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 vertices F (~ 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 4gluon 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) Smatrix 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 the F(~ (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) F(~ fulfill the Slavnov-Taylor identities among themselves. (5) Perturbative renormalization counterterms remain applicable. (6) Bound qc~ systems exist and display an unusual spectrum, with a small finite number of bound states and no q ~ scattering continuum.PACS" ll.15Tk; 12.38.Lg

Gauge bosons at zero and finite temperature

“…Thus, it is worthwhile to compare the results for the gluons to scenarios describing a confinement mechanism, which yield predictions for the correlation functions. Three such scenarios have been of particular relevance recently, the ones of Kugo and Ojima [12,304], of Gribov and Zwanziger [18,68,103], and of Gribov and Stingl [18,[293][294][295]. There exist also other scenarios which give predictions on the analytic structure of the correlation functions [13,305], though those seem not fully compatible with the results obtained, and thus will not be detailed further here.…”

“…There have been various proposals, which form it may have instead. One, the so-called Gribov-Stingl type [18,[293][294][295], has complex poles on the first Riemann sheet, but may have vanishing residues at the poles [293][294][295]. This behavior can be described by a meromorphic function [33] …”

Gribov copies and anomalous scaling

“…(1), if we continue to take the one-loop results seriously. The interpretation of such poles is uncertain, but they have been discussed within a confining picture in [16]. On the other hand if we assume that higher order corrections produce a negative c 2 as well, then as in our discussion at the beginning of the last section there is a range 1/2 < κ < κ max < 1 where the complex poles have been pushed off the first Riemann sheet.…”

“…From (16) it is clear that this would produce a pole on the negative p 2 (spacelike) axis. Thus to go any further for this range of κ we must assume that the sign of c 1 is changed by higher order corrections.…”

“…In fact our previous calculation of the vacuum polarization Π Λ µν (p 2 ) is also modified by these same chains of ghost loops. 5 The net effect is to multiply the c 1 term in (16) by the square bracket multiplying j µ a j aµ in (20). This modification only applies in the infrared.…”