Hadronic contribution to the muon g-2 from a Dyson-Schwinger perspective

A novel approach towards the hadronic contributions to the anomalous magnetic moment of the muon $a_μ$ is presented, namely the Dyson-Schwinger equations of QCD. It has the advantage of being valid for all momentum scales and has the potential to address off-shell amplitudes. We present our first results for the pseudoscalar (PS) meson exchange and the quark loop contributions. The meson exchange ($π^0, η, η'$), $a_μ^{\textrm{LBL;PS}}=(84 \pm 13)\times 10^{-11}$, is commensurate with previous calculations, while the quark loop contribution $a_μ^{\textrm{LBL;quarkloop}} = (107 \pm 48)\times 10^{-11}$, is strongly enhanced by vertex dressing effects in the quark photon vertex. Taken seriously this leads to the estimate of $a_μ=116\,591\,865.0(96.6)\times 10^{-11}$, giving a 1.9 $σ$ deviation between theory and experiment.

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