We have explicitly shown that a mass scale parameter (in what follows it will be called the mass gap, for convenience,
see remarks below as well) can be present in the gluon Schwinger-Dyson (SD) equation without violating its SU(3)
color gauge invariance. In other words, the full gluon propagator in the presence of the mass gap is in agreement with
the corresponding Slavnov-Taylor (ST) identity. The mass gap is generated in the gluon sector of QCD (i.e., in its
Yang-Mills (YM) part) due to the self-interaction of massless gluon modes, so it has not been introduced by hand.
No any truncations/approximations/assumptions, no special gauge choice, etc. have been made, only algebraic (i.e.,
exact) derivations have been used. In the most general way, we have establish the existence of the two types of exact
solutions for the full gluon propagator: massless singular and massive regular at small gluon momenta. One of the
important result obtained is the summation of the severe infrared (IR) singularities originating by the self-interaction
of massless gluon modes in QCD. It makes it possible to accumulate/summarize them into the full gluon propagator
by the help of the mass gap. By the joint use of the theory of distributions, the dimensional regularization method and
some basic theorems from the theory of functions of complex variable, such as Picard or, equivalently, Weierstrass–
Sokhatsky–Casorati, Laurent, etc., we put the severe IR singularities in QCD under a firm mathematical control. The
mass gap approach to QCD is one of the important new advances in modern physics at microscopic quantum level.
For the first time, it has been suggested by A. Jaffe and E. Witten at the beginning of this millennium. Our mass
gap coincides with their mass gap by properties, but not by definition. The description of our results in more detail
and the list of the corresponding references can be found in our recent book
”The Mass Gap and its Applications” (World Scientific, 2013) by V. Gogokhia and G.G. Barnafoldi.