The $\gamma^\ast\to \eta\gamma$ and $\gamma^\ast\to \eta'\gamma$ form factors to NNLO accuracy in perturbative QCD

Abstract

We use conformal symmetry to calculate the NNLO anomalous dimension matrix (three loops) for flavor-singlet axial-vector QCD operators for spin $N \le 8$ from a set of gauge-invariant two-point correlation functions. Combining this result with the recent calculation of the two-loop coefficient functions, we carry out the calculation of the $\gamma\gamma^\ast\to \eta$ and $\gamma\gamma^\ast\to \eta'$ form factors at large momentum transfers to the NNLO accuracy in perturbative QCD.