An Alternative Approach to the Proton Radius Puzzle

Rydberg-state transitions in atomic hydrogen are calculated as an alternative route to addressing the proton radius puzzle without the need of taking into account cross-damping terms and details of experimental line shapes. The proton radius puzzle concerns the discrepancy in the determination of the root-mean-square proton radius from muonic hydrogen transitions versus other experiments that involve both electron scattering as well as precision measurements of transitions in ordinary atomic hydrogen. Specifically, since 2018, certain measurements of atomic hydrogen transitions have resulted in a reported proton radius between, roughly, 0.86 and 0.88 fermi, while muonic hydrogen experiments indicate a value of roughly 0.84 fermi, consistent with other recent measurements that support a smaller proton radius. Many of the precision measurements that indicate a smaller proton radius heavily rely on a very involved analysis of the experimental line shape, which in some cases has to be split to better than one permille in order to access the proton radius. Combining recent theoretical calculations of QED effects and recent advances in laser technology, we find that, with moderate effort, Rydberg-state transitions between atomic hydrogen states with principal quantum numbers around n=18, could lead to a conclusive resolution of the proton radius puzzle, without the need of an excessive splitting of the resonance line. It is crucial to observe that the Rydberg constant and the proton radius are linked through high-precision spectroscopy.