The asymptotics of the transition form factor \gamma\gamma* -> pi^o and QCD sum rules

In this paper we present the result of a direct QCD sum rule calculation of the transition form factor \gamma\gamma* -> pi^o in the region of moderately large invariant momentum Q^2 > 1GeV^2 of the virtual photon. In contrast to pQCD, we make no assumptions about the shape of the pion distribution amplitude \phi_\pi(x). Our results agree with the Brodsky-Lepage proposal that the Q^2-dependence of this form factor is given by an interpolation between its Q^2=0 value fixed by the axial anomaly and 1/Q^2 pQCD behaviour for large Q^2, with normalization corresponding to the asymptotic form \phi_\pi^as (x)=6 f_\pi x (1-x) of the pion distribution amplitude. Our prediction for the from factor $F_{{\gamma }^{\ast }{\gamma }^{\ast }{\pi }^{\circ }}(q_1^2=0,q_2^2=-Q^2)$ is in good agreement with new CLEO data.