How to demonstrate a possible existence of a mass gap in QCD

Abstract

We propose to realize a mass gap in QCD by not imposing the transversality condition on the full gluon self-energy, while preserving the color gauge invariance condition for the full gluon propagator. This is justified by the nonlinear and nonperturbative dynamics of QCD. None of physical observables/processes in low-energy QCD will be directly affected by such a temporary violation of color gauge invariance/symmetry. No truncations/approximations and no special gauge are made for the regularized skeleton loop integrals, contributing to the full gluon self-energy, which enters the Schwinger-Dyson equation for the full gluon propagator. In order to make the existence of a mass gap perfectly clear the corresponding subtraction procedure is introduced. All this allows one to establish the general structure of the full gluon propagator and the gluon Schwinger-Dyson equation in the presence of a mass gap. It is mainly generated by the nonlinear interaction of massless gluon modes. The physical meaning of the mass gap is to be responsible for the large-scale (low-energy/momentum), i.e., nonperturbative structure of the true QCD vacuum. In the presence of a mass gap two different types of solutions for the full gluon propagator are possible. The massive solution leads to an affective gluon mass, which depends on the gauge-fixing parameter explicitly. This solution becomes smooth at small gluon momentum in the Landau gauge. The general iteration solution is always severely singular at small gluon momentum, i.e., the gluons remain massless, and this does not depend on the gauge choice.