Remarks on the effect of bound states and threshold in g-2
  Recently, the contribution of positronium bound states to the electron anomalous magnetic moment was computed in Refs.[1,2]. It was argued there that this O(alpha^5) contribution is missed if electron g-2 is calculated within conventional perturbative QED and, as such, it must be added to the perturbative five-loop result. We show that this conclusion is flawed and that no additional contributions to g-2 are generated in QED beyond the perturbation theory. 
Kirill Melnikov, Arkady Vainshtein and Mikhail Voloshin
hep-ph