A fully basis invariant symmetry map of the 2HDM

• Published in: The journal of high energy physics 2021-02, Vol.2021 (2), Article 220
• Main Authors: Bento, Miguel P., Boto, Rafael, Silva, João P., Trautner, Andreas
• Format: Article
• Language: English
• Subjects: Classical and Quantum Gravitation; Elementary Particles; Flavor (particle physics); High energy physics; Invariants; Mathematical models; Parameters; Particle physics; Physical properties; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Symmetry
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP02(2021)220

A bstract 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.