Dispersion relation for hadronic light-by-light scattering: theoretical foundations
- Author(s)
- Gilberto Colangelo, Martin Hoferichter, Massimiliano Procura, Peter Stoffer
- Abstract
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.
- Organisation(s)
- Particle Physics
- External organisation(s)
- Universität Bern, Technische Universität Darmstadt, GSI Helmholtzzentrum für Schwerionenforschung, University of Washington, Rheinische Friedrich-Wilhelms-Universität Bonn
- Journal
- Journal of High Energy Physics
- Volume
- 2015
- No. of pages
- 77
- ISSN
- 1029-8479
- DOI
- https://doi.org/10.1007/JHEP09(2015)074
- Publication date
- 09-2015
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 103014 Nuclear physics, 103012 High energy physics
- Keywords
- ASJC Scopus subject areas
- Nuclear and High Energy Physics
- Portal url
- https://ucris.univie.ac.at/portal/en/publications/dispersion-relation-for-hadronic-lightbylight-scattering-theoretical-foundations(b2620839-a5f2-437d-9902-fb9d1cbf43db).html