Gauge and Yukawa coupling beta functions of two-Higgs-doublet models to three-loop order

TL;DR

This paper calculates three-loop beta functions for gauge and Yukawa couplings in general two-Higgs-doublet models, providing detailed results and addressing technical issues like poles in anomalous dimensions.

Contribution

It presents the first three-loop beta functions for Yukawa couplings in two-Higgs-doublet models and offers an independent check for the Standard Model.

Findings

Explicit three-loop beta functions for gauge and Yukawa couplings.

Practical prescriptions to handle poles in anomalous dimensions.

First independent verification of Standard Model Yukawa beta functions.

Abstract

We compute the beta functions for the three gauge couplings and the Yukawa matrices of a general two-Higgs-doublet model in the modified minimal subtraction scheme to three loops. The calculations are performed using Lorenz gauge in the unbroken phase. We discuss in detail the occurence of poles in anomalous dimensions and propose practical prescriptions to avoid them. We provide explicit results for the often used $\mathbb{Z}_2$-symmetric versions of the two-Higgs-doublet model of type I, II, X and Y. Furthermore, we provide the first independent cross-check of the three-loop Yukawa coupling beta functions of the Standard Model.