Extended Iterative Scheme for QCD: the Four-Gluon Vertex

TL;DR

This paper investigates a nonperturbative approach to the four-gluon vertex in QCD, using an extended perturbation scheme and Dyson-Schwinger equations to find self-consistent solutions.

Contribution

It introduces a minimal tensor basis and a linear, overdetermined system for the four-gluon vertex, providing approximate solutions in specific QCD scenarios.

Findings

Near decoupling from 2- and 3-point conditions allows least-squares solutions.

Solutions are obtained for N_F=2 massless quarks and pure gluon theory.

The approach offers a nonperturbative perspective on the four-gluon vertex in QCD.

Abstract

We study the self-consistency problem of the generalized Feynman rule (nonperturbatively modified vertex of zeroth perturbative order) for the 4-gluon vertex function in the framework of an extended perturbation scheme accounting for non-analytic coupling dependence through the Lambda scale. Tensorial structure is restricted to a minimal dynamically closed basis set. The self-consistency conditions are obtained at one loop, in Landau gauge, and at the lowest approximation level (r=1) of interest for QCD. At this level, they are found to be linear in the nonperturbative 4-gluon coefficients, but strongly overdetermined due to the lack of manifest Bose symmetry in the relevant Dyson-Schwinger equation. The observed near decoupling from the 2-and-3-point conditions permits least-squares quasisolutions for given 2-and-3-point input within an effective one-parameter freedom. We present such solutions for N_F=2 massless quarks and for the pure gluon theory, adapted to the 2-and-3-point coefficients determined previously.