Renormalization-group improvement of the spectrum of hydrogenlike atoms with massless fermions

We. obtain the next-to-next-to-leading-logarithmic renormalization-group improvement of the spectrum of hydrogenlike atoms with massless fermions by using potential NRQED. These results can also be applied to the computation of the muonic hydrogen spectrum where we are able to reproduce some known double logarithms at O(malpha(s)(6)). We compare with other formalisms dealing with logarithmic resummation available in the literature.