Multi-Higgs Doublet Models

Abstract

This thesis is aimed at the study of softly-broken $A_4$ or $S_4$ 3 Higgs Doublet Models. Regarding these, two topics are discussed.

In the first they are studied via the introduction of parameters that softly break the respective symmetries but preserve the directions of the vacuum expectation values of the triplet. Within this regime, we first conduct an analysis of the masses of physical states, highlighting common properties in the mass spectra of the extended scalar sector. Beyond this, we focus on the decay properties of these particles, with the goal of identifying dark matter candidates. We have identified a particular case where these candidates are accommodated without any further restrictions on the model.

The second topic concerns an adaptation of a geometric method so that it suits softly-broken potentials. We discuss aspects to be taken into account so that our proposed method can be successful.

This is then exemplified in an application to the softly-broken $S_4$ symmetric potential with general diagonal soft-breaking parameters. We conduct a complete determination of all the possible neutral minima the model can have in these circumstances, as well as necessary conditions for these minima to occur.