Exploratory Study of the 3-Gluon Vertex on the Lattice

TL;DR

This study explores the lattice evaluation of the 3-gluon vertex function in momentum space, providing numerical results and investigating finite volume effects, with implications for calculating the QCD running coupling constant.

Contribution

It introduces a method for evaluating the 3-gluon vertex on the lattice and compares results across different volumes to assess finite volume effects.

Findings

Good numerical signals obtained for the vertex function.

Finite volume effects analyzed through volume comparison.

Proposed a method for lattice evaluation of the QCD running coupling.

Abstract

We define and evaluate on the lattice the amputated 3-gluon vertex function in momentum space. We give numerical results for $16^3 \times 40$ and $24^3 \times 40$ quenched lattices at $\beta=6.0$. A good numerical signal is obtained, at the price of enforcing the gauge-fixing condition with high accuracy. By comparing results from two different lattice volumes, we try to investigate the crucial issue of finite volume effects. We also outline a method for the lattice evaluation of the QCD running coupling constant as defined from the 3-gluon vertex, while being aware that a realistic calculation will require larger $\beta$ values and very high statistics.