Is the electron magnetic moment anomaly consistent with the Standard Model?
In plain words
The electron behaves like a tiny magnet whose strength has been measured to about one part in ten trillion. Using $\alpha$ from atom experiments, theory predicts the same number, and any mismatch would point to new particles or forces.
Precise statement
With $g/2 = -\mu_e/\mu_B$ measured to 0.13 ppt ($a_e = (g-2)/2$ to 0.11 ppb, absolute uncertainty 1.3e-13; Fan et al 2023) and $a_e(\mathrm{SM})$ computed from $\alpha(\mathrm{recoil})$ plus QED (five-loop coefficient now agreed between two groups), hadronic and electroweak terms, determine whether $\delta a_e = a_e(\mathrm{exp}) - a_e(\mathrm{SM})$ differs from zero; at present $\delta a_e$ has opposite signs for $\alpha(\mathrm{Cs})$ and $\alpha(\mathrm{Rb})$, at roughly $-2.2\ \sigma$ and $+2\ \sigma$. The answer is $\delta a_e$ with total uncertainty below 1e-13 and its significance.
What would settle it
Resolution of the Cs-Rb $\alpha$ discrepancy combined with an improved $a_{e}$ measurement, yielding a single $\delta a_{e}$ with uncertainty below 1e-13.
Status in the literature
Unverified note
The $5\sigma$ disagreement between the two five-loop QED evaluations was removed in December 2024 (arXiv 2412.06473), so the remaining obstacle is the Cs-Rb $\alpha$ discrepancy.