Hadronic light-by-light scattering in the muon g-2: a Dyson-Schwinger equation approach

Abstract

We determine the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon using the framework of Dyson-Schwinger and Bethe-Salpeter equations of QCD. Our result for the pseudoscalar ($π^0, η, η'$) meson exchange diagram is commensurate with previous calculations. In our calculation of the quark loop contribution we improve previous approaches by implementing constraints due to gauge invariance. As a consequence, our value $a_μ^{\textrm{LBL;quarkloop}} = (136 \pm 59)\times 10^{-11}$ is significantly larger. Taken at face value, this then leads to a revised estimate of the total $a_μ=116\,591\,891.0(105.0)\times 10^{-11}$.

14 pages, 16 figures, 2 tables. Version to appear in Phys. Rev. D