The existence of a mass gap in quantum Yang-Mills theory

Abstract

The skeleton loop integrals which contribute into the gluon self-energy have been iterated (skeleton loops expansion) within the Schwinger-Dyson equation for the full gluon propagator. No any truncations/approximations as well as no special gauge choice have been made. It is explicitly shown that such obtained general iteration solution for the full gluon propagator can be exactly and uniquely decomposed as a sum of the two pricipally different terms. The first term is the Laurent expansion in integer powers of severe (i.e., more singular than $1/q^2$) infrared singularities accompanied by the corresponding powers of the mass gap and multiplied by the corresponding residues. The second (perturbative) term is always as much singular as $1/q^2$ and otherwise remaining undetermined. We have explicitly demonstrated that the mass gap is hidden in the above-mentioned skeleton loop integrals due to the nonlinear interaction of massless gluon modes. It shows explicitly up when the gluon momentum goes to zero. The appropriate regularization scheme has been applied in order to make a gauge-invariant existence of the mass gap perfectly clear. Moreover, it survives an infinite series summation of the relevant skeleton loop contributions into the gluon self-energy. The physical meaning of the mass gap is to be responsible for the large scale structure of the true QCD vacuum.