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Two-pion contribution to hadronic vacuum polarization

  • Gilberto Colangelo
  • Martin Hoferichter
  • Peter StofferEmail author
Open Access
Regular Article - Theoretical Physics
  • 35 Downloads

Abstract

We present a detailed analysis of e+eπ+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 μ ππ |≤ 1 GeV = 495.0(1.5)(2.1) × 10− 10 and a μ ππ |≤ 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, 〈r π 2 〉 = 0.429(1)(4) fm2.

Keywords

Chiral Lagrangians Effective Field Theories Nonperturbative Effects Precision QED 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Gilberto Colangelo
    • 1
  • Martin Hoferichter
    • 2
  • Peter Stoffer
    • 3
    Email author
  1. 1.Albert Einstein Center for Fundamental Physics, Institute for Theoretical PhysicsUniversity of BernBernSwitzerland
  2. 2.Institute for Nuclear TheoryUniversity of WashingtonSeattleU.S.A.
  3. 3.Department of PhysicsUniversity of California at San DiegoLa JollaU.S.A.

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