Pion transition form factor through Dyson-Schwinger equations

TL;DR

This paper uses Dyson-Schwinger equations to compute the pion transition form factor across all space-like momenta, aligning with experimental data and connecting to QCD predictions and pion structure.

Contribution

First continuum QCD calculation of the pion transition form factor over the entire space-like domain using Dyson-Schwinger equations.

Findings

Results agree with CELLO, CLEO, and Belle data.

The form factor approaches the QCD asymptotic limit of 2f_pi.

Unifies predictions for the transition form factor, pion PDA, and electromagnetic form factor.

Abstract

In the framework of Dyson-Schwinger equations (DSE), we compute the $\gamma^*\gamma\to\pi^0$ transition form factor, $G(Q^2)$. For the first time, in a continuum approach to quantun chromodynamics (QCD), it was possible to compute $G(Q^2)$ on the whole domain of space-like momenta. Our result agrees with CELLO, CLEO and Belle collaborations and, with the well-known asymptotic QCD limit, $2f_\pi$. Our analysis unifies this prediction with that of the pion's valence-quark parton distribution amplitude (PDA) and elastic electromagnetic form factor.