Abstract
Composite Higgs models are a branch of Beyond the Standard Model theories which
seek to address the hierarchy problem inherent to the current formulation of the
Standard Model. In this thesis, we discuss and implement extensions to the scalar
sector of the Standard Model, focusing on models of compositeness and their
associated phenomenology. A key area of interest is then the appearance of
compositeness at current and future colliders, which can be used to motivate the
choice of the new era of experimental programs. To that end, this work details the
construction of a number of effective models which are testable at colliders, and which
are linked as extensions to the scalar sector. We include a comparison of twelve
minimal composite Higgs modes featuring an underlying fermionic completion, and
discuss ubiquitous features expected across all such models, including a light
pseudo-scalar, which is shown to be reachable at future lepton colliders with the help
of machine learning techniques. The study also reveals the consideration of bottom
quarks in fermion-loops coupling the light scalar to SM states to be non-negligible.
Phenomenology at future lepton colliders is extended through a study of the most
minimal composite Higgs model of this nature, SU(4)/Sp(4), where we outline a
potential search for the heavy pseudo-Nambu Goldstone boson ÷, considering both
fermiophobic and fermiophilic couplings. While composite Higgs models seek primarily
to address the separation of the electroweak and Planck energy scales, some such
models may also produce dark matter candidates. We conclude this work with an
investigation into heavy dark matter which couples to the top-sector of the Standard
Model via a t-channel interaction, situating it within a composite Higgs model
through its interaction with a heavy fermionic mediator and a top partner. Finally,
the visibility of the model at colliders and astrophysical experiments is examined.