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.
Categories: hep-ph nucl-th