Two-pion contribution to hadronic vacuum polarization

Colangelo, Gilberto; Hoferichter, Martin; Stoffer, Peter

doi:10.1007/jhep02(2019)006

Title: Two-pion contribution to hadronic vacuum polarization

Journal Article · 31 January 2019 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/jhep02(2019)006 · OSTI ID:1609328

Colangelo, Gilberto ^[1]; Hoferichter, Martin ^[2]; Stoffer, Peter ^[3]

Univ. of Bern (Switzerland); DOE/OSTI
Univ. of Washington, Seattle, WA (United States)
Univ. of California, San Francisco, CA (United States)

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, $$\langle$$$$r^{2}_{π}$$$$\rangle$$ = 0.429(1)(4) fm².

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Research Organization:: Univ. of California, San Diego, CA (United States); Univ. of Washington, Seattle, WA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: FG02-00ER41132; SC0009919

OSTI ID:: 1609328

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 2 Vol. 2019; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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The Hadronic Light-by-Light Scattering Contribution to the Muon and Electron Anomalous Magnetic Moments Prades, Joaquim; de Rafael, Eduardo; Vainshtein, Arkady Lepton Dipole Moments https://doi.org/10.1142/9789814271844_0009	book	December 2009
Virtual Photon–Photon Scattering Hoferichter, Martin; Colangelo, Gilberto; Procura, Massimiliano International Journal of Modern Physics: Conference Series, Vol. 35 https://doi.org/10.1142/S2010194514604001	journal	January 2014
Roy-Steiner equations for pion-nucleon scattering Ditsche, Christoph; Hoferichter, Martin; Kubis, Bastian Proceedings of The 7th International Workshop on Chiral Dynamics — PoS(CD12) https://doi.org/10.22323/1.172.0064	conference	July 2013
Dispersive analysis of the scalar form factor of the nucleon Hoferichter, Martin; Ditsche, Christoph; Kubis, Bastian Proceedings of The 7th International Workshop on Chiral Dynamics — PoS(CD12) https://doi.org/10.22323/1.172.0069	conference	July 2013
Charge symmetry breaking in pion-deuteron scattering Hoferichter, Martin; Baru, Vadim; Hanhart, Christoph Proceedings of The 7th International Workshop on Chiral Dynamics — PoS(CD12) https://doi.org/10.22323/1.172.0093	conference	July 2013
Dispersive analysis of the pion transition form factor Hoferichter, Martin; Kubis, Bastian; Leupold, Stefan Springer https://doi.org/10.26083/tuprints-00012830	text	January 2022
Review of Particle Physics Beringer, J.; Arguin, J.; Barnett, R. Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/phppubdb-24149	text	January 2012
Review of Particle Physics Tanabashi, M.; Hagiwara, K.; Hikasa, K. Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2018-03100	text	January 2018
The hadronic vacuum polarization contribution to the muon g − 2 from lattice QCD Della Morte, Michele; Francis, Anthony; Gülpers, Vera ETH Zurich https://doi.org/10.3929/ethz-b-000199093	text	January 2017
Precision calculation of threshold pi^- d scattering, pi N scattering lengths, and the GMO sum rule Baru, V.; Hanhart, C.; Hoferichter, M. arXiv https://doi.org/10.48550/arxiv.1107.5509	text	January 2011
Regge analysis of the pi pi scattering amplitude Caprini, Irinel; Colangelo, Gilberto; Leutwyler, Heinrich arXiv https://doi.org/10.48550/arxiv.1111.7160	text	January 2011
A new Parameterization for the Pion Vector Form Factor Hanhart, C. arXiv https://doi.org/10.48550/arxiv.1203.6839	text	January 2012
Dispersive analysis of the scalar form factor of the nucleon Hoferichter, M.; Ditsche, C.; Kubis, B. arXiv https://doi.org/10.48550/arxiv.1204.6251	text	January 2012
Virtual photon-photon scattering Hoferichter, Martin; Colangelo, Gilberto; Procura, Massimiliano arXiv https://doi.org/10.48550/arxiv.1309.6877	text	January 2013
Anomalous decay and scattering processes of the eta meson Kubis, Bastian; Plenter, Judith arXiv https://doi.org/10.48550/arxiv.1504.02588	text	January 2015
Roy-Steiner-equation analysis of pion-nucleon scattering Hoferichter, Martin; de Elvira, Jacobo Ruiz; Kubis, Bastian arXiv https://doi.org/10.48550/arxiv.1510.06039	text	January 2015
Dispersion relation for hadronic light-by-light scattering: two-pion contributions Colangelo, Gilberto; Hoferichter, Martin; Procura, Massimiliano arXiv https://doi.org/10.48550/arxiv.1702.07347	text	January 2017
A new parametrization for the scalar pion form factors Ropertz, Stefan; Hanhart, Christoph; Kubis, Bastian arXiv https://doi.org/10.48550/arxiv.1809.06867	text	January 2018
Review of Particle Physics Group, Particle Data; Amsler, C.; Doser, M. Elsevier https://doi.org/10.5167/uzh-11249	text	January 2008
Codata Recommended Values Of The Fundamental Physical Constants: 2014 Mohr, Peter J.; Newell, David B.; Taylor, Barry N. Zenodo https://doi.org/10.5281/zenodo.22826	text	January 2015
Hadronic contribution to the muon anomalous magnetic moment to next-to-next-to-leading order Kurz, A.; Liu, T.; Marquard, P. Karlsruhe https://doi.org/10.5445/ir/1000041343	text	January 2014
Rescattering Effects in the Hadronic-Light-by-Light Contribution to the Anomalous Magnetic Moment of the Muon Stoffer, Peter; Procura, Massimiliano; Hoferichter, Martin American Physical Society https://doi.org/10.7892/boris.102039	text	January 2017
Dispersion relation for hadronic light-by-light scattering: two-pion contributions Procura, Massimiliano; Stoffer, Peter; Hoferichter, Martin Springer https://doi.org/10.7892/boris.102040	text	January 2017
Towards a data-driven analysis of hadronic light-by-light scattering Stoffer, Peter; Colangelo, Gilberto; Hoferichter, Martin Elsevier https://doi.org/10.7892/boris.60231	text	January 2014
Remarks on higher-order hadronic corrections to the muon g-2 Colangelo, Gilberto; Stoffer, Peter; Hoferichter, Martin Elsevier https://doi.org/10.7892/boris.60233	text	January 2014
Dispersive approach to hadronic light-by-light scattering Stoffer, Peter; Procura, Massimiliano; Colangelo, Gilberto Springer https://doi.org/10.7892/boris.60234	text	January 2014

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Implications for Electric Dipole Moments of a Leptoquark Scenario for the $B$-Physics Anomalies Altmannshofer, Wolfgang; Gori, Stefania; Patel, Hiren H. arXiv https://doi.org/10.48550/arxiv.2002.01400	text	January 2020
b → sℓ+ℓ− transitions in two-Higgs-doublet models Crivellin, Andreas; Müller, Dario; Wiegand, Christoph Journal of High Energy Physics, Vol. 2019, Issue 6 https://doi.org/10.1007/jhep06(2019)119	journal	June 2019
Three-pion contribution to hadronic vacuum polarization Hoferichter, Martin; Hoid, Bai-Long; Kubis, Bastian Journal of High Energy Physics, Vol. 2019, Issue 8 https://doi.org/10.1007/jhep08(2019)137	journal	August 2019
g − 2 of charged leptons, α ( M Z 2 ) , and the hyperfine splitting of muonium Keshavarzi, Alexander; Nomura, Daisuke; Teubner, Thomas Physical Review D, Vol. 101, Issue 1 https://doi.org/10.1103/physrevd.101.014029	journal	January 2020
Rho resonance, timelike pion form factor, and implications for lattice studies of the hadronic vacuum polarization Erben, Felix; Green, Jeremy R.; Mohler, Daniel Physical Review D, Vol. 101, Issue 5 https://doi.org/10.1103/physrevd.101.054504	journal	March 2020
A dispersive analysis of the pion vector form factor and $$\tau ^{-}\rightarrow K^{-}K_{S}\nu _{\tau }$$ τ - → K - K S ν τ decay Gonzàlez-Solís, Sergi; Roig, Pablo The European Physical Journal C, Vol. 79, Issue 5 https://doi.org/10.1140/epjc/s10052-019-6943-9	journal	May 2019
Rho Resonance, Timelike Pion Form Factor, and Implications for Lattice Studies of the Hadronic Vacuum Polarisation Erben, Felix; Green, Jeremy R.; Mohler, Daniel Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2020-00201	text	January 2019
Rho resonance, timelike pion form factor, and implications for lattice studies of the hadronic vacuum polarization Erben, Felix; Green, Jeremy; Mohler, Daniel Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2020-01787	text	January 2020
Three-pion contribution to hadronic vacuum polarization Hoferichter, Martin; Hoid, Bai-Long; Kubis, Bastian arXiv https://doi.org/10.48550/arxiv.1907.01556	text	January 2019
Rho resonance, timelike pion form factor, and implications for lattice studies of the hadronic vacuum polarisation Erben, Felix; Green, Jeremy R.; Mohler, Daniel arXiv https://doi.org/10.48550/arxiv.1910.01083	text	January 2019
b → sℓ+ℓ− transitions in two-Higgs-doublet models Crivellin, Andreas; Müller, Dario; Wiegand, Christoph Springer https://doi.org/10.5167/uzh-174366	text	January 2019
b → sℓ+ℓ− transitions in two-Higgs-doublet models Crivellin, Andreas; Müller, Dario; Wiegand, Peter Christoph Springer https://doi.org/10.7892/boris.132253	text	January 2019

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