A gauge-technique Ansatz for the three gluon vertex of the background field method

TL;DR

This paper develops a comprehensive gauge-invariant Ansatz for the three-gluon vertex involving background and quantum gluons, satisfying key Ward and Slavnov-Taylor identities crucial for non-perturbative QCD studies.

Contribution

It introduces a novel Ansatz for the three-gluon vertex that fully satisfies gauge symmetry identities, advancing non-perturbative quantum chromodynamics analysis.

Findings

The Ansatz satisfies both Ward and Slavnov-Taylor identities.

Constraints on ghost form-factors are valid to all orders.

Provides a consistent framework for the gluon vertex in background field method.

Abstract

The vertex connecting one background gluon with two quantum ones constitutes a central ingredient in the gauge-invariant Schwinger-Dyson equation that determines the non-perturbative dynamics of the gluon propagator. This vertex satisfies a Ward identity with respect to the background gluon, and a Slavnov-Taylor identity with respect to the two quantum gluons. We present a complete Ansatz for this vertex, which satisfies both aforementioned identities. This entire construction depends crucially on a set of constraints relating the various form-factors of the ghost Green's functions appearing in the Slavnov-Taylor identity satisfied by the vertex. The validity of these constraints is demonstrated to all orders.