Hydrogen spectroscopy as a test of the Standard Model to below 1 part per trillion

Precision spectroscopy of atomic hydrogen is an important way to test bound-state quantum electrodynamics (QED), one of the building blocks of the Standard Model. In its simplest form, such a test consists of the comparison of a measured transition frequency with its QED prediction, which can be calculated with very high precision for the hydrogen atom. However, these calculations require some input in the form of physical constants, such as the Rydberg constant and the proton radius, both of which are determined to a large degree by (electronic and muonic) hydrogen spectroscopy itself. Therefore, the frequency of at least three different transitions needs to be measured in order to test QED. Furthermore, there are multiple recent, but discrepant measurements of the proton radius, so far precluding QED tests at the highest accuracy.

To this end, we have measured the 2S-6P transition in atomic hydrogen using Doppler-free one-photon spectroscopy. We achieved a relative uncertainty of 0.7 parts per trillion (ppt), a six-fold improvement over our previous measurement of the 2S-4P transition. This allows us to determine the proton radius with sufficient precision to distinguish between previous, discrepant values for the proton radius by more than 5 standard deviations. Combined with the measurement of the 1S-2S transition and the proton radius determined from muonic hydrogen, our measurement constitutes a test of bound-state quantum electrodynamics to better than 1 part per trillion. Here, we discuss the measurement and its analysis, and present the results and their implications.