In QCD, the axial singlet quark current $j_5$ is anomalous, which was found by Adler, Bell, and Jackiw (here is a review):

\begin{equation} \partial_\mu j_5^\mu=G\tilde{G}, \end{equation}

where $G$ is the gluon field strength and $\tilde{G}$ its dual. As QCD is a non-Abelian gauge theory, $G\tilde{G}$ contains terms with up to four gluon fields $A$.

However, the anomaly arises from the computation of triangle diagrams with only two external gluon lines.

Now my question is: how can we obtain the above anomaly from such a diagram, even though the term $G\tilde{G}$ involves terms with more than two gluons fields? Do the terms with higher order in $A$ somehow cancel out in the computation?

In QCD, the axial singlet quark current $j_5$ is anomalous, which was found by Adler, Bell, and Jackiw (here is a review):

\begin{equation} \partial_\mu j_5^\mu=G\tilde{G}, \end{equation}

where $G$ is the gluon field strength and $\tilde{G}$ its dual. As QCD is a non-Abelian gauge theory, $G\tilde{G}$ contains terms with up to four gluon fields $A$.

However, the anomaly arises from the computation of triangle diagrams with only two external gluon lines.

Now my question is: How can we obtain the above anomaly from such a diagram, even though the term $G\tilde{G}$ involves terms with more than two gluons fields? Do the terms with higher order in $A$ somehow cancel out in the computation?