  A novel approach towards the hadronic contributions to the anomalous magnetic
moment of the muon $a_{\mu}$ 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 ($\pi^0, \eta, \eta'$), $a_\mu^{\textrm{LBL;PS}}=(84 \pm 13)\times
10^{-11}$, is commensurate with previous calculations, while the quark loop
contribution $a_\mu^{\textrm{LBL;quarkloop}} = (107 \pm 48)\times 10^{-11}$, is
strongly enhanced by vertex dressing effects in the quark photon vertex. Taken
seriously this leads to the estimate of $a_\mu=116\,591\,865.0(96.6)\times
10^{-11}$, giving a 1.9 $\sigma$ deviation between theory and experiment.

High Energy Physics - Phenomenology;Nuclear Theory