Three-loop Three-Linear Vertices and Four-Loop MOM beta functions in massless QCD

TL;DR

This paper computes three-loop three-point functions in massless QCD, relates MSbar and MOM schemes, and determines four-loop beta-function coefficients, impacting the understanding of the running coupling and non-perturbative effects.

Contribution

It provides the first complete three-loop vertex functions in massless QCD and derives four-loop MOM beta-functions, enhancing precision in coupling constant calculations.

Findings

Four-loop MOM beta-function coefficients determined.

Significant 30% reduction in non-perturbative correction estimate.

Improved understanding of the running of the coupling in QCD.

Abstract

In this paper we present a full set of 2- and 3-point functions for massless QCD at three-loop order in the MSbar scheme. The vertex functions are evaluated at the asymmetric point with one vanishing momentum. These results are used to relate the MSbar coupling constant to that of various momentum subtraction renormalization schemes at three-loop order. With the help of the known four-loop MS-bar beta-function we then determine the four-loop coefficients of the corresponding MOM beta-functions. As an application we consider the momentum dependence (running) of the three-gluon asymmetrical vertex recently computed within the lattice approach by Ph. Boucaud et al. (JHEP 04 006 (2000)). An account of the four-loop term in the corresponding beta-function leads to a significant (around 30%) decrease of the value of the non-perturbative power-suppressed correction to the running.