Family symmetries and radiative corrections in multi-scalar extensions of the Standard Model

The four articles contained in this thesis all concern aspects of model building beyond the Standard Model (BSM). While Paper I mainly serves as a ``tool paper'' in which the results can be used to simplify certain calculations of one-loop effects from new heavy particles, Paper II--IV all deal with consequences of family symmetries in several BSM scenarios. Paper I. We derive expressions for any number of derivatives of the Coleman-Weinberg potential in a general renormalisable four-dimensional field theory with arbitrary number of fields with spin~$\leq$~1. These correspond to the one-loop contributions to scalar $n$-point functions neglecting external momenta. The results are applied to two singlet extensions of the Standard Model, where we study the one-loop effects on the triple-Higgs coupling from the new exotic heavy states. Paper II. In this paper we study a non-supersymmetric trinification theory where a novel $\mathrm{SU}(3)_F$ family symmetry is imposed on the model. The tree-level scalar potential often has a global minimum where the trinification gauge group is broken to a Left-Right symmetric gauge group, and after integrating out all particles with masses of the order of the grand unification scale we show that the renormalisation group is able to trigger a radiative breaking down to the Standard Model gauge group with light Higgs doublets still remaining in the spectrum. Paper III. This paper is about a supersymmetrised version of the $\mathrm{SU}(3)_F$ symmetric trinification model of Paper II. The absence of an appropriate scalar potential minimum is rectified by adding novel gauge adjoint chiral superfields. The resulting superpotential allows for a breaking of the grand unification symmetry, while all subsequent symmetry breaking scales are given by soft supersymmetry breaking parameters. The tree-level mass spectrum resulting from this soft breaking of supersymmetry is discussed. Paper IV. A three Higgs doublet model is introduced with a $\mathrm{U}(1) \times \mathrm{U}(1)$ family symmetry that simultaneously enforces a Cabibbo quark mixing under charged current interactions and forbids tree-level flavour changing neutral currents. Furthermore, a hierarchy in the vacuum expectation values of the three doublets produces a SM-like Higgs boson and hierarchical fermion masses, and also causes the exotic scalar states to couple most strongly to the second quark family. A search strategy for the lightest charged scalar boson in the model is proposed that utilises the $c \bar{s}$ fusion channel, and is shown to be capable of probing a large portion of the model's parameter space. This is formulated in a model independent manner such that it can be directly applied to any model with the same discovery channel