Measurement of the Electron Magnetic Moment

The electron magnetic moment, $-\mu /{\mu }_B=g/2=1.00115965218059(13)$ [0.13 ppt], is determined 2.2 times more accurately than the value that stood for fourteen years. The most precisely determined property of an elementary particle tests the most precise prediction of the standard model (SM) to 1 part in ${10}^{12}$. The test would improve an order of magnitude if the uncertainty from discrepant measurements of the fine structure constant $\alpha$ is eliminated since the SM prediction is a function of $\alpha$. The new measurement and SM theory together predict ${\alpha }^{-1}=137.035999166(15)$ [0.11 ppb] with an uncertainty 10 times smaller than the current disagreement between measured $\alpha$ values.

Figure 1

This Northwestern determination (red) and our 2008 Harvard determination (blue) [37]. SM predictions (solid and open black points for slightly differing $C_{10}$ [40, 41]) are functions of discrepant $\alpha$ measurements [38, 39]. A ppt is ${10}^{-12}$.

Figure 2

(a) Cryogenic system supports a 50 mK electron trap upon a 4.2 K solenoid to provide a very stable $B$. (b) Silver electrodes of a cylindrical Penning trap. (c) Quantum spin and cyclotron energy levels used for measurement.

Figure 3

Quantum jump cyclotron (a) and anomaly (b) line shapes that are measured (points), predicted (dashed line) and fit (solid line) vs fractional drive detunings from ${\overline{f}}_c(1+\epsilon )$ and ${\overline{\nu }}_a(1+\epsilon )$ (defined later in the text). (c) A dip in Johnson noise reveals ${\overline{\nu }}_z$.

Figure 4

(a) Measured $g/2-1.00115965218059$ before (white) and after (red) cavity-shift correction. (b) Measurements take place in valleys of the cyclotron damping rate where spontaneous emission is inhibited.

Figure 5

SM prediction of $\alpha$ using $\mu /{\mu }_B$ from this Northwestern measurement (red), and from our 2008 Harvard measurement (blue), with solid and open points for slightly differing $C_{10}$ [40, 41]. The $\alpha$ measurements (black) were made with Cs at Berkeley [38] and Rb in Paris [39]. A ppb is ${10}^{-9}$.