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BaBar's observation of significant deviations of the pion transition formfactor (TFF) from the asymptotic expectation with $Q^2>9$ GeV$^2$ has brought aserious crisis to a fundamental picture established for such a simplest$q\bar{q}$ system by perturbative QCD, i.e. the dominance of collinearfactorization at high momentum transfers for the pion TFF. We show thatnon-factorizable contributions due to open flavors in $\gamma\gamma^*\to\pi^0$could be an important source that contaminates the pQCD asymptotic limit andcauses such deviations with $Q^2>9$ GeV$^2$. Within an effective Lagrangianapproach, the non-factorizable amplitudes can be related to intermediate hadronloops, i.e. $K^{(*)}$ and $D^{(*)}$ etc, and their corrections to the $\pi^0$and $\eta$ TFFs can be estimated.

Novel insights into the $\gamma\gamma^*\to \pi^0$ transition form factor