Symmetries for the 4HDM: II. Extensions by rephasing groups

• Published in: Journal of physics. A, Mathematical and theoretical Vol. 57; no. 38; pp. 385401 - 385427
• Main Authors: Shao, Jiazhen, Ivanov, Igor P, Korhonen, Mikko
• Format: Journal Article
• Language: English
• Published: IOP Publishing 11.10.2024
• Subjects: automorphism groups; global symmetries; group extensions; multi-higgs-doublet models; non-abelian groups
• ISSN: 1751-8113; 1751-8121
• DOI: 10.1088/1751-8121/ad7340

We continue classification of finite groups which can be used as symmetry group of the scalar sector of the four-Higgs-doublet model (4HDM). Our objective is to systematically construct non-abelian groups via the group extension procedure, starting from the abelian groups A and their automorphism groups Aut ( A ) . Previously, we considered all cyclic groups A available for the 4HDM scalar sector. Here, we further develop the method and apply it to extensions by the remaining rephasing groups A , namely A = Z 2 × Z 2 , Z 4 × Z 2 , and Z 2 × Z 2 × Z 2 . As Aut ( A ) grows, the procedure becomes more laborious, but we prove an isomorphism theorem which helps classify all the options. We also comment on what remains to be done to complete the classification of all finite non-abelian groups realizable in the 4HDM scalar sector without accidental continuous symmetries.