Gauge coupling beta functions in the standard model to three loops

In this Letter, we compute the three-loop corrections to the beta functions of the three gauge couplings in the standard model of particle physics using the minimal subtraction scheme and taking into account Yukawa and Higgs self-couplings.

Figure 1

Sample Feynman diagrams contributing to the $W_1{W}_2{W}_3$ vertex [(a), (b) and (c)] and the ghost-$W_3$ vertex [(d) and (e)]. Dashed, dotted, solid, and wavy lines correspond to Higgs boson, ghost, fermion, and $W$ boson lines, respectively. Sample diagrams for gluonic Green’s functions are obtained for (a), (b), (d), and (e) by replacing the $W$ lines by gluon lines.