Vacuum energy density in the quantum Yang–Mills theory

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 types of perturbative contributions now, as well as possessing many other desirable properties such as colorless, gauge independence, etc. Using the trace anomaly relation further, 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 β function. Our numerical result for the bag constant shows good agreement with other phenomenological estimates of the gluon condensate.