Dark Matter and CP Violation in Some SymmetryConstrained 3HDMs

It is now widely recognised that the Standard Model of Particle Physics is not the ultimate theory. Among the simplest extensions capable of addressing many of its shortcomings the multi-Higgs-doublet models. We focus on three-Higgs-doublet models, examining their potential to explain the dark matter puzzle and exploring whether they can introduce new sources of CP violation. Multi-Higgs-doublet models can accommodate a dark matter candidate. An underlying symmetry not only ensures the candidate’s stability but also helps control the number of free parameters.

We consider two scenarios. First, we explore dark matter candidates in the S3-symmetric three-Higgs-doublet model. Notably, our findings reveal that the cases we discuss allow for different dark matter mass ranges compared to other candidates within three-Higgs-doublet models. Additionally, we investigate an alternative to conventional stabilization via discrete symmetries by examining stabilization through continuous symmetries.

This alternative approach exhibits a unique characteristic—the emergence of mass-degenerate states. We also explore the impact of CP violation in the S3-symmetric three-Higgs-doublet model. In extended scalar frameworks, CP violation can arise either directly at the Lagrangian level or indirectly through the vacuum structure. Our analysis investigates how different representations of quarks under the S3 group, combined with various vacuum configurations, lead to distinct phenomenological consequences, including the possibility of very light neutral scalars.

Overall, our extensive classification of promising scenarios for dark matter and CP violation lays a strong foundation for future research. Further detailed studies will be essential to fully explore our results. Our work paves the way for deeper insights into dark matter and CP violation within extended scalar sectors, underscores the rich complexity and potential of multi-Higgs models, and provides numerous results that can be readily utilized by model builders.