Four-loop QCD propagators and vertices with one vanishing external momentum

TL;DR

This paper presents four-loop calculations of QCD propagators and vertices with one vanishing external momentum, providing analytical results useful for high-precision perturbative studies and scheme conversions.

Contribution

The authors computed four-loop self-energies and three-particle vertex functions in massless QCD with full gauge dependence, including the derivation of the five-loop beta function in the MiniMOM scheme.

Findings

Analytical four-loop results for QCD propagators and vertices.

Explicit expressions for master integrals and rational coefficients.

Derivation of the five-loop beta function in the MiniMOM scheme.

Abstract

We have computed the self-energies and a set of three-particle vertex functions for massless QCD at the four-loop level in the MSbar renormalization scheme. The vertex functions are evaluated at points where one of the momenta vanishes. Analytical results are obtained for a generic gauge group and with the full gauge dependence, which was made possible by extensive use of the Forcer program for massless four-loop propagator integrals. The bare results in dimensional regularization are provided in terms of master integrals and rational coefficients; the latter are exact in any space-time dimension. Our results can be used for further precision investigations of the perturbative behaviour of the theory in schemes other than MSbar. As an example, we derive the five-loop beta function in a relatively common alternative, the minimal momentum subtraction (MiniMOM) scheme.