Exploratory study of the three-gluon vertex on the lattice

Abstract

We define and evaluate on the lattice the amputated three-gluon vertex function in momentum space. We give numerical results for ${16}^3$×40 and ${24}^3$×40 quenched lattices at β=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 as defined from the three-gluon vertex, while being aware that a realistic calculation will require larger β values and very high statistics.