Trying to understand scattering for non-relativistic toy models of QED, and in particular in the massless case (i.e. long range interactions) is an active area of research in mathematical physics. You can for instance look at the article
<a href="https://link.springer.com/article/10.1007%2Fs00023-011-0156-6">"Towards a Construction of Inclusive Collision Cross-Sections in the Massless Nelson Model"</a> in AHP 2012 by <a href="https://www-m5.ma.tum.de/Allgemeines/WojciechDybalski">Wojciech Dybalski</a> who is an expert in the field.