The anomalous magnetic moment of the muon: A review of the theoretical contributions

We review the possible contributions to the muon $g$-factor anomaly, ${\alpha }_{\mu }\equiv \frac{1}{2}(g_{\mu }-2)$ which are potentially significant for a comparison between theory and experiment at present. This includes purely quantum electrodynamic (QED) perturbation theory effects up to eighth order; hadronic effects at fourth and sixth order; and weak interaction effects. From these sources we get a total theoretical contribution ${\alpha }_{\mu }\left(\mathrm{theory}\right)=(1\mathrm{} 165 920.6\pm 12.9)\times {10}^{-9\mathrm{}}$, to be compared with the latest CERN experimental result (Bailey et al., 1975), ${\alpha }_{\mu }\left(\mathrm{experiment}\right)=1\mathrm{} 165 895\pm 27)\times {10}^{-9\mathrm{}}$.