Single-transverse-photon contributions of order α⁶ln (α) to the energy levels of positronium

Some of the calculational techniques used to compute the order α⁶ln(α^-1) contribution to the energies of the 1s and 2s states of positronium reported in an earlier paper [Fell, Phys. Rev. Lett. 68, 25 (1992)] are demonstrated. Recently, this same calculation was done by an independent group [Khriplovich, Milstein, and Yelkhovsky, Phys. Lett. B 283, 237 (1992)]. Although the initial results of the two calculations did not agree, this discrepancy has since been resolved in favor of the calculation presented here. We discuss the two calculations and then compare the theoretical and experimental values of the n=2 fine structure and the triplet 2s-1s splitting.