Next-to-next-to-leading order prediction for the photon-to-pion transition form factor

We evaluate the next-to-next-to-leading order corrections to the hard-scattering amplitude of the photon-to-pion transition form factor. Our approach is based on the predictive power of the conformal operator product expansion, which is valid for a vanishing $\beta$ function in the so-called conformal scheme. The Wilson coefficients appearing in the nonforward kinematics are then entirely determined from those of the polarized deep inelastic scattering known to next-to-next-to-leading order accuracy. We propose different schemes to include explicitly also the conformal symmetry breaking term proportional to the $\beta$ function and discuss numerical predictions calculated in different kinematical regions. It is demonstrated that the photon-to-pion transition form factor can provide a fundamental testing ground for our QCD understanding of exclusive reactions.