The Lamb shift in muonic hydrogen and the electric rms radius of the proton

Abstract

The "proton radius puzzle" is the 7-standard-deviations difference of the charge radius of the proton as determined from the Lamb shift in electronic hydrogen and elastic electron scattering off the proton on the one side and the high precision determination from the Lamb shift in muonic hydrogen on the other side. So far the explanation of this difference has been mostly searched for in the limitations of the non-muonic experiments as the extrapolation to $Q^2 \rightarrow 0$ GeV$^2$ for electron scattering. Since the time scale of the vacuum polarization $e^+e^--$pairs, causing the bulk contribution of the Lamb shift in muonic hydrogen, is very much shorter than that of the photon exchanges, causing the Coulomb interaction, it is argued that the muon on its orbit around the proton has to be considered as quasi particle dressed by $e^+e^--$pairs and may not be treated as a bare particle in an external Uehling potential. The proper realization of this view makes the proton radius puzzle disappear. The value for the rms charge radius of the proton determined from the muonic Lamb shift, taking this distinction into account, is $r_p = 0.87455(48) \textrm{fm}$ in agreement with the CODATA-2010 value.