2S-4S spectroscopy in hydrogen atom: The new value for the Rydberg constant and the proton charge radius

The core of the “proton radius puzzle” is the discrepancy of four standard deviations between the proton root mean square charge radii (rp) determined from regular hydrogen (H), and the muonic hydrogen atom (μp). We have measured the 2S-4P transition frequency in H, utilizing a cryogenic beam of H and directly demonstrate that quantum interference of neighboring atomic resonances can lead to line shifts much larger than the proton radius discrepancy. Using an asymmetric fit function we obtain rp = 0.8335(95) fm and the Rydberg constant R∞ = 10 973 731.568 076 (96) m−1. The new value for rp is 3.3 combined standard deviations smaller than the latest CODATA value, but in good agreement with the value from μp.