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