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.
Highlights
We present the beta functions of gauge and Yukawa couplings in general four-dimensional quantum field theory, at four and three loops, respectively
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
Introduction.—Renormalization group equations (RGE) find their numerous applications in many physical problems formulated in the language of quantum field theory (QFT)
Summary
We, for the first time, design simple toy models with specific gauge group structure, each giving constraints on different unknown coefficients. We use diagrams for TS provided in Supplemental Materials of Ref. [25] as a guide, but it is fair to say that we found the required models by trial and error. We use TSs implemented in the prominent code RGBeta [33] to speed up our investigation. General four-dimensional QFT that covers most of possible phenomenological applications can be written in the form [25]
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