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

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.

Comments: v2: reference added, version accepted by JHEP, v3: typo fixed in (3.4)