QCD sum rule calculation of $\gamma\gamma$ --> $\pi^{0}$ transition form factor

We develop a QCD sum rule analysis of the form factor F_{\gamma^*\gamma^*\pi^0}(q^2,Q^2) in the region where virtuality of one of the spacelike photons is small q^2 \ll 1 GeV^2 while another is large: Q^2 \gapprox 1 GeV^2. We construct the operator product expansion suitable for this kinematic situation and obtain a QCD sum rule for F_{\gamma^*\gamma^*\pi^0}(0,Q^2). Our results confirm expectation that the momentum transfer dependence of F_{\gamma^*\gamma^*\pi^0}( 0,Q^2) is close to interpolation between its Q^2=0 value fixed by the axial anomaly and Q^{-2} pQCD behaviour for large Q^2. Our approach, in contrast to pQCD, does not require additional assumptions about the shape of the pion distribution amplitude \varphi_{\pi}(x). The absolute value of the 1/Q^2 term obtained in this paper favours \varphi_{\pi}(x) close to the asymptotic form \varphi_{\pi}^{as} (x)=6 f_{\pi} x (1-x)