Non-perturbative momentum dependence of the coupling constant and hadronic models

TL;DR

This paper explores the non-perturbative momentum dependence of the QCD coupling constant, linking Dyson-Schwinger equations to hadronic models and explaining the effectiveness of perturbative methods at low energies.

Contribution

It introduces a dynamical gluon mass function from Dyson-Schwinger equations, providing a non-perturbative understanding of the infrared behavior of the coupling constant.

Findings

The QCD coupling freezes in the infrared due to gluon mass generation.

Perturbative evolution remains valid despite the small hadronic scale.

Infrared divergences are avoided through dynamical gluon mass effects.

Abstract

Models of hadron structure are associated with a hadronic scale which allows by perturbative evolution to calculate observables in the deep inelastic region. The resolution of Dyson-Schwinger equations leads to the freezing of the QCD running coupling (effective charge) in the infrared, which is best understood as a dynamical generation of a gluon mass function, giving rise to a momentum dependence which is free from infrared divergences. We use this new development to understand why perturbative treatments are working reasonably well despite the smallness of the hadronic scale.