  We discuss different QCD approaches to calculate the form factor
F^{\gamma^*\gamma\pi}(Q^2) of the \gamma^*\gamma\to\pi^{0} transition giving
preference to the light-cone QCD sum rules (LCSR) approach as being the most
adequate. In this context we revise the previous analysis of the CLEO
experimental data on F^{\gamma^*\gamma\pi}(Q^{2}) by Schmedding and Yakovlev.
Special attention is paid to the sensitivity of the results to the (strong
radiative) \alpha_s-corrections and to the value of the twist-four coupling
\delta^2. We present a full analysis of the CLEO data at the NLO level of
LCSRs, focusing particular attention to the extraction of the relevant
parameters to determine the pion distribution amplitude, i.e., the Gegenbauer
coefficients a_2 and a_4. Our analysis confirms our previous results and also
the main findings of Schmedding and Yakovlev: both the asymptotic, as well as
the Chernyak--Zhitnitsky pion distribution amplitudes are completely excluded
by the CLEO data. A novelty of our approach is to use the CLEO data as a means
of determining the value of the QCD vacuum non-locality parameter \lambda^2_q =
<\bar{q}D^2q>/<\bar{q}q> =0.4 GeV^2, which specifies the average virtuality of
the vacuum quarks.
