How to calculate the quantum part of the truly nonperturbative Yang-Mills vacuum energy density in the axial gauge QCD

Using the effective potential approach for composite operators, we have formulated a general method how to calculate the truly nonperturbative vacuum energy density in the axial gauge QCD quantum models of its ground state. It is defined as integrated out the truly nonperturbative part of the full gluon propagator over the deep infrared region (soft momentum region). The 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 presented in any nonperturbative model for the full gluon propagator. If the chosen Ansatz for the full gluon propagator is a realistic one, then our method uniquely determines the truly vacuum energy density, which is always finite, automatically negative and it has no imaginary part (stable vacuum). We illustrate it by considering the Abelian Higgs model of dual QCD ground state. We have explicitly shown that the vacuum of this model without string contributions is unstable against quantum corrections.