Abstract
We analyze effects due to transverse degrees of freedom in QCD calculations of the fundamental hard exclusive amplitude of $\gamma^*\gamma \to \pi^0$ transition. A detailed discussion is given of the relation between the modified factorization approach (MFA) of Sterman et al. and standard factorization (SFA). Working in Feynman gauge, we construct basic building blocks of MFA from the one-loop coefficient function of the SFA, demonstrating that Sudakov effects are distinctly different from higher-twist corrections. We show also that the handbag-type diagram, contrary to naive expectations, does not contain an infinite chain of $(M^2/Q^2)^n$ corrections: they come only from diagrams with transverse gluons emitted from the hard propagator. A simpler picture emerges within the QCD sum rule approach: the sum over soft $\bar q G ... G q$ Fock components is dual to $\bar qq$ states generated by the local axial current. We combine the results based on QCD sum rules with pQCD radiative corrections and observe that the gap between our curves for the asymptotic and CZ distribution amplitudes is sufficiently large for an experimental discrimination between them.
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