Theory of the 2S–2P Lamb shift and 2S hyperfine splitting in muonic hydrogen

The 7σ7σ discrepancy between the proton rms charge radius from muonic hydrogen and the CODATA-2010 value from hydrogen spectroscopy and electron-scattering has caused considerable discussions. Here, we review the theory of the 2S–2P Lamb shift and 2S hyperfine splitting in muonic hydrogen combining the published contributions and theoretical approaches. The prediction of these quantities is necessary for the determination of both proton charge and Zemach radii from the two 2S–2P transition frequencies measured in muonic hydrogen; see Pohl et al. (2010) [9] and Antognini et al. (2013) [71].

► We update the theory of Lamb shift and hyperfine splitting in muonic hydrogen.
► We found no large error or missing contribution larger than 0.001 meV.
► We critically discuss the proton-structure-dependent contributions.
► The proton radius puzzle still remains.