Criterion for a Feynman loop diagram to give a finite value

Question

The contribution of loop diagrams in QFT are often divergent and sometimes convergent as well. For example, the self-energy corrections in QED are divergent. On the other hand, the Zee model of radiative neutrino mass (for example) induces a finite neutrino mass at one-loop.

1. Is there a necessary and/or sufficient condition to tell apriori i.e., without computing the loop explicitly that the loop effect is certainly convergent (or certainly divergent)?

2. Are there cases where no such conclusion can be drawn?

This post imported from StackExchange Physics at 2018-07-01 16:52 (UTC), posted by SE-user SRS

Comments

yes. google superficial degree of divergence, irreducible diagrams, Weinberg theorem, Bogoliubov-Parasiuk-Hepp-Zimmermann renormalization scheme, renormalisation to all orders in perturbation theory, etc. There is plenty of information online. Weinberg's QFT, Vol I is also a very good reference. It would be nice if someone could summarise the essential points here though. It is a good/useful question.

This post imported from StackExchange Physics at 2018-07-01 16:52 (UTC), posted by SE-user AccidentalFourierTransform