Relating the Quark and Gluon Condensates Through the QCD Vacuum Energy

TL;DR

This paper uses the Cornwall-Jackiw-Tomboulis effective potential to relate quark and gluon condensates via the QCD vacuum energy, confirming known relations and analyzing the gluon self-energy behavior.

Contribution

It introduces a method to connect quark and gluon condensates through the vacuum energy, verifying the gluon self-energy behavior in both ultraviolet and infrared regimes.

Findings

Gluon self-energy matches operator product expansion predictions in ultraviolet.

Infrared gluon self-energy is frozen at a scale related to the dynamical gluon mass.

Reproduces the QCD sum rule relation for heavy quarks.

Abstract

Using the Cornwall-Jackiw-Tomboulis effective potential for composite operators we compute the QCD vacuum energy as a function of the dynamical quark and gluon propagators, which are related to their respective condensates as predicted by the operator product expansion. The identification of this result to the vacuum energy obtained from the trace of the energy-momentum tensor allow us to study the gluon self-energy, verifying that it is fairly represented in the ultraviolet by the asymptotic behavior predicted by the operator product expansion, and in the infrared it is frozen at its asymptotic value at one scale of the order of the dynamical gluon mass. We also discuss the implications of this identity for heavy and light quarks. For heavy quarks we recover, through the vacuum energy calculation, the relation $m_{f} <{\bar{\psi_f}}\psi_f> \sim - {1/12} \gc$ obtained many years ago with QCD sum rules.