High-Field Electrong−2Measurement

Abstract

We have measured the $g$-factor anomaly of the free electron to an accuracy of \ifmmode\pm\else\textpm\fi{} 3 ppm (68% confidence level). The method (a refinement of that used by Wilkinson and Crane in 1963) is based on a direct observation of the difference between the spin precession and cyclotron frequencies of 100-keV electrons confined in a precisely measured magnetic mirror trap. An order of magnitude increase in precision over the Wilkinson-Crane experiment has been achieved by (a) a tenfold increase in the magnitude of the magnetic field (to 1 kG), and (b) a tenfold reduction in the relative depth of the magnetic trap (to 60 ppm). An extensive series of tests for systematic effects at the 1-ppm level has also been carried out. With $a=\frac{1}{2}(g\ensuremath{-}2)$, we find ${a}_{\mathrm{expt}}({e}^{\ensuremath{-}})=(1159657.7\ifmmode\pm\else\textpm\fi{}3.5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$. The difference between this result and the current theoretical expression for $a$, as calculated through second order in the fine-structure constant $\ensuremath{\alpha}$, is ${a}_{\mathrm{expt}}({e}^{\ensuremath{-}})\ensuremath{-}[0.5(\frac{\ensuremath{\alpha}}{\ensuremath{\pi}})\ensuremath{-}0.32848{(\frac{\ensuremath{\alpha}}{\ensuremath{\pi}})}^{2}]=(1.68\ifmmode\pm\else\textpm\fi{}0.33){(\frac{\ensuremath{\alpha}}{\ensuremath{\pi}})}^{3}$. In the above, we have used ${\ensuremath{\alpha}}^{\ensuremath{-}1}=137.03608\ifmmode\pm\else\textpm\fi{}0.00026$, as recently recommended by Taylor, Parker, and Langenberg. The uncertainty in the coefficient is the rms sum of our experimental error and the uncertainty in ${\ensuremath{\alpha}}^{\ensuremath{-}1}$. In this form, our result can be interpreted as an experimental determination of the sixthorder quantum-electrodynamic contribution to the anomaly. Current estimates of this quantity are $1.49{(\frac{\ensuremath{\alpha}}{\ensuremath{\pi}})}^{3}$.