The pion-photon transition form factor at two loops in QCD

We report on the fully analytic calculation of the leading-power contribution to the photon-pion transition form factor $\gamma \, \gamma^{\ast} \to \pi^0$ at two loops in QCD. The applied techniques are based on hard-collinear factorization, together with modern multi-loop methods. We focus both, on the technical details such as the treatment of evanescent operators, and the phenomenological implications. Our results indicate that the two-loop correction is numerically comparable to the one-loop effect in the same kinematic domain. We also demonstrate that our results will play a key role in disentangling various models for the twist-two pion distribution amplitude thanks to the envisaged precision at Belle II.