QCD effective charges from lattice data

TL;DR

This paper uses lattice QCD data to extract and compare two definitions of the non-perturbative QCD effective charge, revealing a common infrared freezing value and discussing gauge-related discrepancies with phenomenological estimates.

Contribution

It provides a lattice-based extraction of two QCD effective charges and analyzes their infrared behavior, highlighting gauge dependence effects.

Findings

Both effective charges freeze at a finite, non-zero value in the infrared.

Discrepancies with phenomenological estimates are attributed to gauge differences.

Gauge modifications may explain the observed deviations in freezing values.

Abstract

We use recent lattice data on the gluon and ghost propagators, as well as the Kugo-Ojima function, in order to extract the non-perturbative behavior of two particular definitions of the QCD effective charge, one based on the pinch technique construction, and one obtained from the standard ghost-gluon vertex. The construction relies crucially on the definition of two dimensionful quantities, which are invariant under the renormalization group, and are built out of very particular combinations of the aforementioned Green's functions. The main non-perturbative feature of both effective charges, encoded in the infrared finiteness of the gluon propagator and ghost dressing function used in their definition, is the freezing at a common finite (non-vanishing) value, in agreement with a plethora of theoretical and phenomenological expectations. We discuss the sizable discrepancy between the freezing values obtained from the present lattice analysis and the corresponding estimates derived from several phenomenological studies, and attribute its origin to the difference in the gauges employed. A particular toy calculation suggests that the modifications induced to the non-perturbative gluon propagator by the gauge choice may indeed account for the observed deviation of the freezing values.