A fully basis invariant Symmetry Map of the 2HDM

TL;DR

This paper develops a comprehensive, basis-invariant framework to identify and classify all global symmetries, including CP conservation, in the general two Higgs doublet model, providing a foundational tool for symmetry analysis in related theories.

Contribution

It introduces a basis-invariant 'Symmetry Map' for the 2HDM, detailing how symmetries manifest and deriving conditions for CP conservation solely in terms of invariant quantities.

Findings

Derived necessary and sufficient conditions for all global symmetries in 2HDM.

Established basis-invariant criteria for CP conservation.

Revealed two algebraically distinct ways symmetries can manifest in the model.

Abstract

We derive necessary and sufficient conditions for all global symmetries of the most general two Higgs doublet model (2HDM) scalar potential entirely in terms of reparametrization independent, i.e. basis invariant, objects. This culminates in what we call a "Symmetry Map" of the parameter space of the model and the fundamental insight that there are, in general, two algebraically distinct ways of how symmetries manifest themselves on basis invariant objects: either, basis invariant objects can be non-trivially related, or, basis covariant objects can vanish. These two options have different consequences on the resulting structure of the ring of basis invariants and on the number of remaining physical parameters. Alongside, we derive for the first time necessary and sufficient conditions for CP conservation in the 2HDM entirely in terms of CP-even quantities. This study lays the methodological foundation for analogous investigations of global symmetries in all other models that have unphysical freedom of reparametrization, most notably the Standard Model flavor sector.