 2015

Eichmann, Gernot; Fischer, Christian S.; Heupel, Walter
Physical Review D, Vol. 92, Issue 5
DOI: 10.1103/PhysRevD.92.056006

Towards a data-driven analysis of hadronic light-by-light scattering
journal, November 2014

Colangelo, Gilberto; Hoferichter, Martin; Kubis, Bastian
Physics Letters B, Vol. 738
DOI: 10.1016/j.physletb.2014.09.021

Dispersion relation for hadronic light-by-light scattering: two-pion contributions
journal, April 2017

Colangelo, Gilberto; Hoferichter, Martin; Procura, Massimiliano
Journal of High Energy Physics, Vol. 2017, Issue 4
DOI: 10.1007/JHEP04(2017)161

High-statistics study of the $τ^{-} \to π^{-} π^{0} ν_{τ}$ decay
journal, October 2008

Fujikawa, M.; Hayashii, H.; Eidelman, S.
Physical Review D, Vol. 78, Issue 7
DOI: 10.1103/PhysRevD.78.072006

Electron contribution to the muon anomalous magnetic moment at four loops
journal, March 2016

Kurz, Alexander; Liu, Tao; Marquard, Peter
Physical Review D, Vol. 93, Issue 5
DOI: 10.1103/PhysRevD.93.053017

Complete Tenth-Order QED Contribution to the Muon $g - 2$
journal, September 2012

Aoyama, Tatsumi; Hayakawa, Masashi; Kinoshita, Toichiro
Physical Review Letters, Vol. 109, Issue 11
DOI: 10.1103/PhysRevLett.109.111808

Tenth-order electron anomalous magnetic moment: Contribution of diagrams without closed lepton loops
journal, February 2015

Aoyama, Tatsumi; Hayakawa, Masashi; Kinoshita, Toichiro
Physical Review D, Vol. 91, Issue 3
DOI: 10.1103/PhysRevD.91.033006

Final report of the E821 muon anomalous magnetic moment measurement at BNL
journal, April 2006

Bennett, G. W.; Bousquet, B.; Brown, H. N.
Physical Review D, Vol. 73, Issue 7
DOI: 10.1103/PhysRevD.73.072003

A measurement of the ?0, ? and ?? electromagnetic form factors
journal, September 1991

Behrend, H. -J.; Criegee, L.; Field, J. H.
Zeitschrift f�r Physik C Particles and Fields, Vol. 49, Issue 3
DOI: 10.1007/BF01549692

Pseudoscalar pole terms in the hadronic light-by-light scattering contribution to muon $g - 2$
journal, January 1998

Hayakawa, M.; Kinoshita, T.
Physical Review D, Vol. 57, Issue 1
DOI: 10.1103/PhysRevD.57.465

Hadronic Light-By-Light Scattering Contribution to the Muon $g - 2$ : An Effective Field Theory Approach
journal, January 2002

Knecht, M.; Nyffeler, A.; Perrottet, M.
Physical Review Letters, Vol. 88, Issue 7
DOI: 10.1103/PhysRevLett.88.071802

Rescattering Effects in the Hadronic-Light-by-Light Contribution to the Anomalous Magnetic Moment of the Muon
journal, June 2017

Colangelo, Gilberto; Hoferichter, Martin; Procura, Massimiliano
Physical Review Letters, Vol. 118, Issue 23
DOI: 10.1103/PhysRevLett.118.232001

Pion Pole Contribution to Hadronic Light-By-Light Scattering and Muon Anomalous Magnetic Moment
journal, January 2002

Blokland, Ian; Czarnecki, Andrzej; Melnikov, Kirill
Physical Review Letters, Vol. 88, Issue 7
DOI: 10.1103/PhysRevLett.88.071803

Hadronic light-by-light corrections to the muon $g - 2 :$ The pion-pole contribution
journal, April 2002

Knecht, Marc; Nyffeler, Andreas
Physical Review D, Vol. 65, Issue 7
DOI: 10.1103/PhysRevD.65.073034

Exclusive decays of heavy mesons
journal, July 1982

Chernyak, V. L.; Zhitnitsky, A. R.
Nuclear Physics B, Vol. 201, Issue 3
DOI: 10.1016/0550-3213(82)90445-X

Low-Energy Theorem for $γ \to 3 π$
journal, May 1972

Aviv, Ruvi; Zee, A.
Physical Review D, Vol. 5, Issue 9
DOI: 10.1103/PhysRevD.5.2372

Erratum: Dispersion representations and anomalous singularities of the triangle diagram [Phys. Rev. D 75 , 016001 (2007)]
journal, July 2015

Lucha, Wolfgang; Melikhov, Dmitri; Simula, Silvano
Physical Review D, Vol. 92, Issue 1
DOI: 10.1103/PhysRevD.92.019901

Revised and improved value of the QED tenth-order electron anomalous magnetic moment
journal, February 2018

Aoyama, Tatsumi; Kinoshita, Toichiro; Nio, Makiko
Physical Review D, Vol. 97, Issue 3
DOI: 10.1103/PhysRevD.97.036001

The electroweak contributions to $(g - 2)_{μ}$ after the Higgs-boson mass measurement
journal, September 2013

Gnendiger, C.; Stöckinger, D.; Stöckinger-Kim, H.
Physical Review D, Vol. 88, Issue 5
DOI: 10.1103/PhysRevD.88.053005

A PCAC puzzle: π0→γγ in the σ-model
journal, March 1969

Bell, J. S.; Jackiw, R.
Il Nuovo Cimento A, Vol. 60, Issue 1
DOI: 10.1007/BF02823296

Measurement of the $γ γ^{*} \to π^{0}$ transition form factor
journal, September 2009

Aubert, B.; Karyotakis, Y.; Lees, J. P.
Physical Review D, Vol. 80, Issue 5
DOI: 10.1103/PhysRevD.80.052002

Anomalous decay and scattering processes of the $$\eta $$ η meson
journal, June 2015

Kubis, Bastian; Plenter, Judith
The European Physical Journal C, Vol. 75, Issue 6
DOI: 10.1140/epjc/s10052-015-3495-5

$V V^{'} P$ form factors in resonance chiral theory and the $π - η - η'$ light-by-light contribution to the muon $g - 2$
journal, April 2014

Roig, P.; Guevara, A.; López Castro, G.
Physical Review D, Vol. 89, Issue 7
DOI: 10.1103/PhysRevD.89.073016

Pseudoscalar pole light-by-light contributions to the muon (g − 2) in resonance chiral theory
journal, June 2018

Guevara, A.; Roig, P.; Sanz-Cillero, J. J.
Journal of High Energy Physics, Vol. 2018, Issue 6
DOI: 10.1007/JHEP06(2018)160

Pion transition form factor and distribution amplitudes in large- $N_{c}$ Regge models
journal, August 2006

Arriola, Enrique Ruiz; Broniowski, Wojciech
Physical Review D, Vol. 74, Issue 3
DOI: 10.1103/PhysRevD.74.034008

Quantum-chromodynamic corrections to meson-photon transition form factors
journal, August 1983

Braaten, Eric
Physical Review D, Vol. 28, Issue 3
DOI: 10.1103/PhysRevD.28.524

Lattice calculation of the pion transition form factor $π^{0} \to γ^{} γ^{}$
journal, October 2016

Gérardin, Antoine; Meyer, Harvey B.; Nyffeler, Andreas
Physical Review D, Vol. 94, Issue 7
DOI: 10.1103/PhysRevD.94.074507

Light-by-light-type corrections to the muon anomalous magnetic moment at four-loop order
journal, October 2015

Kurz, Alexander; Liu, Tao; Marquard, Peter
Physical Review D, Vol. 92, Issue 7
DOI: 10.1103/PhysRevD.92.073019

Global aspects of current algebra
journal, August 1983

Witten, Edward
Nuclear Physics B, Vol. 223, Issue 2
DOI: 10.1016/0550-3213(83)90063-9

Hadronic light-by-light scattering contribution to muon $g - 2$
journal, September 1996

Hayakawa, M.; Kinoshita, T.; Sanda, A. I.
Physical Review D, Vol. 54, Issue 5
DOI: 10.1103/PhysRevD.54.3137

Erratum: Tenth-order electron anomalous magnetic moment: Contribution of diagrams without closed lepton loops [Phys. Rev. D 91 , 033006 (2015)]
journal, July 2017

Aoyama, Tatsumi; Hayakawa, Masashi; Kinoshita, Toichiro
Physical Review D, Vol. 96, Issue 1
DOI: 10.1103/PhysRevD.96.019901

Lattice calculation of hadronic light-by-light contribution to the muon anomalous magnetic moment
journal, January 2016

Blum, Thomas; Christ, Norman; Hayakawa, Masashi
Physical Review D, Vol. 93, Issue 1
DOI: 10.1103/PhysRevD.93.014503

Hadronic contributions to the muon g−2 and low-energy QCD
journal, February 1994

de Rafael, Eduardo
Physics Letters B, Vol. 322, Issue 3
DOI: 10.1016/0370-2693(94)91114-2

Extraction of resonance parameter
conference, January 2012

Sato, T.
THE 8TH INTERNATIONAL WORKSHOP ON THE PHYSICS OF EXCITED NUCLEONS: NSTAR 2011, AIP Conference Proceedings
DOI: 10.1063/1.3701187

Dispersion representations and anomalous singularities of the triangle diagram
journal, January 2007

Lucha, Wolfgang; Melikhov, Dmitri; Simula, Silvano
Physical Review D, Vol. 75, Issue 1
DOI: 10.1103/PhysRevD.75.016001

Anomalous Ward Identities in Spinor Field Theories
journal, August 1969

Bardeen, William A.
Physical Review, Vol. 184, Issue 5
DOI: 10.1103/PhysRev.184.1848

Connected and Leading Disconnected Hadronic Light-by-Light Contribution to the Muon Anomalous Magnetic Moment with a Physical Pion Mass
journal, January 2017

Blum, Thomas; Christ, Norman; Hayakawa, Masashi
Physical Review Letters, Vol. 118, Issue 2
DOI: 10.1103/PhysRevLett.118.022005

Structure of the neutral pion and its electromagnetic transition form factor
journal, April 2016

Raya, Khépani; Chang, Lei; Bashir, Adnan
Physical Review D, Vol. 93, Issue 7
DOI: 10.1103/PhysRevD.93.074017

Anomalous magnetic moment of the muon in a dispersive approach
journal, December 2014

Pauk, Vladyslav; Vanderhaeghen, Marc
Physical Review D, Vol. 90, Issue 11
DOI: 10.1103/PhysRevD.90.113012

Pion-Pion Scattering and $K^{\pm} \to 3 π$ Decay
journal, August 1960

Khuri, N. N.; Treiman, S. B.
Physical Review, Vol. 119, Issue 3
DOI: 10.1103/PhysRev.119.1115

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

Jegerlehner, Fred
EPJ Web of Conferences, Vol. 166
DOI: 10.1051/epjconf/201816600022

Analysis of the hadronic light-by-light contributions to the muon g − 2
journal, August 1996

Bijnens, Johan; Pallante, Elisabetta; Prades, Joaquim
Nuclear Physics B, Vol. 474, Issue 2
DOI: 10.1016/0550-3213(96)00288-X

Axial-Vector Vertex in Spinor Electrodynamics
journal, January 1969

Adler, Stephen L.
Physical Review, Vol. 177, Issue 5
DOI: 10.1103/PhysRev.177.2426

Virtual Photon–Photon Scattering
journal, January 2014

Hoferichter, Martin; Colangelo, Gilberto; Procura, Massimiliano
International Journal of Modern Physics: Conference Series, Vol. 35
DOI: 10.1142/S2010194514604001

The muon g−2
journal, June 2009

Jegerlehner, Fred; Nyffeler, Andreas
Physics Reports, Vol. 477, Issue 1-3
DOI: 10.1016/j.physrep.2009.04.003

Higher order hadronic corrections to the anomalous magnetic moment of the muon
journal, March 1976

Calmet, J.; Narison, S.; Perrottet, M.
Physics Letters B, Vol. 61, Issue 3
DOI: 10.1016/0370-2693(76)90150-7

Muon $g - 2$ and $α (M_{Z}^{2})$ : A new data-based analysis
journal, June 2018

Keshavarzi, Alexander; Nomura, Daisuke; Teubner, Thomas
Physical Review D, Vol. 97, Issue 11
DOI: 10.1103/PhysRevD.97.114025

Hadronic Light-by-Light Contribution to Muon $g - 2$ in Chiral Perturbation Theory
journal, July 2002

Ramsey-Musolf, M. J.; Wise, Mark B.
Physical Review Letters, Vol. 89, Issue 4
DOI: 10.1103/PhysRevLett.89.041601

Measurement of $γ γ^{*} \to π^{0}$ transition form factor at Belle
journal, November 2012

Uehara, S.; Watanabe, Y.; Nakazawa, H.
Physical Review D, Vol. 86, Issue 9
DOI: 10.1103/PhysRevD.86.092007

New Measurement of the $π^{0}$ Radiative Decay Width
journal, April 2011

Larin, I.; McNulty, D.; Clinton, E.
Physical Review Letters, Vol. 106, Issue 16
DOI: 10.1103/PhysRevLett.106.162303

$γ^{*} γ \to π^{0}$ transition form factor at low energies from a model-independent approach
journal, November 2012

Masjuan, Pere
Physical Review D, Vol. 86, Issue 9
DOI: 10.1103/PhysRevD.86.094021

Precision of a data-driven estimate of hadronic light-by-light scattering in the muon $g - 2$ : Pseudoscalar-pole contribution
journal, September 2016

Nyffeler, Andreas
Physical Review D, Vol. 94, Issue 5
DOI: 10.1103/PhysRevD.94.053006

Hadronic contribution to the muon anomalous magnetic moment to next-to-next-to-leading order
journal, June 2014

Kurz, Alexander; Liu, Tao; Marquard, Peter
Physics Letters B, Vol. 734
DOI: 10.1016/j.physletb.2014.05.043

The γγ Physics Program at BESIII
journal, January 2018

Redmer, C. F.
EPJ Web of Conferences, Vol. 166
DOI: 10.1051/epjconf/201816600017

Remarks on higher-order hadronic corrections to the muon <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:mi>g</mml:mi><mml:mo>−</mml:mo><mml:mn>2</mml:mn></mml:math>
journal, July 2014

Colangelo, Gilberto; Hoferichter, Martin; Nyffeler, Andreas
Physics Letters B, Vol. 735
DOI: 10.1016/j.physletb.2014.06.012

Radiative resonance couplings in $γ π \to π π$
journal, December 2017

Hoferichter, Martin; Kubis, Bastian; Zanke, Marvin
Physical Review D, Vol. 96, Issue 11
DOI: 10.1103/PhysRevD.96.114016

Pseudoscalar-pole contribution to the $(g_{μ} - 2)$ : A rational approach
journal, March 2017

Masjuan, Pere; Sanchez-Puertas, Pablo
Physical Review D, Vol. 95, Issue 5
DOI: 10.1103/PhysRevD.95.054026

Hadronic Light-by-Light Scattering Effect on Muon $g - 2$
journal, July 1995

Hayakawa, M.; Kinoshita, T.; Sanda, A. I.
Physical Review Letters, Vol. 75, Issue 5
DOI: 10.1103/PhysRevLett.75.790

Reevaluation of the hadronic vacuum polarisation contributions to the Standard Model predictions of the muon $$g-2$$ g - 2 and $${\alpha (m_Z^2)}$$ α ( m Z 2 ) using newest hadronic cross-section data
journal, December 2017

Davier, M.; Hoecker, A.; Malaescu, B.
The European Physical Journal C, Vol. 77, Issue 12
DOI: 10.1140/epjc/s10052-017-5161-6

ππ scattering
journal, June 2001

Colangelo, G.; Gasser, J.; Leutwyler, H.
Nuclear Physics B, Vol. 603, Issue 1-2
DOI: 10.1016/S0550-3213(01)00147-X

Lattice QCD Calculation of Hadronic Light-by-Light Scattering
journal, November 2015

Green, Jeremy; Gryniuk, Oleksii; von Hippel, Georg
Physical Review Letters, Vol. 115, Issue 22
DOI: 10.1103/PhysRevLett.115.222003

Systematic estimation of theoretical uncertainties in the calculation of the pion-photon transition form factor using light-cone sum rules
journal, June 2016

Mikhailov, S. V.; Pimikov, A. V.; Stefanis, N. G.
Physical Review D, Vol. 93, Issue 11
DOI: 10.1103/PhysRevD.93.114018

Pion-pion scattering amplitude. IV. Improved analysis with once subtracted Roy-like equations up to 1100 MeV
journal, April 2011

García-Martín, R.; Kamiński, R.; Peláez, J. R.
Physical Review D, Vol. 83, Issue 7
DOI: 10.1103/PhysRevD.83.074004

Model-independent approach to <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>η</mml:mi><mml:mo>→</mml:mo><mml:msup><mml:mi>π</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:mi>γ</mml:mi></mml:math> and <mml:math altimg="si2.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msup><mml:mi>η</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mo>→</mml:mo><mml:msup><mml:mi>π</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:mi>γ</mml:mi></mml:math>
journal, January 2012

Stollenwerk, F.; Hanhart, C.; Kupsc, A.
Physics Letters B, Vol. 707, Issue 1
DOI: 10.1016/j.physletb.2011.12.008

Dispersive approach to hadronic light-by-light scattering
journal, September 2014

Colangelo, G.; Hoferichter, M.; Procura, M.
Journal of High Energy Physics, Vol. 2014, Issue 9
DOI: 10.1007/JHEP09(2014)091

Comment on the pion pole part of the light-by-light contribution to the muon g−2
journal, April 2002

Bijnens, Johan; Pallante, Elisabetta; Prades, Joaquim
Nuclear Physics B, Vol. 626, Issue 1-2
DOI: 10.1016/S0550-3213(02)00074-3

Study of the process $e^{+} e^{-} \to π^{+} π^{-} π^{0}$ in the energy region $\sqrt{s}$ from 0.98 to 1.38 GeV
journal, August 2002

Achasov, M. N.; Aulchenko, V. M.; Beloborodov, K. I.
Physical Review D, Vol. 66, Issue 3
DOI: 10.1103/PhysRevD.66.032001

On the solution of certain singular integral equations of quantum field theory
journal, April 1958

Omnès, E.
Il Nuovo Cimento, Vol. 8, Issue 2
DOI: 10.1007/BF02747746

The decays Z → Wπ, Z → γπ, and the pion form factor
journal, July 1990

Manohar, Aneesh V.
Physics Letters B, Vol. 244, Issue 1
DOI: 10.1016/0370-2693(90)90276-C

Hadronic Light-by-Light Contributions to the Muon $g - 2$
journal, November 1995

Bijnens, Johan; Pallante, Elisabetta; Prades, Joaquím
Physical Review Letters, Vol. 75, Issue 20
DOI: 10.1103/PhysRevLett.75.3781

Erratum to: Dispersive analysis for $$\eta \rightarrow \gamma \gamma ^\star $$ η → γ γ ⋆
journal, June 2015

Hanhart, C.; Kupść, A.; Meißner, U. -G.
The European Physical Journal C, Vol. 75, Issue 6
DOI: 10.1140/epjc/s10052-015-3429-2

$ω \to π^{0} γ^{}$ and $ϕ \to π^{0} γ^{}$ transition form factors in dispersion theory
journal, September 2012

Schneider, Sebastian P.; Kubis, Bastian; Niecknig, Franz
Physical Review D, Vol. 86, Issue 5
DOI: 10.1103/PhysRevD.86.054013

Exclusive processes in quantum chromodynamics: Evolution equations for hadronic wavefunctions and the form factors of mesons
journal, November 1979

Peter Lepage, G.; Brodsky, Stanley J.
Physics Letters B, Vol. 87, Issue 4
DOI: 10.1016/0370-2693(79)90554-9

Dispersive analysis for η→γγ ⋆
journal, December 2013

Hanhart, C.; Kupść, A.; Meißner, U. -G.
The European Physical Journal C, Vol. 73, Issue 12
DOI: 10.1140/epjc/s10052-013-2668-3

On the large- Q 2 behavior of the pion transition form factor
journal, November 2017

Eichmann, Gernot; Fischer, Christian S.; Weil, Esther
Physics Letters B, Vol. 774
DOI: 10.1016/j.physletb.2017.10.002

Erratum: Refinements in electroweak contributions to the muon anomalous magnetic moment [Phys. Rev. D 67 , 073006 (2003)]
journal, June 2006

Czarnecki, Andrzej; Marciano, William J.; Vainshtein, Arkady
Physical Review D, Vol. 73, Issue 11
DOI: 10.1103/PhysRevD.73.119901

Dispersive analysis of the pion transition form factor
journal, November 2014

Hoferichter, M.; Kubis, B.; Leupold, S.
The European Physical Journal C, Vol. 74, Issue 11
DOI: 10.1140/epjc/s10052-014-3180-0

Study of the process $e^{+} e^{-} \to π^{+} π^{-} π^{0}$ in the energy region $\sqrt{s}$ below 0.98 GeV
journal, September 2003

Achasov, M. N.; Beloborodov, K. I.; Berdyugin, A. V.
Physical Review D, Vol. 68, Issue 5
DOI: 10.1103/PhysRevD.68.052006

Low-Energy Theorem for $γ + γ \to π + π + π$
journal, December 1971

Adler, Stephen L.; Lee, Benjamin W.; Treiman, S. B.
Physical Review D, Vol. 4, Issue 11
DOI: 10.1103/PhysRevD.4.3497

Pion transition form factor in the Regge approach and incomplete vector-meson dominance
journal, May 2010

Arriola, Enrique Ruiz; Broniowski, Wojciech
Physical Review D, Vol. 81, Issue 9
DOI: 10.1103/PhysRevD.81.094021

Two-hadron saturation for the pseudoscalar–vector–vector correlator and phenomenological applications
journal, December 2015

Husek, Tomáš; Leupold, Stefan
The European Physical Journal C, Vol. 75, Issue 12
DOI: 10.1140/epjc/s10052-015-3778-x

Dispersion relation for hadronic light-by-light scattering: theoretical foundations
journal, September 2015

Colangelo, Gilberto; Hoferichter, Martin; Procura, Massimiliano
Journal of High Energy Physics, Vol. 2015, Issue 9
DOI: 10.1007/JHEP09(2015)074

Hadronic Light-by-Light Scattering Contribution to the Muon Anomalous Magnetic Moment from Lattice QCD
journal, January 2015

Blum, Thomas; Chowdhury, Saumitra; Hayakawa, Masashi
Physical Review Letters, Vol. 114, Issue 1
DOI: 10.1103/PhysRevLett.114.012001

Dispersive analysis of ω→3π and ϕ→3π decays
journal, May 2012

Niecknig, Franz; Kubis, Bastian; Schneider, Sebastian P.
The European Physical Journal C, Vol. 72, Issue 5
DOI: 10.1140/epjc/s10052-012-2014-1

Using infinite-volume, continuum QED and lattice QCD for the hadronic light-by-light contribution to the muon anomalous magnetic moment
journal, August 2017

Blum, Thomas; Christ, Norman; Hayakawa, Masashi
Physical Review D, Vol. 96, Issue 3
DOI: 10.1103/PhysRevD.96.034515

Precision measurement of the neutral pion radiative decay width at Jefferson Lab
conference, June 2016

Gasparian, Ashot
Proceedings of The 8th International Workshop on Chiral Dynamics — PoS(CD15)
DOI: 10.22323/1.253.0048

Regge analysis of the ππ scattering amplitude
journal, February 2012

Caprini, I.; Colangelo, G.; Leutwyler, H.
The European Physical Journal C, Vol. 72, Issue 2
DOI: 10.1140/epjc/s10052-012-1860-1

Asymptotic behaviour of exclusive processes in QCD
journal, October 1984

Chernyak, V.
Physics Reports, Vol. 112, Issue 3-4
DOI: 10.1016/0370-1573(84)90126-1

Exclusive processes in perturbative quantum chromodynamics
journal, November 1980

Lepage, G. Peter; Brodsky, Stanley J.
Physical Review D, Vol. 22, Issue 9
DOI: 10.1103/PhysRevD.22.2157

Light cone sum rules for the $π^{0} γ^{*} γ$ form factor revisited
journal, March 2011

Agaev, S. S.; Braun, V. M.; Offen, N.
Physical Review D, Vol. 83, Issue 5
DOI: 10.1103/PhysRevD.83.054020

Precision muon physics
journal, September 2015

Gorringe, T. P.; Hertzog, D. W.
Progress in Particle and Nuclear Physics, Vol. 84
DOI: 10.1016/j.ppnp.2015.06.001

Use and misuse of QCD sum rules, factorization and related topics
journal, May 1984

Novikov, V. A.; Shifman, M. A.; Vainshtein, A. I.
Nuclear Physics B, Vol. 237, Issue 3
DOI: 10.1016/0550-3213(84)90006-3

La résonance dans la diffusion méson π— méson π et le moment magnétique anormal du méson μ
journal, January 1961

Bouchiat, Claude; Michel, Louis
Journal de Physique et le Radium, Vol. 22, Issue 2
DOI: 10.1051/jphysrad:01961002202012101

Form factors of pseudoscalar mesons
journal, July 2012

Gorchtein, Mikhail; Guo, Peng; Szczepaniak, Adam P.
Physical Review C, Vol. 86, Issue 1
DOI: 10.1103/PhysRevC.86.015205

Form factors of γ * ρ → π and γ * γ → π 0 transitions and light-cone sum rules
journal, January 1999

Khodjamirian, A.
The European Physical Journal C, Vol. 6, Issue 3
DOI: 10.1007/s100529800938

Hadronic Light-by-Light Contribution to the Muon $g - 2$
journal, August 1995

Bijnens, Johan; Pallante, Elisabetta; Prades, Joaquím
Physical Review Letters, Vol. 75, Issue 8
DOI: 10.1103/PhysRevLett.75.1447

Erratum: Pseudoscalar pole terms in the hadronic light-by-light scattering contribution to muon $g - 2$ [Phys. Rev. D $57,$ 465 (1998)]
journal, July 2002

Hayakawa, M.; Kinoshita, T.
Physical Review D, Vol. 66, Issue 1
DOI: 10.1103/PhysRevD.66.019902

Chiral expansions of the $π^{0}$ lifetime
journal, April 2009

Kampf, Karol; Moussallam, Bachir
Physical Review D, Vol. 79, Issue 7
DOI: 10.1103/PhysRevD.79.076005

Extracting the chiral anomaly from $γ π \to π π$
journal, December 2012

Hoferichter, Martin; Kubis, Bastian; Sakkas, Dimitrios
Physical Review D, Vol. 86, Issue 11
DOI: 10.1103/PhysRevD.86.116009

Higher order QCD corrections to an exclusive two-photon process
journal, December 1981

Del Aguila, F.; Chase, M. K.
Nuclear Physics B, Vol. 193, Issue 2
DOI: 10.1016/0550-3213(81)90344-8

Measurements of the meson-photon transition form factors of light pseudoscalar mesons at large momentum transfer
journal, January 1998

Gronberg, J.; Hill, T. S.; Kutschke, R.
Physical Review D, Vol. 57, Issue 1
DOI: 10.1103/PhysRevD.57.33

Refinements in electroweak contributions to the muon anomalous magnetic moment
journal, April 2003

Czarnecki, Andrzej; Marciano, William J.; Vainshtein, Arkady
Physical Review D, Vol. 67, Issue 7
DOI: 10.1103/PhysRevD.67.073006

Hadronic light-by-light scattering contribution to the muon anomalous magnetic moment reexamined
journal, December 2004

Melnikov, Kirill; Vainshtein, Arkady
Physical Review D, Vol. 70, Issue 11
DOI: 10.1103/PhysRevD.70.113006

Large-angle two-photon exclusive channels in quantum chromodynamics
journal, October 1981

Brodsky, Stanley J.; Lepage, G. Peter
Physical Review D, Vol. 24, Issue 7
DOI: 10.1103/PhysRevD.24.1808

Process π± → π0π± in coulomb field and anomalous divergence of neutral axial-vector current
journal, March 1972

Terent'ev, M. V.
Physics Letters B, Vol. 38, Issue 6
DOI: 10.1016/0370-2693(72)90171-2

Works referencing / citing this record:

Generic loop effects of new scalars and fermions in b → sℓ+ℓ− and a vector-like 4th generation
journal, June 2019

Arnan, Pere; Crivellin, Andreas; Fedele, Marco
Journal of High Energy Physics, Vol. 2019, Issue 6
DOI: 10.1007/jhep06(2019)118

b → sℓ+ℓ− transitions in two-Higgs-doublet models
journal, June 2019

Crivellin, Andreas; Müller, Dario; Wiegand, Christoph
Journal of High Energy Physics, Vol. 2019, Issue 6
DOI: 10.1007/jhep06(2019)119

Dispersion relations for γ∗γ∗ → ππ: helicity amplitudes, subtractions, and anomalous thresholds
journal, July 2019

Hoferichter, Martin; Stoffer, Peter
Journal of High Energy Physics, Vol. 2019, Issue 7
DOI: 10.1007/jhep07(2019)073

Generic loop effects of new scalars and fermions in b → sℓ+ℓ− and a vector-like 4th generation
journal, June 2019

Arnan, Pere; Crivellin, Andreas; Fedele, Marco
Journal of High Energy Physics, Vol. 2019, Issue 6
DOI: 10.1007/jhep06(2019)118

b → sℓ+ℓ− transitions in two-Higgs-doublet models
journal, June 2019

Crivellin, Andreas; Müller, Dario; Wiegand, Christoph
Journal of High Energy Physics, Vol. 2019, Issue 6
DOI: 10.1007/jhep06(2019)119

Dispersion relations for γ∗γ∗ → ππ: helicity amplitudes, subtractions, and anomalous thresholds
journal, July 2019

Hoferichter, Martin; Stoffer, Peter
Journal of High Energy Physics, Vol. 2019, Issue 7
DOI: 10.1007/jhep07(2019)073

Kaon-box contribution to the anomalous magnetic moment of the muon
journal, March 2020

Eichmann, Gernot; Fischer, Christian S.; Williams, Richard
Physical Review D, Vol. 101, Issue 5
DOI: 10.1103/physrevd.101.054015

Two-pion contribution to hadronic vacuum polarization
journal, February 2019

Colangelo, Gilberto; Hoferichter, Martin; Stoffer, Peter
Journal of High Energy Physics, Vol. 2019, Issue 2
DOI: 10.1007/jhep02(2019)006

Low-energy lepton physics in the MRSSM: (g − 2)μ, μ→eγ and μ→e conversion
journal, August 2019

Kotlarski, Wojciech; Stöckinger, Dominik; Stöckinger-Kim, Hyejung
Journal of High Energy Physics, Vol. 2019, Issue 8
DOI: 10.1007/jhep08(2019)082

Dispersion relation for hadronic light-by-light scattering: pion pole
journal, October 2018

Hoferichter, Martin; Hoid, Bai-Long; Kubis, Bastian
Journal of High Energy Physics, Vol. 2018, Issue 10
DOI: 10.1007/jhep10(2018)141

Electromagnetic form factors of the transition from the spin-3/2 $Σ$ to the $Λ$ hyperon
journal, January 2020

Junker, Olov; Leupold, Stefan; Perotti, Elisabetta
Physical Review C, Vol. 101, Issue 1
DOI: 10.1103/physrevc.101.015206

Lattice calculation of the pion transition form factor with $N_{f} = 2 + 1$ Wilson quarks
journal, August 2019

Gérardin, Antoine; Meyer, Harvey B.; Nyffeler, Andreas
Physical Review D, Vol. 100, Issue 3
DOI: 10.1103/physrevd.100.034520

$g - 2$ of charged leptons, $α (M_{Z}^{2})$ , and the hyperfine splitting of muonium
journal, January 2020

Keshavarzi, Alexander; Nomura, Daisuke; Teubner, Thomas
Physical Review D, Vol. 101, Issue 1
DOI: 10.1103/physrevd.101.014029

Precise Determination of the Branching Ratio of the Neutral-Pion Dalitz Decay
journal, January 2019

Husek, Tomáš; Goudzovski, Evgueni; Kampf, Karol
Physical Review Letters, Vol. 122, Issue 2
DOI: 10.1103/physrevlett.122.022003

Opportunities for Lattice QCD in quark and lepton flavor physics
journal, November 2019

Lehner, Christoph; Meinel, Stefan; Blum, Tom
The European Physical Journal A, Vol. 55, Issue 11
DOI: 10.1140/epja/i2019-12891-2

Hadronic light-by-light scattering in the anomalous magnetic moment of the muon
text, January 2019

Asmussen, Nils; Gerardin, Antoine; Nyffeler, Andreas
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2020-00087

Figures / Tables found in this record:

Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.

Similar Records in DOE PAGES and OSTI.GOV collections:

Dispersion relation for hadronic light-by-light scattering: pion pole

Journal Article Hoferichter, Martin ; Hoid, Bai -Long ; Kubis, Bastian ; ... - Journal of High Energy Physics (Online)

Here, the pion-pole contribution to hadronic light-by-light scattering in the anomalous magnetic moment of the muon (g – 2)_μ is fully determined by the doubly-virtual pion transition form factor. Although this crucial input quantity is, in principle, directly accessible in experiment, a complete measurement covering all kinematic regions relevant for (g –2)_μ is not realistic in the foreseeable future. Here, we report in detail on a reconstruction from available data, both space- and time-like, using a dispersive representation that accounts for all the low-lying singularities, reproduces the correct high- and low-energy limits, and proves convenient for the evaluation of themore »« less
Cited by 244
https://doi.org/10.1007/JHEP10(2018)141

Full Text Available
Rescattering Effects in the Hadronic-Light-by-Light Contribution to the Anomalous Magnetic Moment of the Muon

Journal Article Colangelo, Gilberto ; Hoferichter, Martin ; Procura, Massimiliano ; ... - Physical Review Letters

We present a first model-independent calculation of ππ intermediate states in the hadronic-light-by-light (HLBL) contribution to the anomalous magnetic moment of the muon (g - 2)_μ that goes beyond the scalar QED pion loop. To this end, we combine a recently developed dispersive description of the HLBL tensor with a partial-wave expansion and demonstrate that the known scalar-QED result is recovered after partial-wave resummation. Using dispersive fits to high-statistics data for the pion vector form factor, we provide an evaluation of the full pion box a^π_μ^box = –15.9(2) x 10^-11. We then construct a suitable input for the γ*γ* →more »« less
Cited by 87
https://doi.org/10.1103/PhysRevLett.118.232001
Dispersion relation for hadronic light-by-light scattering: two-pion contributions

Journal Article Colangelo, Gilberto ; Hoferichter, Martin ; Procura, Massimiliano ; ... - Journal of High Energy Physics (Online)

In our third paper of a series dedicated to a dispersive treatment of the hadronic light-by-light (HLbL) tensor, we derive a partial-wave formulation for two-pion intermediate states in the HLbL contribution to the anomalous magnetic moment of the muon (g - 2)_μ, including a detailed discussion of the unitarity relation for arbitrary partial waves. We show that obtaining a final expression free from unphysical helicity partial waves is a subtle issue, which we thoroughly clarify. As a by-product, we obtain a set of sum rules that could be used to constrain future calculations of γ*γ* → ππ. We validate the formalism extensively using the pion-box contribution, defined by two-pion intermediate states with a pion-pole left-hand cut, and demonstrate how the full known result is reproduced when resumming the partial waves. Using dispersive fits to high-statistics data for the pion vector form factor, we provide an evaluation of the full pion box, amore »« less
Cited by 255
https://doi.org/10.1007/JHEP04(2017)161

Full Text Available
Longitudinal short-distance constraints for the hadronic light-by-light contribution to (g - 2)_μ with large-N_c Regge models

Journal Article Colangelo, Gilberto ; Hagelstein, Franziska ; Hoferichter, Martin ; ... - Journal of High Energy Physics (Online)

While the low-energy part of the hadronic light-by-light (HLbL) tensor can be constrained from data using dispersion relations, for a full evaluation of its contribution to the anomalous magnetic moment of the muon (g – 2)_μ also mixed- and high-energy regions need to be estimated. Both can be addressed within the operator product expansion (OPE), either for configurations where all photon virtualities become large or one of them remains finite. Imposing such short-distance constraints (SDCs) on the HLbL tensor is thus a major aspect of a model-independent approach towards HLbL scattering. Here, we focus on longitudinal SDCs, which concern the amplitudes containing the pseudoscalar-pole contributions from π^o, η, η'. Since these conditions cannot be fulfilled by a finite number of pseudoscalar poles, we consider a tower of excited pseudoscalars, constraining their masses and transition form factors from Regge theory, the OPE, and phenomenology. Implementing a matching of the resulting expressions for the HLbL tensor onto the perturbative QCD quark loop, we are able to further constrain our calculation and significantly reduce its model dependence. We find that especially for the π0 the corresponding increase of the HLbL contribution is much smaller than previous prescriptions in the literature would imply. Overall, we estimate that longitudinal SDCs increase the HLbL contribution by Δamore »« less
https://doi.org/10.1007/jhep03(2020)101

Full Text Available
Two-pion contribution to hadronic vacuum polarization

Journal Article Colangelo, Gilberto ; Hoferichter, Martin ; Stoffer, Peter - Journal of High Energy Physics (Online)

We present a detailed analysis of e⁺e^- → π⁺π^- data up to $ \sqrt{s}=1 $ GeV in the framework of dispersion relations. Starting from a family of ππ P-wave phase shifts, as derived from a previous Roy-equation analysis of ππ scattering, we write down an extended Omnès representation of the pion vector form factor in terms of a few free parameters and study to which extent the modern high-statistics data sets can be described by the resulting fit function that follows from general principles of QCD. We find that statistically acceptable fits do become possible as soon as potential uncertainties in the energy calibration are taken into account, providing a strong cross check on the internal consistency of the data sets, but preferring a mass of the ω meson significantly lower than the current PDG average. In addition to a complete treatment of statistical and systematic errors propagated from the data, we perform a comprehensive analysis of the systematic errors in the dispersive representation and derive the consequences for the two-pion contribution to hadronic vacuum polarization. In a global fit to both time- and space-like data sets we find a^ππ_μ|_{≤ 1 GeV} = 495.0(1.5)(2.1) × 10^-10 and a^ππ_μ|_{≤ 0.63 GeV} = 132.8(0.4)(1.0) × 10^-10. While the constraints are thus most stringent for low energies, we obtain uncertainty estimates throughout the whole energy range that should prove valuable in corroborating the corresponding contribution to the anomalous magnetic moment of the muon. As side products, we obtain improved constraints on the ππ P-wave, valuable input for future global analyses of low-energy ππ scattering, as well as a determination of the pion charge radius,more »« less
Cited by 268
https://doi.org/10.1007/jhep02(2019)006

Full Text Available

Similar Records

Title: Pion-Pole Contribution to Hadronic Light-By-Light Scattering in the Anomalous Magnetic Moment of the Muon

Abstract

Citation Formats

Figures / Tables:

High-precision calculation of the 4-loop contribution to the electron g -2 in QED journal, September 2017

Study of the e + e − → π + π − π 0 process using initial state radiation with BABAR journal, October 2004

Review of Particle Physics journal, October 2016

Four-point functions and the permutation group S 4 journal, September 2015

Towards a data-driven analysis of hadronic light-by-light scattering journal, November 2014

Dispersion relation for hadronic light-by-light scattering: two-pion contributions journal, April 2017

High-statistics study of the τ − → π − π 0 ν τ decay journal, October 2008

Electron contribution to the muon anomalous magnetic moment at four loops journal, March 2016

Complete Tenth-Order QED Contribution to the Muon g − 2 journal, September 2012

Tenth-order electron anomalous magnetic moment: Contribution of diagrams without closed lepton loops journal, February 2015

Final report of the E821 muon anomalous magnetic moment measurement at BNL journal, April 2006

A measurement of the ?0, ? and ?? electromagnetic form factors journal, September 1991

Pseudoscalar pole terms in the hadronic light-by-light scattering contribution to muon g − 2 journal, January 1998

Hadronic Light-By-Light Scattering Contribution to the Muon g − 2 : An Effective Field Theory Approach journal, January 2002

Rescattering Effects in the Hadronic-Light-by-Light Contribution to the Anomalous Magnetic Moment of the Muon journal, June 2017

Pion Pole Contribution to Hadronic Light-By-Light Scattering and Muon Anomalous Magnetic Moment journal, January 2002

Hadronic light-by-light corrections to the muon g − 2 : The pion-pole contribution journal, April 2002

Exclusive decays of heavy mesons journal, July 1982

Low-Energy Theorem for γ → 3 π journal, May 1972

Erratum: Dispersion representations and anomalous singularities of the triangle diagram [Phys. Rev. D 75 , 016001 (2007)] journal, July 2015

Revised and improved value of the QED tenth-order electron anomalous magnetic moment journal, February 2018

The electroweak contributions to ( g − 2 ) μ after the Higgs-boson mass measurement journal, September 2013

A PCAC puzzle: π0→γγ in the σ-model journal, March 1969

Measurement of the γ γ * → π 0 transition form factor journal, September 2009

Anomalous decay and scattering processes of the $$\eta $$ η meson journal, June 2015

V V ′ P form factors in resonance chiral theory and the π − η − η ′ light-by-light contribution to the muon g − 2 journal, April 2014

Pseudoscalar pole light-by-light contributions to the muon (g − 2) in resonance chiral theory journal, June 2018

Pion transition form factor and distribution amplitudes in large- N c Regge models journal, August 2006

Quantum-chromodynamic corrections to meson-photon transition form factors journal, August 1983

Lattice calculation of the pion transition form factor π 0 → γ * γ * journal, October 2016

Light-by-light-type corrections to the muon anomalous magnetic moment at four-loop order journal, October 2015

Global aspects of current algebra journal, August 1983

Hadronic light-by-light scattering contribution to muon g − 2 journal, September 1996

Erratum: Tenth-order electron anomalous magnetic moment: Contribution of diagrams without closed lepton loops [Phys. Rev. D 91 , 033006 (2015)] journal, July 2017

Lattice calculation of hadronic light-by-light contribution to the muon anomalous magnetic moment journal, January 2016

Hadronic contributions to the muon g−2 and low-energy QCD journal, February 1994

Extraction of resonance parameter conference, January 2012

Dispersion representations and anomalous singularities of the triangle diagram journal, January 2007

Anomalous Ward Identities in Spinor Field Theories journal, August 1969

Connected and Leading Disconnected Hadronic Light-by-Light Contribution to the Muon Anomalous Magnetic Moment with a Physical Pion Mass journal, January 2017

Structure of the neutral pion and its electromagnetic transition form factor journal, April 2016

Anomalous magnetic moment of the muon in a dispersive approach journal, December 2014

Pion-Pion Scattering and K ± → 3 π Decay journal, August 1960

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

Analysis of the hadronic light-by-light contributions to the muon g − 2 journal, August 1996

Axial-Vector Vertex in Spinor Electrodynamics journal, January 1969

Virtual Photon–Photon Scattering journal, January 2014

The muon g−2 journal, June 2009

Higher order hadronic corrections to the anomalous magnetic moment of the muon journal, March 1976

Muon g − 2 and α ( M Z 2 ) : A new data-based analysis journal, June 2018

Hadronic Light-by-Light Contribution to Muon g − 2 in Chiral Perturbation Theory journal, July 2002

Measurement of γ γ * → π 0 transition form factor at Belle journal, November 2012

New Measurement of the π 0 Radiative Decay Width journal, April 2011

γ * γ → π 0 transition form factor at low energies from a model-independent approach journal, November 2012

Precision of a data-driven estimate of hadronic light-by-light scattering in the muon g − 2 : Pseudoscalar-pole contribution journal, September 2016

Hadronic contribution to the muon anomalous magnetic moment to next-to-next-to-leading order journal, June 2014

The γγ Physics Program at BESIII journal, January 2018

Radiative resonance couplings in γ π → π π journal, December 2017

Pseudoscalar-pole contribution to the ( g μ − 2 ) : A rational approach journal, March 2017

Hadronic Light-by-Light Scattering Effect on Muon g − 2 journal, July 1995

Reevaluation of the hadronic vacuum polarisation contributions to the Standard Model predictions of the muon $$g-2$$ g - 2 and $${\alpha (m_Z^2)}$$ α ( m Z 2 ) using newest hadronic cross-section data journal, December 2017

ππ scattering journal, June 2001

Lattice QCD Calculation of Hadronic Light-by-Light Scattering journal, November 2015

Systematic estimation of theoretical uncertainties in the calculation of the pion-photon transition form factor using light-cone sum rules journal, June 2016

Pion-pion scattering amplitude. IV. Improved analysis with once subtracted Roy-like equations up to 1100 MeV journal, April 2011

Dispersive approach to hadronic light-by-light scattering journal, September 2014

Comment on the pion pole part of the light-by-light contribution to the muon g−2 journal, April 2002

Study of the process e + e − → π + π − π 0 in the energy region s from 0.98 to 1.38 GeV journal, August 2002

On the solution of certain singular integral equations of quantum field theory journal, April 1958

The decays Z → Wπ, Z → γπ, and the pion form factor journal, July 1990

Hadronic Light-by-Light Contributions to the Muon g − 2 journal, November 1995

Erratum to: Dispersive analysis for $$\eta \rightarrow \gamma \gamma ^\star $$ η → γ γ ⋆ journal, June 2015

ω → π 0 γ * and ϕ → π 0 γ * transition form factors in dispersion theory journal, September 2012

Exclusive processes in quantum chromodynamics: Evolution equations for hadronic wavefunctions and the form factors of mesons journal, November 1979

Dispersive analysis for η→γγ ⋆ journal, December 2013

On the large- Q 2 behavior of the pion transition form factor journal, November 2017

High-precision calculation of the 4-loop contribution to the electron g -2 in QED
journal, September 2017

Study of the $e^{+} e^{-} \to π^{+} π^{-} π^{0}$ process using initial state radiation with BABAR
journal, October 2004

Review of Particle Physics
journal, October 2016

Four-point functions and the permutation group $S_{4}$
journal, September 2015

Towards a data-driven analysis of hadronic light-by-light scattering
journal, November 2014

Dispersion relation for hadronic light-by-light scattering: two-pion contributions
journal, April 2017

High-statistics study of the $τ^{-} \to π^{-} π^{0} ν_{τ}$ decay
journal, October 2008

Electron contribution to the muon anomalous magnetic moment at four loops
journal, March 2016

Complete Tenth-Order QED Contribution to the Muon $g - 2$
journal, September 2012

Tenth-order electron anomalous magnetic moment: Contribution of diagrams without closed lepton loops
journal, February 2015

Final report of the E821 muon anomalous magnetic moment measurement at BNL
journal, April 2006

A measurement of the ?0, ? and ?? electromagnetic form factors
journal, September 1991

Pseudoscalar pole terms in the hadronic light-by-light scattering contribution to muon $g - 2$
journal, January 1998

Hadronic Light-By-Light Scattering Contribution to the Muon $g - 2$ : An Effective Field Theory Approach
journal, January 2002

Rescattering Effects in the Hadronic-Light-by-Light Contribution to the Anomalous Magnetic Moment of the Muon
journal, June 2017

Pion Pole Contribution to Hadronic Light-By-Light Scattering and Muon Anomalous Magnetic Moment
journal, January 2002

Hadronic light-by-light corrections to the muon $g - 2 :$ The pion-pole contribution
journal, April 2002

Exclusive decays of heavy mesons
journal, July 1982

Low-Energy Theorem for $γ \to 3 π$
journal, May 1972

Erratum: Dispersion representations and anomalous singularities of the triangle diagram [Phys. Rev. D 75 , 016001 (2007)]
journal, July 2015

Revised and improved value of the QED tenth-order electron anomalous magnetic moment
journal, February 2018

The electroweak contributions to $(g - 2)_{μ}$ after the Higgs-boson mass measurement
journal, September 2013

A PCAC puzzle: π0→γγ in the σ-model
journal, March 1969

Measurement of the $γ γ^{*} \to π^{0}$ transition form factor
journal, September 2009

Anomalous decay and scattering processes of the $$\eta $$ η meson
journal, June 2015

$V V^{'} P$ form factors in resonance chiral theory and the $π - η - η'$ light-by-light contribution to the muon $g - 2$
journal, April 2014

Pseudoscalar pole light-by-light contributions to the muon (g − 2) in resonance chiral theory
journal, June 2018

Pion transition form factor and distribution amplitudes in large- $N_{c}$ Regge models
journal, August 2006

Quantum-chromodynamic corrections to meson-photon transition form factors
journal, August 1983

Lattice calculation of the pion transition form factor $π^{0} \to γ^{} γ^{}$
journal, October 2016

Light-by-light-type corrections to the muon anomalous magnetic moment at four-loop order
journal, October 2015

Global aspects of current algebra
journal, August 1983

Hadronic light-by-light scattering contribution to muon $g - 2$
journal, September 1996

Erratum: Tenth-order electron anomalous magnetic moment: Contribution of diagrams without closed lepton loops [Phys. Rev. D 91 , 033006 (2015)]
journal, July 2017

Lattice calculation of hadronic light-by-light contribution to the muon anomalous magnetic moment
journal, January 2016

Hadronic contributions to the muon g−2 and low-energy QCD
journal, February 1994

Extraction of resonance parameter
conference, January 2012

Dispersion representations and anomalous singularities of the triangle diagram
journal, January 2007

Anomalous Ward Identities in Spinor Field Theories
journal, August 1969

Connected and Leading Disconnected Hadronic Light-by-Light Contribution to the Muon Anomalous Magnetic Moment with a Physical Pion Mass
journal, January 2017

Structure of the neutral pion and its electromagnetic transition form factor
journal, April 2016

Anomalous magnetic moment of the muon in a dispersive approach
journal, December 2014

Pion-Pion Scattering and $K^{\pm} \to 3 π$ Decay
journal, August 1960

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

Analysis of the hadronic light-by-light contributions to the muon g − 2
journal, August 1996

Axial-Vector Vertex in Spinor Electrodynamics
journal, January 1969

Virtual Photon–Photon Scattering
journal, January 2014

The muon g−2
journal, June 2009

Higher order hadronic corrections to the anomalous magnetic moment of the muon
journal, March 1976

Muon $g - 2$ and $α (M_{Z}^{2})$ : A new data-based analysis
journal, June 2018

Hadronic Light-by-Light Contribution to Muon $g - 2$ in Chiral Perturbation Theory
journal, July 2002

Measurement of $γ γ^{*} \to π^{0}$ transition form factor at Belle
journal, November 2012

New Measurement of the $π^{0}$ Radiative Decay Width
journal, April 2011

$γ^{*} γ \to π^{0}$ transition form factor at low energies from a model-independent approach
journal, November 2012

Precision of a data-driven estimate of hadronic light-by-light scattering in the muon $g - 2$ : Pseudoscalar-pole contribution
journal, September 2016

Hadronic contribution to the muon anomalous magnetic moment to next-to-next-to-leading order
journal, June 2014

The γγ Physics Program at BESIII
journal, January 2018

Radiative resonance couplings in $γ π \to π π$
journal, December 2017

Pseudoscalar-pole contribution to the $(g_{μ} - 2)$ : A rational approach
journal, March 2017

Hadronic Light-by-Light Scattering Effect on Muon $g - 2$
journal, July 1995

Reevaluation of the hadronic vacuum polarisation contributions to the Standard Model predictions of the muon $$g-2$$ g - 2 and $${\alpha (m_Z^2)}$$ α ( m Z 2 ) using newest hadronic cross-section data
journal, December 2017

ππ scattering
journal, June 2001

Lattice QCD Calculation of Hadronic Light-by-Light Scattering
journal, November 2015

Systematic estimation of theoretical uncertainties in the calculation of the pion-photon transition form factor using light-cone sum rules
journal, June 2016

Pion-pion scattering amplitude. IV. Improved analysis with once subtracted Roy-like equations up to 1100 MeV
journal, April 2011

Dispersive approach to hadronic light-by-light scattering
journal, September 2014

Comment on the pion pole part of the light-by-light contribution to the muon g−2
journal, April 2002

Study of the process $e^{+} e^{-} \to π^{+} π^{-} π^{0}$ in the energy region $\sqrt{s}$ from 0.98 to 1.38 GeV
journal, August 2002

On the solution of certain singular integral equations of quantum field theory
journal, April 1958

The decays Z → Wπ, Z → γπ, and the pion form factor
journal, July 1990

Hadronic Light-by-Light Contributions to the Muon $g - 2$
journal, November 1995

Erratum to: Dispersive analysis for $$\eta \rightarrow \gamma \gamma ^\star $$ η → γ γ ⋆
journal, June 2015

$ω \to π^{0} γ^{}$ and $ϕ \to π^{0} γ^{}$ transition form factors in dispersion theory
journal, September 2012

Exclusive processes in quantum chromodynamics: Evolution equations for hadronic wavefunctions and the form factors of mesons
journal, November 1979

Dispersive analysis for η→γγ ⋆
journal, December 2013

On the large- Q 2 behavior of the pion transition form factor
journal, November 2017

Erratum: Refinements in electroweak contributions to the muon anomalous magnetic moment [Phys. Rev. D 67 , 073006 (2003)]
journal, June 2006

Dispersive analysis of the pion transition form factor
journal, November 2014

Study of the process $e^{+} e^{-} \to π^{+} π^{-} π^{0}$ in the energy region $\sqrt{s}$ below 0.98 GeV
journal, September 2003

Low-Energy Theorem for $γ + γ \to π + π + π$
journal, December 1971