Axial-vector contributions in two-photon reactions: Pion transition form factor and deeply-virtual Compton scattering at NNLO in QCD

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 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 γ * γ → π 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 (DVCS) 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.

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

“…Collecting all individual pieces in (15) together, all the poles in ε are canceled explicitly as expected, which represents a nontrivial check for our calculation. As stated earlier, our final analytic result for the hard CF T (2) 2 (x) agrees with that of a parallel computation [11], which uses quite a different approach based on arguments from conformal symmetry. The result for T…”

“…The full analytic NNLO QCD prediction of the TFF F γπ (Q 2 ) in γ γ * → π 0 was first put forward in [10], with a parallel computation appearing in [11] and the two results being in full agreement with each other. Our computation takes advantage of the soft-collinear effective theory (SCET) factorization program.…”

“…We would like to thank the authors of [11] for useful correspondence, and for sharing their analytic results with us prior to publication.…”

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

“…(2) 2 (x) agrees with that of a parallel computation [11], which uses quite a different approach based on arguments from conformal symmetry. The result for T (2) 2 (x) is split up into three colour factors and can be expressed as…”

Resummation of threshold logarithms in deeply-virtual Compton scattering

“…It is well-known that there is ambiguity in defining γ 5 in dimensional regularization. In the two-loop calculation of C q [12,13] Larins scheme [14] was used and the result is then converted by a finite renormalization to the conventional MS-scheme, which is defined by demanding that the evolution equation agrees with the vector case [15]. Larins scheme can be implemented by making the exchange…”