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

Understand

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.