Extended Iterative Scheme for QCD: Three-point Vertices

TL;DR

This paper develops an extended iterative scheme for QCD that modifies three-point vertices, ensuring self-consistency and physical solutions by canceling unphysical poles and analyzing propagator pole structures.

Contribution

It introduces a generalized iterative framework for QCD vertices, incorporating Lambda-modified vertices and addressing unphysical poles through a self-consistent formalism.

Findings

Automatic cancellation of unphysical poles in the equations.

Existence of parameter ranges with real vertex coefficients.

Conditions under which propagators exhibit complex-conjugate poles.

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 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.