The proton radius puzzle – 9 years later

Abstract

High-precision measurements of the proton radius via scattering, electric hydrogen spectroscopy and muonic hydrogen spectroscopy do not agree on the level of more than 5 σ. This proton radius puzzle persists now for almost a decade. This paper gives a short summary over the progress in the solution of the puzzle as well as an overview over the planned experiments to finally solve this puzzle at the interface of atomic and nuclear physics.

Energy Interval 1S–2S in Muonic Hydrogen and Helium

“…Correction to muon self energy -5.0876 and muon form factors 25 Radiative-recoil corrections of order -0.0724 α(Zα) 5 and proton form factor correction Z 2 α(Zα) 4…”

“…This formula correctly takes into account the recoil correction m 2 1 /m 2 2 (Zα) 4 for nuclei with spin 1/2 [24] (see section 4). Recoil effects of order (Zα) 6 are not taken into account in formula (1) and are discussed in Section 5.…”

“…The Breit potential contributes to the energy of S -states in the leading order (Zα) 4 . The effect of vacuum polarization leads to a change not only in the Coulomb potential, but also in other terms in the Breit potential, which will contribute to the energy spectrum of order α(Zα) 4 . This order of contribution suggests that the numerical values of the corrections can be significant.…”

“…The total contribution of relativistic corrections taking into account the one-loop vacuum polarization is presented in line 8 of Table I. In order to increase the accuracy of the calculation we also take into account the contribution of relativistic corrections with effects of two-loop vacuum polarization of order α 2 (Zα) 4 . The main term in the interaction potential is:…”

“…The contribution to the energy spectrum of the same order α(Zα) 4 is determined by the same effects in the second order of the perturbation theory (see Fig. 7(c)) by the following integral expressions:…”