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Home > Journal of High Energy Physics (Springer/SISSA) > Dispersion relation for hadronic light-by-light scattering: theoretical foundations |

Colangelo, Gilberto (Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, 3012, Bern, Switzerland) ; Hoferichter, Martin (Institut für Kernphysik, Technische Universität Darmstadt, 64289, Darmstadt, Germany) (ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291, Darmstadt, Germany) (Institute for Nuclear Theory, University of Washington, Seattle, WA, 98195-1550, United States) (Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, 3012, Bern, Switzerland) ; Procura, Massimiliano (Fakultät für Physik, Universität Wien, Boltzmanngasse 5, 1090, Wien, Austria) (Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, 3012, Bern, Switzerland) ; Stoffer, Peter (Helmholtz-Institut für Strahlen- und Kernphysik (Theory) and Bethe Center for Theoretical Physics, University of Bonn, 53115, Bonn, Germany) (Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, 3012, Bern, Switzerland)

15 September 2015

**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.

**Published in: ****JHEP 1509 (2015) 074**
**Published by: **Springer/SISSA

**DOI: **10.1007/JHEP09(2015)074

**arXiv: **1506.01386

**License: **CC-BY-4.0