Pion-pole contribution to hadronic light-by-light scattering in the anomalous magnetic moment of the muon
Martin Hoferichter🇺🇸 · Bai-Long Hoid🇩🇪 · Bastian Kubis🇩🇪 · Stefan Leupold🇸🇪 · Sebastian P. Schneider🇩🇪
The pole constitutes the lowest-lying singularity of the hadronic light-by-light (HLbL) tensor, and thus provides the leading contribution in a dispersive approach to HLbL scattering in the anomalous magnetic moment of the muon . It is unambiguously defined in terms of the doubly-virtual pion transition form factor, which in principle can be accessed in its entirety by experiment. We demonstrate that, in the absence of a direct measurement, the full space-like doubly-virtual form factor can be reconstructed very accurately based on existing data for , , and the decay width. We derive a representation that incorporates all the low-lying singularities of the form factor, matches correctly onto the asymptotic behavior expected from perturbative QCD, and is suitable for the evaluation of the loop integral. The resulting value, , for the first time, represents a complete data-driven determination of the pion-pole contribution with fully controlled uncertainty estimates. In particular, we show that already improved singly-virtual measurements alone would allow one to further reduce the uncertainty in .