QCD effective charge from the three-gluon vertex of the background-field method

TL;DR

This paper explores a method to determine the infrared finite QCD effective charge using a special three-gluon vertex function, which simplifies the analysis by relating it directly to the gluon propagator without ghost sector complications.

Contribution

It introduces a novel approach to extract the QCD effective charge from a specific background gluon vertex, leveraging a Ward identity to relate it solely to the gluon wave function.

Findings

Effective charge can be extracted from a specific vertex function.

The method reduces dependence on transverse form factors.

Preliminary results suggest insensitivity to numerical uncertainties.

Abstract

In this article we study in detail the prospects of determining the infrared finite QCD effective charge from a special kinematic limit of the vertex function corresponding to three background gluons. This particular Green's function satisfies a QED-like Ward identity, relating it to the gluon propagator, with no reference to the ghost sector. Consequently, its longitudinal form factors may be expressed entirely in terms of the corresponding gluon wave function, whose inverse is proportional to the effective charge. After reviewing certain important theoretical properties, we consider a typical lattice quantity involving this vertex, and derive its exact dependence on the various form factors, for arbitrary momenta. We then focus on the particular momentum configuration that eliminates any dependence on the (unknown) transverse form factors, projecting out only the desired quantity. A preliminary numerical analysis indicates that the effective charge is relatively insensitive to the numerical uncertainties that may afflict future simulations of the aforementioned lattice quantity. The numerical difficulties associated with a parallel determination of the dynamical gluon mass are briefly discussed.