Perturbative Effects in the Form Factor $γγ^*\to π^0$ and Extraction of the Pion Wave Function from CLEO Data

We study the perturbative QCD contribution of the twist-2 operator to the light-cone QCD sum rule for the $\gamma\gamma^*\to\pi^0$ form factor. We derive QCD sum rules at next-to-leading order (NLO), which give predictions for the $F^{\pi \gamma\gamma^*}(Q^2)$ form factor. We perform a detailed numerical analysis. Using CLEO experimental data, we extract the shape of the pion wave function of twist-2. We estimate the Gegenbauer coefficients as $a_2=0.19 \pm 0.04 (stat.)\pm 0.09 (syst.)$ and $a_4=-0.14\pm 0.03 (stat.)\mp 0.09 (syst.)$ at $\mu=2.4$ GeV. We compare our results with those existing in the literature.