  In view of the recently observed discrepancy of theory and experiment for
muonic hydrogen [R. Pohl et al., Nature vol. 466, p. 213 (2010)], 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 < r^3 >_2 in the determination of the
proton radius from the measurement is estimated. An updated theoretical
prediction for the 2S-2P transition is given.
