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

Abstract

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 (${\pi }^0,\eta ,{\eta }^{\prime }$), $a_{\mu }^{\text{LBL;PS}}=(84\pm 13)\times 10^{-11}$, is commensurate with previous calculations, while the quark loop contribution $a_{\mu }^{\text{LBL;quarkloop}}=(107\pm 48)\times 10^{-11}$, is strongly enhanced by vertex dressing effects in the quark photon vertex. Taken seriously this leads to the estimate of $a_{\mu }=116591865.0(96.6)\times 10^{-11}$, giving a 1.9 $\sigma$ deviation between theory and experiment.

Comments: 3 pages, 5 figures; Contribution to the proceedings of `Quark Confinement And The Hadron Spectrum IX', Madrid, Sept. 2010