Nine $\sigma$ discrepancy in the ionization energy of metastable helium
This text mentions work from 2024 on. Those parts were partly written without a live literature search and have not been checked by an editor yet.
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: it names recent work and was partly written without a live literature search; it awaits a check by an editor.
The 2025 ETH Zurich Rydberg-series measurement improved precision five-fold and confirmed the discrepancy.
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