Muonic hydrogen and the proton size

We reexamine the structure of the n = 2 levels of muonic hydrogen using a two-body potential that includes all relativistic, recoil and one-loop corrections. The potential was originally derived from QED to describe the muonium atom and accounts for all contributions to order alpha(5). Since one-loop corrections are included, the anomalous magnetic moment contributions of the muon can be identified and replaced by the proton anomalous magnetic moment to describe muonic hydrogen with a pointlike proton. This serves as a convenient starting point to include the dominant electron vacuum polarization corrections to the spectrum and extract the proton's mean squared radius r(p) = root < r(2)>. Our results are consistent with other theoretical calculations that find that the muonic hydrogen value for r(p) is smaller than the result obtained from electron scattering.