Abstract
In this paper we analyse in detail an $S_3$-symmetric three-Higgs-doublet model with a specific vacuum configuration. This analysis allows us to illustrate important features of models with several Higgs doublets, such as the possibility of having spontaneous CP violation. We start with a real potential and pick a particularly interesting complex vacuum configuration, which does not violate CP before adding soft breaking terms to the potential. We study the r\^ ole played by different soft symmetry breaking terms. These are essential for our choice of vacuum in order to remove unwanted massless scalars which arise from the spontaneous breaking of an accidental continuous symmetry. We list scalar sector and scalar-gauge sector-couplings for the particular case we consider in detail in this work. Results presented in this paper will be useful for model building, in particular for implementations of models with $S_3$ symmetry and spontaneous CP violation, extensions of the fermionic sector with realistic Yukawa couplings and for Dark Matter studies.
Highlights
In the Standard Model there is only one Higgs doublet, leading, through the Higgs mechanism [1,2,3,4], to the existence of one Higgs boson
We have presented a detailed discussion of some 3HDM vacua obtained from an S3-symmetric potential with soft symmetry breaking
We have shown that some vacuum solutions require conditions on the parameters of the potential that lead to accidental continuous symmetries that in turn are broken by the vacuum
Summary
In the Standard Model there is only one Higgs doublet, leading, through the Higgs mechanism [1,2,3,4], to the existence of one Higgs boson. These massless states are due to the spontaneous breaking of accidental continuous symmetries resulting from constraints imposed on the region of parameters arising from the minimization conditions, with a few rare exceptions that will be pointed out in the paper The identification of such symmetries is of great relevance and has been dealt with in the context of general three-Higgs-doublet models (3HDMs) by several authors [21,22] Results presented in this paper will be important for model building, in particular for implementations of models with S3 symmetry and spontaneous CP violation, extensions of the fermionic sector with realistic Yukawa couplings and for dark matter studies
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
