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Using the effective potential approach for composite operators, we haveformulated a general method of calculation of the truly nonperturbativeYang-Mills vacuum energy density in the covariant gauge QCD ground statequantum models. It is defined as an integration of the truly nonperturbativepart of the full gluon propagator over the deep infrared region (soft momentumregion). A nontrivial minimization procedure makes it possible to determine thevalue of the soft cutoff in terms of the corresponding nonperturbative scaleparameter, which is inevitably present in any nonperturbative model for thefull gluon propagator. We have shown for specific models of the full gluonpropagator explicitly that the use of the infrared enhanced and finite gluonpropagators lead to the vacuum energy density which is finite, always negativeand it has no imaginary part (stable vacuum), while the infrared vanishingpropagators lead to unstable vacuum and therefore they are physicallyunacceptable.Comment: 21 pages, 1 figure, no tables, typos corrected, references added,  some clarification is introduced, to appear soon Phys. Rev.

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