Multi-Higgs and beyond: an odyssey from the vacuum to anomalies

The Standard Model of particle physics describes the structure of matter and fundamental interactions, whose content was complete with the observation of the Higgs boson in 2012, predicted exactly 60 years ago. However, the full puzzle remains unresolved with several indications that physics beyond the standard theory is needed. In this thesis we delve into extensions of the scalar sector, one of the most interesting possibilities of physics beyond the Standard Model.

We review extensions with one extra (real or complex) singlet, complex doublet, or complex triplet. Scalar triplet extensions provide an interesting playground for the explanation of neutrino masses. We do a thorough vacuum stability analysis in the model with just one complex triplet, illustrating the possible occurrence of non-physical minima. Propelled by the possible connections with leptonic chargeparity symmetry violation, we also explore the mass spectrum of the model with two complex triplets. If charge-parity is broken spontaneously by the vacuum, the existence of particles lighter than the Higgs boson is unavoidable.

Considering doublet extensions, we build a lepton-specific four-doublet model, in which scalars can have substantial decays into electrons and muons, in contrast to the usual leptonic decays into taus. Finally, we look at two experimental measurements that continue to defy a Standard Model explanation.

The anomalous magnetic moment of the muon can be accommodated in the framework of two-Higgs-doublet models but it clashes with other experimental constraints. We show that adding vector-like leptons that do not mix with Standard Model leptons can alleviate this issue, but problems with perturbativity arise.

We then revisit one of the first solutions put forward to the ATOMKI anomalies in the form of a new gauge boson whose charge is the difference between the baryon and the lepton number. We clarify its several drawbacks, even after adding vector-like leptons.