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.

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

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• Algorithm FIRE -- Feynman Integral REduction
• FIRE5: a C++ implementation of Feynman Integral REduction
• Towards the five-loop Beta function for a general gauge group
• Anomalous dimensions of gauge fields and gauge coupling beta-functions in the Standard Model at three loops
• Leading QCD-induced four-loop contributions to the $\beta$-function of the Higgs self-coupling in the SM and vacuum stability

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