Double-Logarithmic Two-Loop Self-Energy Corrections to the Lamb Shift

Abstract

Self-energy corrections involving logarithms of the parameter Zalpha can often be derived within a simplified approach, avoiding calculational difficulties typical of the problematic non-logarithmic corrections (as customary in bound-state quantum electrodynamics, we denote by Z the nuclear charge number, and by alpha the fine-structure constant). For some logarithmic corrections, it is sufficient to consider internal properties of the electron characterized by form factors. We provide a detailed derivation of related self-energy ``potentials'' that give rise to the logarithmic corrections; these potentials are local in coordinate space. We focus on the double-logarithmic two-loop coefficient B_62 for P states and states with higher angular momenta in hydrogenlike systems. We complement the discussion by a systematic derivation of B_62 based on nonrelativistic quantum electrodynamics (NRQED). In particular, we find that an additional double logarithm generated by the loop-after-loop diagram cancels when the entire gauge-invariant set of two-loop self-energy diagrams is considered. This double logarithm is not contained in the effective-potential approach.

14 pages, 1 figure; references added and typographical errors corrected; to appear in Phys. Rev. A

References in corpus (5)

• Logarithmic two-loop corrections to the Lamb shift in hydrogen
• Two-loop self-energy correction in H-like ions
• Two-Loop Self-Energy Corrections to the Fine-Structure
• Radiative-Recoil Corrections of Order $\alpha (Z\alpha {)}^5(m/M)m$ to Lamb Shift Revisited
• Breit Hamiltonian and QED Effects for Spinless Particles

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• Two-Loop Bethe Logarithms for non-S Levels
• Two-Loop Bethe Logarithms for Higher Excited S Levels
• Two-Loop QED Bound-State Calculations and Squared Decay Rates