Next-to-next-to-leading order prediction for the photon-to-pion transition form factor -: art. no. 014013

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.