Mass divergences in annihilation processes. II. Cancellation of divergences in cut vacuum polarization diagrams

The cancellation of mass divergences in cut vacuum polarization diagrams is investigated. Ensembles of states are identified, the summation over which produces transition probabilities which are free of mass divergences. States included in these ensembles can be characterized as having a "jetlike" structure. The reasoning is extended to a large class of renormalizable field theories, including non-Abelian gauge theories.