Residual tensions in proton radius and Rydberg constant determinations
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
In 2010 muonic hydrogen (a muon orbiting a proton) gave a proton about 4% smaller than electron measurements did. New hydrogen measurements now agree with the small value, but some older hydrogen and scattering results still give the large value.
Precise statement
Muonic hydrogen gives $r_p = 0.84087(39)\,\mathrm{fm}$ and the 2026 hydrogen 2S-6P measurement (Maisenbacher et al) gives $0.8406(15)\,\mathrm{fm}$, while the LKB 1S-3S (2018), H 2S-8D (2022) and Mainz electron scattering ($0.879\,\mathrm{fm}$) determinations favor larger values. Establish whether all hydrogen lines, combined with 1S-2S, yield a single $(R_{\infty}, r_{p})$ pair consistent at the $10^{-12}$ level in $R_{\infty}$.
What would settle it
A global fit of all hydrogen and deuterium transition frequencies, with outliers explained by identified systematics, giving $R_{\infty}$ and $r_p$ consistent with muonic values within uncertainties.
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 2026 $2\mathrm{S}-6\mathrm{P}$ measurement agrees with muonic hydrogen and tests bound-state QED at 0.5 ppm; CODATA 2022 still reports a $2.8\sigma$ difference between hydrogen-only and muonic data.
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