Symmetries for the 4HDM: extensions of cyclic groups

Abstract

Multi-Higgs models equipped with global symmetry groups, either exact or softly broken, offer a rich framework for constructions beyond the Standard Model and lead to remarkable phenomenological consequences. Knowing all the symmetry options within each class of models can guide its phenomenological exploration, as confirmed by the vast literature on the two- and three-Higgs-doublet models. Here, we begin a systematic study of finite non-abelian symmetry groups which can be imposed on the scalar sector of the four-Higgs-doublet model (4HDM) without leading to accidental symmetries. In this work, we derive the full list of such non-abelian groups available in the 4HDM that can be constructed as extensions of cyclic groups by their automorphism groups. This list is remarkably restricted but it contains cases which have not been previously studied. Since the methods we develop may prove useful for other classes of models, we present them in a pedagogical manner.

v2: 36 pages, 2 tables, additional clarifications, matches the published version

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Cited by in corpus (5)

• Lie symmetry analysis of the two-Higgs-doublet model field equations
• Symmetries for the 4HDM. II. Extensions by rephasing groups
• Symmetries from outer automorphisms and unorthodox group extensions
• Computable conditions for order-2 $CP$ symmetry in NHDM potentials
• Representation-theoretical characterization of canonical custodial symmetry in NHDM potentials