Perturbative Analysis of the Three Gluon Vertex in Different Gauges at One-Loop

In this study, we present a perturbative analysis of the three-gluon vertex for a kinematical symmetric configuration in dimensions n=4-2 & varepsilon;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=4-2\epsilon $$\end{document} and different covariant gauges. Our study can describe the form factors of the three gluon vertex in a wide range of momentum. We employ a momentum subtraction scheme to define the renormalized vertex. We give an in-depth review of three commonly used vector representations for the vertex, and explicitly show the expressions to change from one representation to the other. Although our estimates are valid only in the perturbative regime, we extend our numerical predictions to the infrared domain and show that in n=4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=4$$\end{document} some nonperturbative properties are qualitatively present already at perturbation theory. In particular, we find a critical gauge above which the leading form factor displays the so-called zero crossing. We contrast our findings to those of other models and observe a fairly good agreement.