Numerical Study of the Ghost-Ghost-Gluon Vertex on the Lattice

TL;DR

This paper presents a preliminary lattice QCD study of the ghost-ghost-gluon vertex in Landau gauge, aiming to verify its finiteness and constancy non-perturbatively through Monte Carlo simulations.

Contribution

It provides the first non-perturbative numerical analysis of the ghost-ghost-gluon vertex in SU(2) lattice Landau gauge, extending understanding beyond perturbation theory.

Findings

Data suggest the vertex renormalization function is finite.

Results are consistent with perturbative predictions.

Study covers multiple lattice couplings and sizes.

Abstract

It is well known that, in Landau gauge, the renormalization function of the ghost-ghost-gluon vertex \widetilde{Z}_1(p^2) is finite and constant, at least to all orders of perturbation theory. On the other hand, a direct non-perturbative verification of this result using numerical simulations of lattice QCD is still missing. Here we present a preliminary numerical study of the ghost-ghost-gluon vertex and of its corresponding renormalization function using Monte Carlo simulations in SU(2) lattice Landau gauge. Data were obtained in 4 dimensions for lattice couplings beta = 2.2, 2.3, 2.4 and lattice sides N = 4, 8, 16.