Origin of the $5\,\sigma$ gap between cesium and rubidium $\alpha$
In plain words
Two labs measured $\alpha$ by timing how fast an atom moves after absorbing a photon, one with cesium and one with rubidium, and their answers differ by more than five times their stated errors. At least one experiment has an error nobody has found.
Precise statement
Atom-interferometric photon-recoil determinations give $\alpha^{-1}(\mathrm{Cs},\ \mathrm{Berkeley}\ 2018) = 137.035999046(27)$ and $\alpha^{-1}(\mathrm{Rb},\ \mathrm{LKB}\ 2020) = 137.035999206(11)$, a $5.4\,\sigma$ difference. Identify the systematic effect (or new physics distinguishing the two species) responsible, or produce new $h/m_{\mathrm{Cs}}$ and $h/m_{\mathrm{Rb}}$ values that agree at the 0.1 ppb level.
What would settle it
An independent remeasurement of h/m for Cs or Rb (or both) at below 0.1 ppb with a fully re-evaluated error budget that either reproduces one value or exposes a specific missing systematic.
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.
As of 2025 the gap is unexplained and no new h/m result at the required level has been published.
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