Proton size from precision experiments on hydrogen and muonic hydrogen atoms

TL;DR

This paper discusses the resolution of the proton radius puzzle through precision measurements in hydrogen and muonic hydrogen, emphasizing the role of interference effects in atomic transition experiments for accurate proton size determination.

Contribution

It demonstrates that interference effects in two-photon $2s-nd$ transitions significantly impact the measurement of the proton charge radius and Rydberg constant.

Findings

Proton radius from hydrogen experiments aligns with muonic hydrogen results.

Interference effects influence two-photon transition frequency measurements.

Addressing interference effects improves the accuracy of fundamental constant determinations.

Abstract

The "proton radius puzzle" was recently solved by reducing the four-standard deviation discrepancy between the results for electronic hydrogen ($H$) and muonic hydrogen ($\mu H$) atoms to $3.3$ value. The value of the root-mean-square radius of the proton ($r_p$), extracted from experiments on measuring the one-photon $2s-4p$ transition and the Lamb shift in hydrogen, is now $0.8335(95)$ fm, that is in good agreement with the muonic hydrogen experiments, $0.84087(39)$ fm. Even so, these values deviate significantly from the CODATA value, which is determined as the average using the results for various spectral lines including two-photon transitions in the hydrogen atom. The solution of the proton radius puzzle was realized by taking into account the influence of interference effect in one-photon scattering processes. The importance of interfering effects in atomic frequencies measurements gives an impetus to the study of experiments based on two-photon spectroscopy with the suchlike thoroughness. It is shown here that the effect of interfering pathways for two-photon $2s-nd$ transitions in a hydrogen atom is also significant in determining the proton charge radius and Rydberg constant.