Vacuum Energy Density in the Quantum Yang - Mills Theory

TL;DR

This paper introduces a non-perturbative method to calculate the vacuum energy density in Yang-Mills theory, specifically the Bag constant, which is free from perturbative contamination and relates to the gluon condensate.

Contribution

It develops a novel effective potential approach for non-perturbative vacuum energy calculation that is gauge-independent and does not rely on weak coupling assumptions.

Findings

Numerical Bag constant aligns with phenomenological gluon condensate estimates.

Method effectively isolates non-perturbative contributions in Yang-Mills vacuum energy.

Formalism relates Bag constant to gluon condensate without weak coupling approximation.

Abstract

Using the effective potential approach for composite operators, we have formulated a general method of calculation of the truly non-perturbative Yang-Mills vacuum energy density (this is, by definition, the Bag constant apart from the sign). It is the main dynamical characteristic of the QCD ground state. Our method allows one to make it free of the perturbative contributions ('contaminations'), by construction. We also perform an actual numerical calculation of the Bag constant for the confining effective charge. Its choice uniquely defines the Bag constant, which becomes free of all the types of the perturbative contributions now, as well as possessing many other desirable properties as colorless, gauge independence, etc. Using further the trace anomaly relation, we develop a general formalism which makes it possible to relate the Bag constant to the gluon condensate not using the weak coupling solution for the corresponding $\beta$ function. Our numerical result for the Bag constant shows a good agreement with other phenomenological estimates of the gluon condensate.