The Rydberg constant and proton size from atomic hydrogen

At the core of the “proton radius puzzle” is a four–standard deviation discrepancy between the proton root-mean-square charge radii (r p) determined from the regular hydrogen (H) and the muonic hydrogen (μp) atoms. Using a cryogenic beam of H atoms, we measured the 2S-4P transition frequency in H, yielding the values of the Rydberg constant R ∞ = 10973731.568076(96) per meter and r p = 0.8335(95) femtometer. Our r p value is 3.3 combined standard deviations smaller than the previous H world data, but in good agreement with the μp value. We motivate an asymmetric fit function, which eliminates line shifts from quantum interference of neighboring atomic resonances.