Symmetries of the 2HDM: an invariant formulation and consequences

TL;DR

This paper systematically analyzes the symmetries of the Two-Higgs-Doublet Model, providing invariant conditions and exploring their implications for physical parameters and renormalization group behavior.

Contribution

It offers a comprehensive invariant formulation of 2HDM symmetries, detailing conditions on masses and couplings, and examining their stability under renormalization.

Findings

Derived necessary and sufficient conditions for each symmetry.

Identified relations among physical parameters that are invariant under renormalization group.

Analyzed the interplay between potential symmetries and vacuum expectation values.

Abstract

Symmetries of the Two-Higgs-Doublet Model (2HDM) potential that can be extended to the whole Lagrangian, i.e. the CP-symmetries CP1, CP2, CP3 and the Higgs-family symmetries Z2, U(1) and SO(3) are discussed. Sufficient and necessary conditions in terms of constraints on masses and physical couplings for the potential to respect each of these symmetries are found. Each symmetry can be realized through several alternative cases, each case being a set of relations among physical parameters. We will show that some of those relations are invariant under the renormalization group, but others are not. The cases corresponding to each symmetry group are illustrated by analyzing the interplay between the potential and the vacuum expectation values.