# The 3-loop Beta Function of QCD

## TL;DR

This paper calculates the 3-loop beta function for lattice SU(N) gauge theories using the background field method, providing new results for pure gluonic cases and progress on QCD with Wilson fermions.

## Contribution

It presents the first 3-loop beta function calculation for lattice SU(N) gauge theories and compares results with recent studies, advancing understanding of lattice QCD.

## Key findings

- 3-loop beta function computed for pure gluonic SU(N)
- Comparison with recent results by Luescher and Weisz
- Progress reported on QCD with Wilson fermions

## Abstract

Using the background field technique, we calculate the 3-loop beta function of lattice $SU(N)$ gauge theories. In the pure gluonic case, we present our results, comparing to those recently obtained by Luescher and Weisz. We also provide a progress report in the case of QCD with Wilson fermions.