Journal of High Energy Physics

, 2015:74 | Cite as

Dispersion relation for hadronic light-by-light scattering: theoretical foundations

  • Gilberto Colangelo
  • Martin Hoferichter
  • Massimiliano Procura
  • Peter Stoffer
Open Access
Regular Article - Theoretical Physics

Abstract

In this paper we make a further step towards a dispersive description of the hadronic light-by-light (HLbL) tensor, which should ultimately lead to a data-driven evaluation of its contribution to (g − 2) μ . We first provide a Lorentz decomposition of the HLbL tensor performed according to the general recipe by Bardeen, Tung, and Tarrach, generalizing and extending our previous approach, which was constructed in terms of a basis of helicity amplitudes. Such a tensor decomposition has several advantages: the role of gauge invariance and crossing symmetry becomes fully transparent; the scalar coefficient functions are free of kinematic singularities and zeros, and thus fulfill a Mandelstam double-dispersive representation; and the explicit relation for the HLbL contribution to (g − 2) μ in terms of the coefficient functions simplifies substantially. We demonstrate explicitly that the dispersive approach defines both the pion-pole and the pion-loop contribution unambiguously and in a model-independent way. The pion loop, dispersively defined as pion-box topology, is proven to coincide exactly with the one-loop scalar QED amplitude, multiplied by the appropriate pion vector form factors.

Keywords

Chiral Lagrangians QCD 

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) 2015

Authors and Affiliations

  • Gilberto Colangelo
    • 1
  • Martin Hoferichter
    • 2
    • 3
    • 4
    • 1
  • Massimiliano Procura
    • 5
    • 1
  • Peter Stoffer
    • 6
    • 1
  1. 1.Albert Einstein Center for Fundamental Physics, Institute for Theoretical PhysicsUniversity of BernBernSwitzerland
  2. 2.Institut für KernphysikTechnische Universität DarmstadtDarmstadtGermany
  3. 3.ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbHDarmstadtGermany
  4. 4.Institute for Nuclear TheoryUniversity of WashingtonSeattleUnited States
  5. 5.Fakultät für PhysikUniversität WienWienAustria
  6. 6.Helmholtz-Institut für Strahlen- und Kernphysik (Theory) and Bethe Center for Theoretical PhysicsUniversity of BonnBonnGermany

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