Lamb shift in muonic hydrogen—I. Verification and update of theoretical predictions

In view of the recently observed discrepancy of theory and experiment for muonic hydrogen [R. Pohl et al., Nature 466 (2010) 213], we reexamine the theory on which the quantum electrodynamic (QED) predictions are based. In particular, we update the theory of the 2P–2S Lamb shift, by calculating the self-energy of the bound muon in the full Coulomb + vacuum polarization (Uehling) potential. We also investigate the relativistic two-body corrections to the vacuum polarization shift, and we analyze the influence of the shape of the nuclear charge distribution on the proton radius determination. The uncertainty associated with the third Zemach moment 〈r³〉₂ in the determination of the proton radius from the measurement is estimated. An updated theoretical prediction for the 2S–2P transition is given.