Two-Loop Self-Energy Corrections to the Fine Structure
We investigate two-loop higher order binding corrections to the fine structure, which contribute to the spin-dependent part of the Lamb shift. Our calculation focuses on the so-called 'two-loop self-energy' involving two virtual closed photon loops. For bound states, this correction has proved to be notoriously difficult to evaluate. The calculation of the binding corrections to the bound-state two-loop self-energy is simplified by a separate treatment of hard and soft virtual photons. The two photon-energy scales are matched at the end of the calculation. We explain the significance of the mathematical methods employed in the calculation in a more general context, and present results for the fine-structure difference of the two-loop self-energy through the order of α8.
U. D. Jentschura and K. Pachucki, "Two-Loop Self-Energy Corrections to the Fine Structure," Journal of Physics A: Mathematical and General, vol. 35, no. 8, pp. 1927-1942, IOP Publishing, Mar 2002.
The definitive version is available at https://doi.org/10.1088/0305-4470/35/8/310
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