In textbooks when discussing radiative corrections to QED scattering they normally only consider the loops corresponding to the vertex function and corrections to the electron and photon propagators, and also the diagrams for emission of soft photons from external legs (see e.g. Chapter 6, diagram 6.1 in Peskin and Schroeder).
But there are additional loops, for instance electron positron scattering via intermediate two photon annihilation
This diagram has no ultraviolet divergence, but as one of the virtual photon momenta $k\rightarrow 0$ the electron propagators go on shell and there is an infrared divergence.
My question is how is this divergence resolved? My thought is that the electron propagators are modified by the field of the external legs in higher order diagrams, and that shifts the pole by something on the order of a binding energy.
But is this interpretation correct and does it have anything to do with the Lamb shift? How is this divergence dealt with in practice in calculations?
