The Complete α8m Contributions to the 1s Lamb Shift in Hydrogen

Precision studies of simple atoms, such as hydrogen, play an essential role in tests of bound-state QED and determining fundamental constants, such as the Rydberg constant and the proton charge radius. One of the QED predictions is for the Lamb shift of hydrogenic energy levels and, in particular, of the ground state. The value of the $$1s$$ Lamb shift in hydrogen and deuterium is required for an accurate determination of the Rydberg constant and the proton charge radius utilizing data from high-resolution spectroscopy of hydrogen and deuterium atoms, as well as for precision tests of bound-state QED. The dominant QED contribution to the uncertainty is due to the $${{\alpha }^{8}}m$$ external-field contributions. We discuss here our recent results on the two- and three-loop contributions, which essentially reduce the theoretical uncertainty. Combined with recent calculations of Laporta on the slope of the Dirac form factor in the three-loop level, our results allow for completion of calculations of $${{\alpha }^{8}}m$$ contributions to the Lamb shift of the ground state in the hydrogen atom.