  The physical meaning of a mass gap introduced by Jaffe and Witten is to be
responsible for the large-scale (low-energy/momentum), i.e., the
non-perturbative structure of the true QCD vacuum. In order to make the
existence of a mass gap pefrectly clear it is defined as the difference between
the regularized full gluon self-energy and its subtracted (also regularized)
counterpart. The mass gap is mainly generated by the nonlinear interaction of
massless gluon modes. A self-consistent violation of SU(3) color gauge
invariance/symmetry is duscussed in order to realize a mass gap in QCD. For
this purpose, we propose not to impose the transversality condition on the full
gluon self-energy, while restoring the transversality of the full gluon
propagtor relevant for the non-perturbative QCD at the final stage. At the same
time, the Slavnov-Taylor identity for the full gluon propagator is always
preserved. All this allows one to establish the general structure of the full
gluon propagator in the presence of a mass gap. In this case, two independent
types of formal solutions for the full gluon propagator have been established.
The nonlinear iteration solution at which the gluons remain massless is
explicitly present. The existence of the solution with an effective gluon mass
is also demonstrated.
