Four-Loop Gauge and Three-Loop Yukawa Beta Functions in a General Renormalizable Theory

Abstract

We present the beta functions of gauge and Yukawa couplings in general four-dimensional quantum field theory, at four and three loops, respectively. The essence of our approach is fixing unknown coefficients in the most general ansatz for beta functions by direct calculation in several simplified models. We apply our results to the standard model and its extension with an arbitrary number of Higgs doublets and provide expressions for all four-loop gauge couplings beta functions with matrix Yukawa interactions.