%0 Journal Article
%T Logarithms of alpha in QED bound states from the renormalization group
%A Aneesh V. Manohar
%A Iain W. Stewart
%J Physics
%D 2000
%I arXiv
%R 10.1103/PhysRevLett.85.2248
%X The velocity renormalization group is used to determine ln(alpha) contributions to QED bound state energies. The leading order anomalous dimension for the potential gives the alpha^5 ln(alpha) Bethe logarithm in the Lamb shift. The next-to-leading order anomalous dimension determines the alpha^6 ln(alpha), alpha^7 ln^2(alpha), and alpha^8 ln^3 (alpha) corrections to the energy. These are used to obtain the alpha^8 ln^3(alpha) Lamb shift and alpha^7 ln^2(alpha) hyperfine splitting for Hydrogen, muonium and positronium, as well as the alpha^2 ln(alpha) and alpha^3 ln^2(alpha) corrections to the ortho- and para-positronium lifetimes.
%U http://arxiv.org/abs/hep-ph/0004018v1