Non-perturbative QCD effective charges

TL;DR

This paper constructs the non-perturbative QCD effective charge using gluon and ghost propagators from Schwinger-Dyson equations, showing it freezes in the infrared, aligning with theoretical and phenomenological expectations.

Contribution

It introduces two different definitions of the QCD effective charge that yield consistent results and demonstrates their infrared freezing, supported by a detailed review of the theoretical framework.

Findings

Effective charge freezes in the deep infrared.

Two definitions produce qualitatively similar results.

Theoretical ingredients and subtleties are thoroughly discussed.

Abstract

Using gluon and ghost propagators obtained from Schwinger-Dyson equations (SDEs), we construct the non-perturbative effective charge of QCD. We employ two different definitions, which, despite their distinct field-theoretic origin, give rise to qualitative comparable results, by virtue of a crucial non-perturbative identity. Most importantly, the QCD charge obtained with either definition freezes in the deep infrared, in agreement with theoretical and phenomenological expectations. The various theoretical ingredients necessary for this construction are reviewed in detail, and some conceptual subtleties are briefly discussed.