# Gauge Technique approximation to the $\pi \gamma$ production and the pion transition form factor

## TL;DR

This paper computes the pion transition form factor across all momentum ranges using a continuum quantum field theory approach, employing the Gauge Technique and Dyson-Schwinger equations to incorporate nonperturbative QCD effects.

## Contribution

It introduces a novel application of the Gauge Technique combined with Minkowski space Dyson-Schwinger solutions to accurately calculate the pion transition form factor.

## Key findings

- Successful computation of $G(q^2)$ in spacelike and timelike regions.
- Demonstrates the effectiveness of the Gauge Technique in nonperturbative QCD.
- Highlights the role of dynamical chiral symmetry breaking in form factor calculations.

## Abstract

The pion transition form factor $G(q^2)$ is computed on the entire domain of spacelike and timelike momenta using a quantum field theory continuum approach. In analytical continuation of the function $G(Q^2)$ we utilized the Gauge Technique with the quark propagator determined from Minkowski space solution of QCD Dyson-Schwinger equations. The scale is set up by the phenomena of dynamical chiral symmetry breaking, which is a striking feature of low energy QCD.