# Four-loop renormalization of QCD with a reducible fermion representation of the gauge group: anomalous dimensions and renormalization constants

## TL;DR

This paper provides four-loop analytical calculations of renormalization constants and anomalous dimensions in an extended QCD model with multiple fermion representations, including gauge parameter dependence, advancing precision in quantum field theory computations.

## Contribution

It delivers the first four-loop results for renormalization constants and anomalous dimensions in a generalized QCD model with arbitrary fermion representations and gauge parameter.

## Key findings

- Analytical four-loop renormalization constants for gauge, ghost, and fermion fields.
- Results applicable to supersymmetric models with gluinos in the adjoint representation.
- Gauge parameter dependence included in the renormalization constants.

## Abstract

We present analytical results at four-loop level for the renormalization constants and anomalous dimensions of an extended QCD model with one coupling constant and an arbitrary number of fermion representations. One example of such a model is the QCD plus gluinos sector of a supersymmetric theory where the gluinos are Majorana fermions in the adjoint representation of the gauge group. The renormalization constants of the gauge boson, ghost and fermion fields are analytically computed as well as those for the ghost-gluon vertex, the fermion-gluon vertex and the fermion mass. All other renormalization constants can be derived from these. Some of these results were already produced in Feynman gauge for the computation of the beta-function of this model, which was recently published. Here we present results for an arbitrary gauge parameter.