A Compact Representation of the Three-Gluon Vertex

TL;DR

This paper presents a highly compact, unified representation of the one-loop three-gluon vertex in nonabelian gauge theory using the worldline formalism, revealing structural insights and sum rules.

Contribution

It introduces a unified, compact formula for scalar, spinor, and gluon loop contributions to the one-loop three-gluon vertex using the worldline formalism.

Findings

Derived a compact representation of the one-loop three-gluon vertex.

Established a SUSY-related sum rule from off-shell Bern-Kosower rules.

Connected the vertex structure to the low-energy effective action.

Abstract

The three-gluon vertex is a basic object of interest in nonabelian gauge theory. It contains important structural information, in particular on infrared divergences, and also figures prominently in the Schwinger-Dyson equations. At the one-loop level, it has been calculated and analyzed by a number of authors. Here we use the worldline formalism to unify the calculations of the scalar, spinor and gluon loop contributions to the one-loop vertex, leading to an extremely compact representation. The SUSY - related sum rule found by Binger and Brodsky follows from an off-shell extension of the Bern-Kosower replacement rules. We explain the relation of the structure of our representation to the low-energy effective action.