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

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