Logarithms of alpha in QED bound states from the renormalization group

Details Logarithms of alpha in QED bound states from the renormalization group Logarithms of alpha in QED bound states from the renormalization group

2000-04-04

arxiv.org/abs/hep-ph/0004018v1

Phys.Rev.Lett. 85 (2000) 2248-2251

Physics

High Energy Physics

High Energy Physics - Phenomenology

4 pages

Scientific paper

10.1103/PhysRevLett.85.2248

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.

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