More on the three-gluon vertex in SU(2) Yang-Mills theory in three and four dimensions

TL;DR

This paper provides an updated lattice study of the three-gluon vertex in SU(2) Yang-Mills theory across multiple dimensions, revealing a zero crossing and infrared divergence in three dimensions, with preliminary findings in four dimensions.

Contribution

It offers new lattice calculations of the three-gluon vertex in various configurations, confirming infrared divergence and zero crossing in three dimensions, and extending insights into four dimensions.

Findings

Zero crossing of the form-factor in 3D observed.

Infrared divergence consistent with power-law behavior.

Preliminary results in 4D suggest similar infrared behavior.

Abstract

The three-gluon vertex has been found to be a vital ingredient in non-perturbative functional approaches. We present an updated lattice calculation of it in various kinematical configurations for all tensor structures and multiple lattice parameters in three dimensions, and in a subset of those in four dimensions, for SU(2) Yang-Mills theory in minimal Landau gauge. In three dimensions an unambiguous zero crossing for the tree-level form-factor is established, and consistency for all investigated form factors with a power-like divergence towards the infrared is observed. Using very coarse lattices this is even seen towards momenta as low as about 15 MeV. The results in four dimensions are consistent with such a behavior, but do not yet reach deep enough into the infrared to establish it.