Gauge Coupling Beta Functions in the Standard Model to Three Loops

TL;DR

The three-loop corrections to the beta functions of the three gauge couplings in the standard model of particle physics are computed using the minimal subtraction scheme and taking into account Yukawa and Higgs self-couplings.

Abstract

In this paper 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.

Figures (1)

• Figure 1: Sample Feynman diagrams contributing to the $W_1W_2W_3$ 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.