New Determination of the Fine Structure Constant from the Electron $g$ Value and QED

Quantum electrodynamics (QED) predicts a relationship between the dimensionless magnetic moment of the electron ($g$) and the fine structure constant ($\alpha$). A new measurement of $g$ using a one-electron quantum cyclotron, together with a QED calculation involving 891 eighth-order Feynman diagrams, determine ${\alpha }^{-1}=137.035999710(96)[0.70\mathrm{ppb}]$. The uncertainties are 10 times smaller than those of nearest rival methods that include atom-recoil measurements. Comparisons of measured and calculated $g$ test QED most stringently, and set a limit on internal electron structure.

Figure 1

The least uncertain $\alpha$ determinations [3, 5, 6] (a), with older determinations [2] on a 10 times larger scale (b). Measured $g$ are converted to $\alpha$ using current QED theory.

Figure 2

Contributions to $g/2$ for the experiment (green), terms in the QED series (black), and from short-distance physics (blue). Uncertainties are in red. The $\mu$, $\tau$, and $\mu \tau$ indicate terms dependent on mass ratios $m_e/m_{\mu }$, $m_e/m_{\tau }$ and the two ratios, $m_e/m_{\mu }$ and $m_e/m_{\tau }$, respectively.

Figure 3

Typical diagrams from each gauge invariant subgroup that contributes to the eighth-order electron magnetic moment. Solid and wiggly curves represent the electron and photon, respectively. Solid horizontal lines represent the electron in an external magnetic field.