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

TL;DR

This paper presents a fully analytic two-loop calculation of the photon-pion transition form factor in QCD, highlighting the importance of higher-order corrections for understanding pion structure and aiding future experimental analyses.

Contribution

The paper introduces a novel two-loop analytic calculation of the photon-pion transition form factor using advanced multi-loop techniques and discusses its implications for pion distribution amplitude models.

Findings

Two-loop correction is comparable to one-loop effect in magnitude.

Results enhance the precision of theoretical predictions for Belle II.

The study improves understanding of the pion distribution amplitude.

Abstract

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