ILM gluons in perturbative QCD

TL;DR

This paper investigates the gluon propagator within the Instanton Liquid Model of QCD, demonstrating that instantons induce a dynamical gluon mass and do not contribute to infrared renormalons, with implications for heavy quarkonium studies.

Contribution

It extends previous work by systematically analyzing the gluon polarization operator in ILM, showing the absence of IR renormalons due to instanton effects and the generation of a dynamical gluon mass.

Findings

ILM gluon propagator does not have IR renormalons.

Instantons generate a dynamical gluon mass.

Analysis includes both perturbative and nonperturbative effects.

Abstract

In this paper we extend our previous work on gluon propagator in the Instanton Liquid Model (ILM) of the QCD vacuum. This objects presents a lot of interest for studies of the heavy quarkonium $Q\bar Q$ observables in the framework of potential Nonrelativistic QCD (pNRQCD). Our goal is to evaluate the gluon polarization operator in ILM, and understand if it gets contributions from infrared (IR) renormalons. We perform a systematic analyis, taking into account both perturbative and nonperturbative effects, and making a double series expansion in terms of the strong coupling $\alpha_s(\rho)\sim 0.5$ (the scale is given by average instanton size $\rho\approx1/3$ fm) and the instanton gas packing fraction $\lambda=\rho^4/R^4\sim 0.01$ ($R\approx 1$ fm is average inter-instanton distance). We demonstrate that there are no IR renormalon related to ILM gluon propagator, since instantons generate a ILM gluon dynamical mass.