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A fully basis invariant Symmetry Map of the 2HDM

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arxiv 2009.01264 v1 pith:V457CJ4J submitted 2020-09-02 hep-ph hep-th

Miguel P. Bento , Rafael Boto , João P. Silva , Andreas Trautner This is my paper · ORCID
classification hep-phhep-th
keywords basisinvariantobjectsmodelsymmetriesconditionsderiveentirely
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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.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. GOOFy-compatible 3HDMs and beyond

    hep-ph 2026-08 conditional novelty 7.0 of 10

    A GOOFy-compatible quadratic sector requires a sign character realized in R*otimesR, and the RG stability of the 2HDM r0 relation is a unique SU(2) accident.

  2. The Hilbert Series and the Flavor Invariants of the 3HDM

    hep-th 2026-04 unverdicted novelty 6.0 of 10

    The full multigraded Hilbert series of the 3HDM is computed in closed form, and a basis of SU(3)-invariant operators is constructed up to cubic order in the quartic couplings.

  3. Systematic analysis of 3HDM symmetries

    hep-ph 2025-12 conditional novelty 6.0 of 10

    A systematic catalogue of realisable Higgs-family, general-CP, and GOOFy/T-GOOFy symmetries in three-Higgs-doublet models, with new invariant potentials and a corrected U(1)◦V4 group structure.

  4. Dark Matter and CP Violation in Some Symmetry-Constrained 3HDMs

    hep-ph 2025-06 conditional novelty 4.0 of 10

    S3-symmetric three-Higgs-doublet models allow dark matter in a 29-42 GeV window, exclude heavy candidates above 500 GeV, and admit MeV-scale light scalars, while continuous-symmetry variants produce mass-degenerate da...

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