QCD sum rule calculation of γγ∗ → π0 transition form factor

We develop a QCD sum rule analysis of the form factor Fγ∗γ∗π0(q2,Q2)in the region where virtuality of one of the spacelike photons is small q2 ⪡ 1 GeV2 while another is large: Q2 ≳ 1 GeV2. We construct the operator product expansion suitable for this kinematic situation and obtain a QCD sum rule for Fγ∗γ∗π0(0,Q2) ≡ Fγγ∗π0(Q2). Our results confirm expectation that the momentum transfer dependence of the leading-order contribution to Fγ∗π0(Q2) is close to interpolatio between its Q2 = 0 value fixed by the axial anomaly and 1Q2 pQCD behaviour for large Q2. Our approach, in contrast to pQCD, does not require explicit assumptions about the shape of the pion distribution amplitude ϕπ(x). The absolute value of the 1Q2 term obtained in this paper favours ϕπ(x) close to the asymptotic form ϕπas(x) = 6fπx(1 − x).