Why two 1S-3S hydrogen measurements give different proton radii
In plain words
Two labs measured the same hydrogen line and extracted proton sizes that disagree by more than two standard errors. Finding why would tell which systematic effects affect such experiments.
Precise statement
The LKB Paris 1S-3S measurement (Fleurbaey et al 2018) gives $r_p = 0.877(13)\,\mathrm{fm}$, while the MPQ Garching 1S-3S measurement (Grinin et al 2020) gives $r_p = 0.8482(38)\,\mathrm{fm}$. Identify the systematic shift (second-order Doppler, quantum interference of neighboring lines, light shift, pressure shift) responsible for the difference of about 6 kHz (2.1 combined sigma) in the 1S-3S transition frequency.
What would settle it
A remeasurement of 1S-3S in the LKB apparatus with a revised line-shape model that agrees with the Garching value, or a third 1S-3S measurement.