# On the large-Q^2 behavior of the pion transition form factor

## TL;DR

This paper investigates the transition from non-perturbative to perturbative QCD in the pion transition form factor across all momentum scales, revealing agreement with perturbative laws and experimental data, and identifying modifications to established scaling at high energies.

## Contribution

It provides a comprehensive analysis of the pion transition form factor using Dyson-Schwinger/Bethe-Salpeter methods, including new insights into scaling violations at high off-shell photon momenta.

## Key findings

- Good agreement with perturbative asymptotic scaling laws for doubly virtual form factor.
- Results align with Belle data for singly virtual form factor.
- Identification of a mechanism causing modifications to Efremov-Radyushkin-Brodsky-Lepage scaling at large off-shell photon momenta.

## Abstract

We study the transition of non-perturbative to perturbative QCD in situations with possible violations of scaling limits. To this end we consider the singly- and doubly-virtual pion transition form factor $\pi^0\to\gamma\gamma$ at all momentum scales of symmetric and asymmetric photon momenta within the Dyson-Schwinger/Bethe-Salpeter approach. For the doubly virtual form factor we find good agreement with perturbative asymptotic scaling laws. For the singly-virtual form factor our results agree with the Belle data. At very large off-shell photon momenta we identify a mechanism that introduces quantitative modifications to Efremov-Radyushkin-Brodsky-Lepage scaling.