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In this work, the $\gamma\to3\pi$ form factor is calculated within theDyson-Schwinger equations framework using a contact interaction model withinthe so-called modified rainbow ladder truncation. The present calculation takesinto account the pseudovector component in the pion Bethe-Salpeter amplitude(BSA) and $\pi-\pi$ scattering effects, producing a $\gamma\to3\pi$ anomalywhich is $1+6\mathcal{R}_\pi^2$ larger than the low energy prediction. Here$\mathcal{R_\pi}$ is the relative ratio of the pseudovector and pseudoscalarcomponents in the pion BSA; with our parameters input, this correction raisesthe $\gamma\to3\pi$ anomaly by around $10\%$. The main outcome of this work isthe unveiling of the origin of such correction, which could be a possibleexplanation of the discrepancy between the existing experimental data and thelow energy prediction. Moreover, it is highlighted how the magnitude of theanomaly is affected in effective theories that require an irremovableultraviolet cutoff. We find that for both the anomalous processes$\pi\to2\gamma$ and $\gamma\to 3\pi$, the missing contribution to the anomalycan be compensated by the additional structures related with the quarkanomalous magnetic moment.

QCD anomalies in electromagnetic processes: A solution to the $\gamma\to3\pi$ puzzle