Towards the five-loop Beta function for a general gauge group

TL;DR

This paper computes new five-loop Beta function terms for general gauge groups, confirming some previous results and extending knowledge for others, which is crucial for understanding gauge theory behaviors at high energies.

Contribution

It provides the first analytical calculations of the $N_f^3$ five-loop Beta function term for general gauge groups, expanding beyond previous SU(3) specific results.

Findings

The $N_f^4$ term agrees with large-$N_f$ studies.

The $N_f^3$ term is newly calculated for general gauge groups.

Results enhance understanding of gauge theories at high loop orders.

Abstract

We present analytical results for the $N_f^4$ and $N_f^3$ terms of the five-loop Beta function, for a general gauge group. While the former term agrees with results available from large-$N_f$ studies, the latter is new and extends the value known for SU(3) from an independent calculation.