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.

Research highlights
► The QED theory of muonic hydrogen energy levels is verified and updated.
► Previously obtained results of Pachucki and Borie are confirmed.
► The influence of the vacuum polarization potential onto the Bethe logarithm is calculated nonperturbatively.
► A model-independent estimate of the Zemach moment correction is given.
► Parametrically, the observed discrepancy of theory and experiment is shown to be substantial and large.