Two loop QCD vertices at the symmetric point

TL;DR

This paper calculates two-loop QCD vertex functions at the symmetric point, providing detailed renormalization constants and anomalous dimensions in multiple schemes, enhancing precision in quantum chromodynamics computations.

Contribution

It presents the first analytical computation of three schemes' vertex functions and their conversion functions at two loops, including three-loop anomalous dimensions and beta-functions.

Findings

Good agreement with previous Landau gauge estimates

Analytical expressions for conversion functions derived

Three-loop anomalous dimensions obtained for various schemes

Abstract

We compute the triple gluon, quark-gluon and ghost-gluon vertices of QCD at the symmetric subtraction point at two loops in the MSbar scheme. In addition we renormalize each of the three vertices in their respective momentum subtraction schemes, MOMggg, MOMq and MOMh. The conversion functions of all the wave functions, coupling constant and gauge parameter renormalization constants of each of the schemes relative to MSbar are determined analytically. These are then used to derive the three loop anomalous dimensions of the gluon, quark, Faddeev-Popov ghost and gauge parameter as well as the beta-function in an arbitrary linear covariant gauge for each MOM scheme. There is good agreement of the latter with earlier Landau gauge numerical estimates of Chetyrkin and Seidensticker.