Non-perturbative Green's functions and the QCD effective charge

TL;DR

This paper investigates two non-perturbative definitions of the QCD effective charge derived from Green's functions, demonstrating their near equivalence and infrared freezing, consistent with theoretical and phenomenological expectations.

Contribution

It derives a fundamental identity linking different Green's functions in QCD and discusses a renormalization scheme that preserves this identity in non-perturbative analyses.

Findings

The two effective charges are nearly identical across all momenta.

The QCD charge freezes in the infrared due to gluon propagator finiteness.

A renormalization procedure preserving key identities is outlined.

Abstract

Using as ingredients the non-perturbative solutions of various QCD Green's function obtained from Schwinger-Dyson equations (SDEs), we study two versions of the QCD effective charge. The first one obtained from the pinch technique gluon self-energy, and the second from the ghost-gluon vertex. Despite the distinct nature of their buildings blocks, the two effectives charges are almost identical in the entire range of momenta, due to a fundamental identity relating the ghost dressing function with the two form factors of Green's function, which is of central importance in the PT-BFM formalism. In this talk, we outline how to derive this crucial identity from the SDEs of the aforementioned Green's functions. The renormalization procedure that preserves the validity of this identity is discussed in detail. Most importantly, we show that due to the infrared finiteness of the gluon propagator, the QCD charge obtained with either definition freezes in the deep infrared, in agreement with theoretical and phenomenological expectations.