Extended iterative scheme for QCD: three-point vertices
L. Driesen - J. Fromm - J. Kuhrs - M. Stingl
Institute for Theoretical Physics I, University of Münster, D-48149 Münster (Westf.), Germany
Received: 1 September 1998 / Revised version: 1 December 1998 Communicated by F. Lenz
Abstract
In the framework of a generalized iterative scheme introduced previously
to account for the non-analytic coupling dependence associated with the
renormalization-group invariant mass scale , we establish the
self-consistency equations of the extended Feynman rules (
-modified
vertices of zeroth perturbative order) for the three-gluon vertex, the two
ghost vertices, and the two vertices of massless quarks. Calculations
are performed to one-loop-order, in Landau gauge, and at the lowest
approximation level (r=1) of interest for QCD. We discuss the phenomenon
of compensating poles inherent in these equations, by which the formalism
automatically cancels unphysical poles on internal lines, and the
role of composite-operator information in the form of equation-of-motion
condensate conditions. The observed near decoupling of
the four-gluon conditions permits a solution to the 2-and-3-point conditions
within an effective one-parameter freedom. There exists a parameter range
in which one solution has all vertex coefficients real, as required for
a physical solution, and a narrower range in which the transverse-gluon
and massless-quark propagators both exhibit complex-conjugate pole pairs.
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