The hadronic contributions to the anomalous magnetic moment of the muon

Abstract

We present a new, completely revised calculation of the muon anomalous magnetic moment, $a_{\mu }=(g_{\mu }-2)/2$, 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 and experimental determinations give the very precise numbers, $$10^{11}\times a_μ=\cases{116 591 806\pm50\pm10 ({\rm rad.})\pm30 (\ell\times\ell)\quad\hbox{[Th., no $τ$]}\cr 116 591 889\pm49\pm10 ({\rm rad.})\pm30 (\ell\times\ell)\quad\hbox{[Theory, $τ$]}\cr 116 592 080\pm60\quad\hbox{[Experiment]}.\cr}$$ In the theoretical evaluations, the first quantity does not, and the second one does, use information from $\tau$ 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 $Z$, ${\bar{\alpha }}_{Q.E.D.}(M_Z^2)$, of the masses and widths of the (charged and neutral) rho resonances, of the scattering length and effective range for the P wave in $\pi \pi$ scattering, and of the quadratic radius and second coefficient of the pion form factor.

Version to be published by Phys. Rev. D; comparison with other calculations aincluded.Plain TeX; 7 figures; 22 pages