Transition form factor γγ∗ → π0and QCD sum rules Original Research Article

The transition γ∗ (q1)γ∗ (q2) → π0(p) is studied within the QCD sum rule framework. As a first step, we analyze the kinematic situation when both photon virtualities are spacelike and large. We construct a QCD sum rule for Fγ∗γ∗π0(q12, q22) and show that, in the asymptotic limit |q12|, |q22| → ∞, it reproduces the leading-order pQCD result. Then we study the limit |q 2| → 0, in which one of the photons is (almost) real. We develop a factorization procedure for the infrared singularities ln(q12, 1/q14, etc., emerging in this limit. The infrared-sensitive contributions are absorbed in this approach by bilocal correlators, which can be also interpreted as the distribution amplitudes for the (almost) real photon. Under explicitly formulated assumptions concerning the form of these amplitudes, we obtain a QCD sum rule for Fγ∗γ∗π0(q12 = 0, q22 = −Q2) and study its Q2 dependence. In contrast to pQCD, we make no assumptions about the shape of the pion distribution amplitude ϕπ(x). Our results agree with the Brodsky-Lepage proposal that the Q2 dependence of this form factor is given by an interpolation between its Q2 = 0 value fixed by the axial anomaly and 1/Q2 pQCD behaviour for large Q2, provided that one interpolates to a value close to that dictated by the asymptotic form ϕπas(x) = 6fπx(1 − x) of the pion distribution amplitude. We interpret this as evidence that ϕπ(x) is rather close to the asymptotic form.