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

TL;DR

The paper computes the full set of massless QCD 2-point and 3-point functions at three-loop order in the MSbar scheme for an asymmetric kinematic point with one vanishing momentum (the ZP). Using these results, it derives conversion factors to four tilde MOM-like schemes and determines their four-loop beta-function coefficients by leveraging the known four-loop MSbar beta-function. The authors apply the framework to the lattice-determined running of the three-gluon asymmetrical vertex, showing that including the four-loop term reduces the non-perturbative $1/p^2$ contribution by about 30%. This work provides high-precision perturbative inputs for lattice renormalization and strengthens the consistency between perturbative QCD and lattice determinations within the MOM scheme framework.

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.