Gauge coupling beta functions to four-loop order in the Standard Model

We compute the beta functions of the three Standard Model gauge couplings to four-loop order in the modified minimal subtraction scheme. At this order a proper definition of $γ_5$ in $D=4-2ε$ space-time dimensions is required; however, in our calculation we determine the $γ_5$-dependent terms by exploiting relations with beta function coefficients at lower loop orders.

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