Recognizing symmetries in 3HDM in basis-independent way

Abstract

Higgs doublets may come in three generations. The scalar sector of the resulting three-Higgs-doublet model (3HDM) may be constrained by global symmetry groups $G$ leading to characteristic phenomenology. There exists the full list of symmetry groups $G$ realizable in the 3HDM scalar sector and the expressions for $G$-symmetric scalar potentials written in special bases where the generators of $G$ take simple form. However recognizing the presence of a symmetry in a generic basis remains a major technical challenge, which impedes efficient exploration of the 3HDM parameter space. In this paper, we solve this problem using the recently proposed approach, in which basis-independent conditions are formulated as relations among basis-covariant objects. We develop the formalism and derive basis-independent necessary and sufficient conditions for the 3HDM scalar sector to be invariant under each of the realizable symmetry group. We also comment on phenomenological consequences of these results.

39 pages

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Cited by in corpus (13)

• Unitarity bounds for all symmetry-constrained 3HDMs
• Exploring multi-Higgs models with softly broken large discrete symmetry groups
• Complex $S_3$-symmetric 3HDM
• Anomaly-free axion dark matter in three Higgs doublet model and its phenomenological implications
• Softly-broken $A_4$ or $S_4$ 3HDMs with stable states
• $U(1)$-charged Dark Matter in three-Higgs-doublet models
• Symmetries for the 4HDM: extensions of cyclic groups
• Systematic analysis of 3HDM symmetries
• Computable conditions for order-2 $CP$ symmetry in NHDM potentials
• Symmetries from outer automorphisms and unorthodox group extensions
• Discriminating between $CP$ and family transformations in the bilinear space of NHDM
• Representation-theoretical characterization of canonical custodial symmetry in NHDM potentials
• The Hilbert Series and the Flavor Invariants of the 3HDM