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Hadrons and Nuclei
Eur. Phys. J. A 4, 381-400

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

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 $\Lambda$, we establish the self-consistency equations of the extended Feynman rules ($\Lambda$-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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