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.

Computable conditions for order-2 CP symmetry in NHDM potentials

“…Below are the numerical values for the parameter point used in the example analyzed in section 4.3. All the non-zero elements are listed, except those which can be obtained by JHEP05(2024)260 3,4,5,6,22,23,24,25,26,27, 8,10,11,12,15,28,29,31,32,33,36,40,41,42, 16,17,19,20,21,34,37,38, Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.…”

“…As an example with four doublets, we now study a Z 6 -symmetric 4HDM potential which has both non-CP 2 and CP 2-symmetric parameter points [37]. Consider the following numerical instance…”