High-Field Electrong−2Measurement

Abstract

We have measured the $g$-factor anomaly of the free electron to an accuracy of ± 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 $a=\frac{1}{2}\mathrm{}(g-2\mathrm{})\mathrm{}$, we find $a_{\mathrm{expt}}\left(e^{-}\right)=(1159657.7\mathrm{}\pm 3.5)\times {10}^{-9\mathrm{}}$. The difference between this result and the current theoretical expression for $a$, as calculated through second order in the fine-structure constant $\alpha$, is $a_{\mathrm{expt}}\left(e^{-}\right)-\left[0.5\mathrm{}\right(\frac{\alpha }{\pi })-0.32848\mathrm{}{\left(\frac{\alpha }{\pi }\right)}^2]=(1.68\mathrm{}\pm 0.33){\left(\frac{\alpha }{\pi }\right)}^3$. In the above, we have used ${\alpha }^{-1\mathrm{}}=137.03608\mathrm{}\pm 0.00026$, 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 ${\alpha }^{-1\mathrm{}}$. 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 $1.49{\left(\frac{\alpha }{\pi }\right)}^3$.