S3 as flavour symmetry: Higgs sector and Dark matter
Myriam Mondragon (UNAM)

We present models with an extended Higgs sector, three Higgs doublets, which have an underlying S3 flavour symmetry.
S3 is the smallest non-Abelian discrete group, corresponding to the permutation of three objects, which makes it naturally suitable for a flavour symmetry. We apply this symmetry "universally" to the fermionic and scalar sectors.
We review some previous results in the fermionic sector (quarks and leptons), as well as recent results in the Higgs sector derived from the minimization of the potential and the explicit calculation of the Higgs-Higgs and Higgs-gauge boson couplings. We show that in the exact alignment limit (when only one of the Higgs bosons couples to the gauge bosons), the results at tree level coincide exactly with the Standard Model ones. We present the allowed parameter space for the scalar masses in the two possible alignment scenarios, with some interesting consequences. We also present the results for a dark matter candidate coming from this type of models, with a fourth inert Higgs.