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It is a non-perturbative effect because it is 1-loop exact. The triangle diagram is actually the least insightful method to think about this, in my opinion. The core of the matter is the anomaly of the chiral symmetry, which you can also, for example, calculate by the Fujikawa method examining the change of the path integral measure under the chiral ...


This Bardeen counterterm is an elusive beast, I must say. Yet I will share what I have found and understand: Define a $\mathrm{U}(1)$ gauge theory by writing its action in left- and right-handed chiral spinors as $$ S_{\mathrm{chiral}}[A] = \int \bar \psi_L (\mathrm{i} {\not \hspace{-4px} \partial} - \not \hspace{-5px} A)\psi_L + \bar \psi_R (\mathrm{i} ...

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