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

Author(s)
Gilberto Colangelo, Martin Hoferichter, Massimiliano Procura, Peter Stoffer
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)(mu). 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 doubledispersive representation; and the explicit relation for the HLbL contribution to (g - 2)(mu) 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
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
103012 High energy physics, 103014 Nuclear physics
Keywords
Portal url
https://ucris.univie.ac.at/portal/en/publications/dispersion-relation-for-hadronic-lightbylight-scattering-theoretical-foundations(b2620839-a5f2-437d-9902-fb9d1cbf43db).html