Nine $\sigma$ discrepancy in the ionization energy of metastable helium
In plain words
Helium has two electrons, which makes its energy levels harder to compute than hydrogen's, but theory now claims sub-MHz accuracy. The measured binding energy of a long-lived excited state disagrees with this theory by nine standard errors.
Precise statement
The measured ionization energy of $\mathrm{He}\,(1\mathrm{s})(2\mathrm{s})\,2^{3}\mathrm{S}_1$ is $1152842742.7082(60)\,\mathrm{MHz}$ (Clausen et al 2025), versus the theoretical $1152842742.231(52)\,\mathrm{MHz}$ (Patkos, Yerokhin, Pachucki), a $9\sigma$ difference; a similar $7\sigma$ deviation affects $2^{1}\mathrm{S}_0$. Identify whether the error lies in the $\alpha^{7} m$ QED contribution, higher-order terms, or the experiments.
What would settle it
An independent complete $\alpha^{7} m$ calculation for helium singlet and triplet S states, or an independent measurement of the same ionization energy with a different method.
Status in the literature
Unverified note
The 2025 ETH Zurich Rydberg-series measurement improved precision five-fold and confirmed the discrepancy.