Positronium contribution to the electron $g\text{−}2$

The contribution of positronium to the electron $g\text{−}2$ ($a_e$) has been computed in G. Mishima, arXiv:1311.7109, and found to be of the same order of $\alpha$ as that of five-loop perturbative QED. We confirm this result and correct a few errors in its first derivation. As recently calculated in K. Melnikov, A. Vainshtein, and M. Voloshin, arXiv:1402.5690, a continuum nonperturbative contribution to $a_e$ cancels one-half of the positronium one. We show by explicit calculation that the remaining half is already included in the five-loop perturbative result. We also show that it arises from the class I(i) of five-loop diagrams containing only one closed electron loop.

Figure 1

Leading vacuum polarization contribution to $a_e$.

Figure 2

Leading contribution of positronium to $a_e$.