After a long history of searches, a Higgs boson H was discovered by the ATLAS and the CMS experiments at the Large Hadron Collider (LHC) in 2012. Its properties fit well the ones predicted by the Standard Model (SM) of particle physics. However, the SM can not explain other established properties of Nature, such as the existence of Dark Matter. For this reason, models beyond the SM should be considered. In this talk, I will give a summary of my PhD-thesis which I succesfully defended on the 27th of February.

By confronting some 2HDMs with publically available data from the LHC, using the codes HiggsBounds and HiggsSignals, compatible parameter spaces are obtained.

A new kind of 2HDM, called the Stealth Doublet Model, is presented and the properties of its Higgs bosons are studied. In this model, it is shown that in particular the properties of the charged Higgs boson H± have new features not exhibited in earlier studied models. Within the parameter space compatible with the LHC results, the production cross section for H± can be sizeable enough to be experimentally observed.

Finally, the discovery prospects at the LHC, for a H± in the pp → tH± process, with the decays H± → HW± and H → bb, is studied in various models beyond the Standard Model. It is shown that for supersymmetric models (MSSM and NMSSM), this channel is beyond the discovery reach of the LHC. In some of the other studied models, in particular the Aligned 2HDM, the situation is improved and the channel is feasible.