Yang-Mills vacuum instability due to infrared finite lattice gluon propagator

Abstract

Using the effective potential approach for composite operators, we have analytically evaluated the truly nonperturbative vacuum energy density as obtained by using a model infrared finite gluon propagator which was suggested by lattice simulations. The truly nonperturbative vacuum energy density is defined as the truly nonperturbative part of the full gluon propagator integrated over the deep infrared region (soft momentum region). With this definition, it is a manifestly gauge invariant quantity. We have explicitly shown that the corresponding effective potential has always an imaginary part which means that the vacuum of this model is unstable. Thus this model cannot have a true ground state.