Four-loop QCD $\beta$-function with different fermion representations of the gauge group

TL;DR

This paper provides a detailed four-loop calculation of the QCD $eta$-function for various fermion representations, including implications for supersymmetric models, advancing precision in gauge coupling evolution.

Contribution

It presents the first analytical four-loop $eta$-function for a generic gauge group with multiple fermion representations, including gluino contributions in supersymmetry.

Findings

Analytical four-loop $eta$-function for generic gauge groups.

Explicit gluino contribution to the strong coupling $eta$-function.

Enhanced precision for gauge coupling evolution in theories beyond the Standard Model.

Abstract

We present analytical results at four-loop level for the $\beta$-function of the coupling of a generic gauge group and any number of different quark representations. From this we can directly derive the gluino contribution to the strong coupling $\beta$-function of supersymmetric extensions of the Standard Model.