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

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 ({pi}{sup 0},{eta},{eta}{sup '}) meson-exchange diagram is commensurate with previous calculations. In our calculation of the quark-loop contribution we improve upon previous approaches by explicitly implementing constraints due to gauge invariance. The impact of transverse contributions, presumably dominated by vector-meson poles, are only estimated at this stage. As a consequence, our value a{sub {mu}}{sup LBL;quarkloop}=(136{+-}59)x10{sup -11} is significantly larger. Taken at face value, this then leads to a revised estimate of the total a{sub {mu}=}116 591 891.0(105.0)x10{sup -11}.