Hadronic contributions to the anomalous magnetic moment of the muon

Abstract

We present a new, completely revised calculation of the muon anomalous magnetic moment ${a}_{\ensuremath{\mu}}=({g}_{\ensuremath{\mu}}\ensuremath{-}2)/2$ comparing it with the more recent experimental determination of this quantity; this furnishes an important test of theories of strong, weak, and electromagnetic interactions. These theoretical determinations give the very precise numbers, ${10}^{11}\ifmmode\times\else\texttimes\fi{}{a}_{\ensuremath{\mu}}=116\text{ }591\text{ }806\ifmmode\pm\else\textpm\fi{}50\ifmmode\pm\else\textpm\fi{}10(\mathrm{rad})\ifmmode\pm\else\textpm\fi{}30(\ensuremath{\ell}\ifmmode\times\else\texttimes\fi{}\ensuremath{\ell})\text{ }\phantom{\rule{0ex}{0ex}}[\mathrm{Theory},\mathrm{no}\text{ }\text{ }\ensuremath{\tau}]$ and ${10}^{11}\ifmmode\times\else\texttimes\fi{}{a}_{\ensuremath{\mu}}=116\text{ }591\text{ }889\ifmmode\pm\else\textpm\fi{}49\ifmmode\pm\else\textpm\fi{}10(\mathrm{rad})\ifmmode\pm\else\textpm\fi{}30(\ensuremath{\ell}\ifmmode\times\else\texttimes\fi{}\ensuremath{\ell})\text{ }[\mathrm{Theory},\ensuremath{\tau}]$ to be compared with the experimental number, ${10}^{11}\ifmmode\times\else\texttimes\fi{}{a}_{\ensuremath{\mu}}=116\text{ }592\text{ }080\ifmmode\pm\else\textpm\fi{}60$. In the theoretical evaluations, the first quantity does not, and the second one does, use information from $\ensuremath{\tau}$ decay. The first errors for the theoretical evaluations include statistical plus systematic errors; the other ones are the estimated errors due to incomplete treatment of radiative corrections and the estimated error in the light-by-light scattering contribution. We thus have a significant mismatch between theory and experiment. We also use part of the theoretical calculations to give a precise evaluation of the electromagnetic coupling on the $Z$, ${\overline{\ensuremath{\alpha}}}_{\mathrm{QED}}({M}_{Z}^{2})$, of the masses and widths of the (charged and neutral) rho resonances, of the scattering length and effective range for the $P$ wave in $\ensuremath{\pi}\ensuremath{\pi}$ scattering, and of the quadratic radius and second coefficient of the pion form factor.