Multiscalar models - theoretical puzzles and LHC searches

The Standard model contains a single elementary scalar particle, the Higgs boson, discovered at the LHC in 2012. The Model is remarkably successful, but it leaves a great deal of unanswered questions. There have been many attempts to addressed some of those open issues, by enlarging the scalar sector, thus predicting a richer spectrum of spin-0 elementary particles. This allows one to create models where one may: have Dark Matter candidates complying with all current experiemental constraints; predict spontaneous (or explicit) CP violation arising from the scalar sector; or explain eventual excesses in LHC search channels.

A larger scalar spectrum, however, raises problems of its own: the size of the parameter space increases, with potentially a large number of parameters with unknown values and ranges reducing the model's predictivity. The vacuum state of the theory is no longer guaranteed, in many multiscalar models, to lead to the correct electroweak symmetry breaking. Tree-level flavour changing neutral currents (FCNC) mediated by neutral scalars are on many occasions possible, the magnitude of those couplings heavily restricted by existing experimental data.

In this seminar I'll review the basic constraints one needs to ask of multiscalar models to be certain it is a viable model; and the "tools of the trade" to help when one is creating a model with specific purposes. I'll also show several recent results  discussing vacuum stability in several multiscalar models; a simple solution to the strong-CP problem; constraints on multiscalar parameter space from dark matter searches; and exotic sources of CP violation.