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

Abstract

We report on the fully analytic calculation of the leading-power contribution to the photon-pion transition form factor \gamma \, \gamma^{\ast} \to \pi^0γγ*→π0 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.

Resummation of threshold logarithms in deeply-virtual Compton scattering

“…In fact it can be found that for the result in [12,13] we get f = f , h = h up to two-loops (and possibly to higher orders). Hence the same formulas as in eq.…”

“…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…”