Dispersion relation for hadronic light-by-light scattering

^a CERN Theory Division, 1211 Geneva 23, Switzerland
^b Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, 3012 Bern, Switzerland
^c Institute for Nuclear Theory, University of Washington, Seattle, WA 98195-1550, USA
^d Helmholtz-Institut für Strahlen- und Kernphysik (Theory) and Bethe Center for Theoretical Physics, University of Bonn, 53115 Bonn, Germany

^a e-mail: massimiliano.procura@cern.ch
^b e-mail: gilberto@itp.unibe.ch
^c e-mail: mhofer@uw.edu
^d e-mail: stoffer@hiskp.uni-bonn.de

Published online: 26 April 2016

Abstract

The largest uncertainties in the Standard Model calculation of the anomalous magnetic moment of the muon (g − 2)_μ come from hadronic contributions. In particular, in a few years the subleading hadronic light-by-light (HLbL) contribution might dominate the theory uncertainty. We present a dispersive description of the HLbL tensor, which is based on unitarity, analyticity, crossing symmetry, and gauge invariance. This opens up the possibility of a data-driven determination of the HLbL contribution to (g − 2)_μ with the aim of reducing model dependence and achieving a reliable error estimate.

Our dispersive approach defines unambiguously the pion-pole and the pion-box contribution to the HLbL tensor. Using Mandelstam’s double-spectral representation, we have proven that the pion-box contribution coincides exactly with the one-loop scalar QED amplitude, multiplied by the appropriate pion vector form factors.