Beyond basis invariants

Abstract

Physical observables cannot depend on the basis one chooses to describe fields. Therefore, all physically relevant properties of a model are, in principle, expressible in terms of basis-invariant combinations of the parameters. However, in many cases it becomes prohibitively difficult to establish key physical features exclusively in terms of basis invariants. Here, we advocate an alternative route in such cases: the formulation of basis-invariant statements in terms of basis-covariant objects. We give several examples where the basis-covariant path is superior to the traditional approach in terms of basis invariants. In particular, this includes the formulation of necessary and sufficient basis-invariant conditions for various physically distinct forms of CP conservation in two- and three-Higgs-doublet models.

20 pages, no figures

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• Comparing 2HDM $+$ Scalar and Pseudoscalar Simplified Models at LHC
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• Exploring multi-Higgs models with softly broken large discrete symmetry groups
• Complex $S_3$-symmetric 3HDM
• Softly-broken $A_4$ or $S_4$ 3HDMs with stable states
• $U(1)$-charged Dark Matter in three-Higgs-doublet models
• Global Symmetries and Effective Potential of 2HDM in Orbit Space
• A fully basis invariant Symmetry Map of the 2HDM
• Symmetries from outer automorphisms and unorthodox group extensions
• Discriminating between $CP$ and family transformations in the bilinear space of NHDM
• The Hilbert Series and the Flavor Invariants of the 3HDM