A nonperturbative solution to the Dyson-Schwinger equations of QCD

Abstract

We continue the study, initiated in the preceding paper, of a mechanism for generating nonperturbatively modified, zeroth-order QCD verticesΓ(0) in the sense of a generalized perturbation expansion. In a pure gluon theory, we discuss the one-loop self-consistency conditions for the 2-gluon and 3-gluon zeroth-order vertices, using a version of the 3-point Dyson-Schwinger equation which at the one-loop level has no coupling to the 4-gluon function. We find one of several solutions which fulfills the self-consistency requirement of the nonperturbative gluon propagator remarkably well, so that the latter may be taken as well-confirmed. The solution also has unphysical features which can be traced to a partial violation of BRS invariance in the specific one-loop approximation adopted. We then discuss the following general properties of the nonperturbative vertex set: (1) S-matrix elements for production of free gluons and quarks vanish. (2) Vacuum condensates exist and can be calculated in terms of the spontaneous mass scale in theΓ(0)'s. (3) Propagators of the elementary fields have no physical singularities on the real axis and describe short-lived elementary excitations, whose lifetime grows with energy. (4)Γ(0)'s fulfill the Slavnov-Taylor identities among themselves. (5) Perturbative renormalization counterterms remain applicable. (6) Boundq¯q systems exist and display an unusual spectrum, with a small finite number of bound states and noq¯q scattering continuum.