The axial-vector contributions in two-photon reactions: pion transition form factor and deeply-virtual Compton scattering at NNLO in QCD

TL;DR

This paper calculates the two-loop axial-vector contributions to two-photon processes in QCD, completing NNLO predictions for the pion transition form factor and impacting studies of deeply-virtual Compton scattering at various experiments.

Contribution

It provides the missing two-loop coefficient function for axial-vector contributions in two-photon processes at NNLO in QCD, enabling more precise theoretical predictions.

Findings

NNLO corrections are significant and must be included.

The results facilitate constraints on the pion light-cone distribution amplitude.

The coefficient function impacts analyses at JLAB, CERN, and future EIC experiments.

Abstract

Using the approach based on conformal symmetry we calculate the two-loop coefficient function for the axial-vector contributions to two-photon processes in the $\overline{\rm MS}$ scheme. This is the last missing element for the complete next-to-next-to-leading order (NNLO) calculation of the the pion transition form factor $\gamma^\ast\gamma\to \pi $ in perturbative QCD. The corresponding high-statistics measurement is planned by the Belle II collaboration and will allow one to put strong constraints on the pion light-cone distribution amplitude. The calculated NNLO corrections prove to be rather large and have to be taken into account. The same coefficient function determines the contribution of the axial-vector generalized parton distributions to deeply-virtual Compton scattering which is investigated at the JLAB 12 GeV accelerator, by COMPASS at CERN, and in the future will be studied at the Electron Ion Collider EIC.