# On the self-consistency of off-shell Slavnov-Taylor identities in QCD

## TL;DR

This paper investigates the off-shell Slavnov-Taylor identities in QCD using algebraic and diagrammatic methods, demonstrating their consistency at one loop for gluon vertices and self-energies.

## Contribution

It introduces a Hopf-algebraic and diagrammatic framework to analyze off-shell Slavnov-Taylor identities in QCD, including explicit relations for gluon vertices at one loop.

## Key findings

- Gluon self-energy can be replaced by ghost self-energy via longitudinal projection.
- Derived consistent relations for triple and quartic gluon vertices at one loop.
- Validated identities at specific off-shell momentum configurations.

## Abstract

Using Hopf-algebraic structures as well as diagrammatic techniques for determining the Slavnov-Taylor identities for QCD we construct the relations for the triple and quartic gluon vertices at one loop. By making the longitudinal projection on an external gluon of a Green's function we show that the gluon self-energy of that leg is consistently replaced by a ghost self-energy. The resulting identities are then studied by evaluating all the graphs for an off-shell non-exceptional momentum configuration. In the case of the 3-point function this is for the most general momentum case and for the 4-point function we consider the fully symmetric point.

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Source: https://tomesphere.com/paper/1906.07996