Exploring the Quark-Gluon Vertex with Slavnov-Taylor Identities and Lattice Simulations

TL;DR

This paper investigates the longitudinal quark-gluon vertex in QCD using Slavnov-Taylor identities and lattice simulations, revealing how the vertex's form factors behave in the soft gluon limit and connecting them to the gluon propagator.

Contribution

It derives exact relations for the longitudinal form factors of the quark-gluon vertex in the soft gluon limit using STI and lattice data, providing new insights into their non-perturbative structure.

Findings

The form factor λ₁ aligns with the gluon propagator's momentum dependence.

Relations between form factors λ₂ and λ₃ are established through lattice and STI analysis.

The study connects the vertex structure to the gluon propagator via a dressed one-loop Bethe-Salpeter equation.

Abstract

The soft gluon limit of the longitudinal part of the quark-gluon vertex is studied by resorting to non-perturbative approaches to Quantum Chromodynamics (QCD). Based on a Slavnov-Taylor identity (STI), the longitudinal form factors is expressed in terms of the quark-ghost kernel, the quark self energy and the quark wave function. An exact relation between the non-vanishing longitudinal form factors is derived for the soft gluon limit and explored to understand the behaviour of the vertex. Within a Ball-Chiu vertex, the form factor $\lambda_1$ was analysed using recent lattice simulations for full QCD for the soft gluon limit. The lattice data shows that the gluon propagator resumes the momentum dependence of such component of the vertex. This connection is understood via a fully dressed one-loop Bethe-Salpeter equation. The behaviour of the remaining longitudinal form factors $\lambda_2(p^2)$ and $\lambda_3(p^2)$ is investigated combining both the information of lattice simulations and the derived relations based on the STI.