Nonresonant effects in the two-photon spectroscopy of a hydrogen atom: application to the calculation of the charge radius of the proton

A discrepancy of 4$\sigma$ ($\sigma$ is the standard deviation) between the proton radii obtained by measuring transition frequencies in electron (H) and muonic ($\mu$H) hydrogen atoms has been actively discussed in the last decade. Theoretical and experimental efforts are focused on the test of this discrepancy and search for effects removing it. Recent measurements of the 2s–4p transition and the Lamb shift in the electron hydrogen atom approach the solution of the “proton radius puzzle”. The rms proton radius rp calculated from these experimental data is 0.8335(95) fm, which is in agreement within the indicated errors with a value of 0.84087(39) fm obtained from experiment with muon hydrogen. This agreement between the results has been achieved by including interference effects appearing in the processes of single-photon scattering on the hydrogen atom, whereas experiments on muonic hydrogen are insensitive to these effects. However, the charge radius of the proton cannot be calculated taking into account only single-photon transitions and measured frequencies corresponding to two-photon transitions should be taken into account. In this work, it has been shown that interference effects in the 2s-nd transitions in the hydrogen atom can make a significant contribution to the determination of the charge radius of the proton and Rydberg constant.