Next-to-Next-to-Leading-Order QCD Prediction for the Photon-Pion Form Factor

TL;DR

This paper presents a complete two-loop QCD calculation of the photon-pion transition form factor, highlighting the importance of higher-order corrections and their potential to distinguish between different pion distribution amplitude models.

Contribution

It provides the first full two-loop computation of the leading-twist contribution to the photon-pion form factor using advanced multi-loop techniques.

Findings

Two-loop correction is numerically significant.

Results will aid in differentiating pion distribution amplitude models.

Predictions are relevant for upcoming Belle II measurements.

Abstract

We accomplish the complete two-loop computation of the leading-twist contribution to the photon-pion transition form factor $\gamma \, \gamma^{\ast} \to \pi^0$ by applying the hard-collinear factorization theorem together with modern multi-loop techniques. The resulting predictions for the form factor indicate that the two-loop perturbative correction is numerically important. We also demonstrate that our results will play a key role in disentangling various models of the twist-two pion distribution amplitude thanks to the envisaged precision at Belle II.