Two-Loop Bethe Logarithms

Abstract

We calculate the two-loop Bethe logarithm correction to atomic energy levels in hydrogen-like systems. The two-loop Bethe logarithm is a low-energy quantum electrodynamic (QED) effect involving multiple summations over virtual excited atomic states. Although much smaller in absolute magnitude than the well-known one-loop Bethe logarithm, the two-loop analog is quite significant when compared to the current experimental accuracy of the 1S-2S transition: it contributes -8.19 and -0.84 kHz for the 1S and the 2S state, respectively. The two-loop Bethe logarithm has been the largest unknown correction to the hydrogen Lamb shift to date. Together with the ongoing measurement of the proton charge radius at the Paul Scherrer Institute its calculation will bring theoretical and experimental accuracy for the Lamb shift in atomic hydrogen to the level of 10^(-7).

4 pages, RevTeX

References in corpus (8)

• Theory of Light Hydrogenlike Atoms
• Calculation of the Electron Self Energy for Low Nuclear Charge
• QED theory of the nuclear recoil effect in atoms
• Two-loop self-energy correction in high-Z hydrogen-like ions
• The three loop slope of the Dirac form factor and the 1S Lamb shift in hydrogen
• Logarithmic two-loop corrections to the Lamb shift in hydrogen
• The second-order electron self-energy in hydrogen-like ions
• Radiative energy shifts induced by local potentials

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