# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1703.08532