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

Abstract

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 ${\gamma }_5$ in $D=4-2ϵ$ space-time dimensions is required; however, in our calculation we determine the ${\gamma }_5$-dependent terms by exploiting relations with beta function coefficients at lower loop orders.

Comments: 6 pages, 2 figures