Determination of the quantum part of the truly nonperturbative Yang-Mills vacuum energy density in covariant gauge QCD

Abstract

Using the effective potential approach for composite operators, we formulate a general method of calculation of the truly nonperturbative Yang-Mills vacuum energy density in the covariant gauge QCD ground state quantum models. It is defined as an integration of the truly nonperturbative part of the full gluon propagator over the deep infrared region (soft momentum region). A nontrivial minimization procedure makes it possible to determine the value of the soft cutoff in terms of the corresponding nonperturbative scale parameter, which is inevitably present in any nonperturbative model for the full gluon propagator. We have shown for specific models of the full gluon propagator explicitly that the use of the infrared-enhanced and finite gluon propagators leads to the vacuum energy density which is finite, always negative, and has no imaginary part (stable vacuum), while the infrared vanishing propagators lead to an unstable vacuum and therefore they are physically unacceptable.