On three-loop RGE for the Higgs sector of 2HDM

TL;DR

This paper derives three-loop renormalization group equations for the Higgs sector in the general Two-Higgs-Doublet Model, focusing on self-couplings and using invariants to simplify the structure.

Contribution

It provides the first three-loop RGE results for the 2HDM Higgs sector, utilizing invariants and the Cayley-Hamilton theorem to simplify tensor structures.

Findings

Discovered inaccuracies in two-loop RGE implementations in public packages.

Derived minimal set of invariants for Higgs sector RGE.

Highlighted importance of correct RGE for scalar sector in multi-Higgs models.

Abstract

We discuss renormalization group equations (RGE) for the parameters of the Higgs sector in general Two-Higgs-Doublet Model (2HDM). We present the three-loop results but consider only contributions due to self-couplings of the Higgs doublets. We study the structure of RGE and express beta-functions in terms of reparametrization invariants with respect to higgs-basis rotations. The Cayley-Hamilton theorem is utilized to reduce both the number of independent tensor structures in matrix RGE and the number of invariants to a minimal set. As a by-product of our calculation we discovered that two-loop RGE of the scalar sector in general QFT with multiple higgses were not properly implemented in a number of public packages. The latter give rise to a wrong result when mixing in the scalar sector is allowed.