| Summary: | A Thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in
ful llment of the requirements for the degree of Doctor of Philosophy.
April 2018 === In this thesis we discuss various gauge group structures in the gauge-Higgs uni -
cation models. The rst group we considered was a toy SU(3) model, where it is
possible to have the uni cation of gauge and top Yukawa couplings, which is an attractive
feature of gauge-Higgs uni cation models in extra-dimensions. This feature
is usually considered di cult to obtain based on simple group theory analyses. We
reconsider several minimal toy models calculating the renormalisation group running
at one loop. Our results show that the gauge couplings unify asymptotically
at high energies, and that this may result from the presence of an UV xed point.
The Yukawa coupling in our toy models is enhanced at low energies, showing that a
genuine uni cation of gauge and Yukawa couplings may be achieved.
Furthermore, the evolution of the Cabibbo-Kobayashi-Maskawa matrix elements,
the Jarlskog invariant and the quark mixings are derived for the one-loop renormalisation
group equations in a ve-dimensional models for an SU(3) gauge group
compacti ed on an S1=Z2 orbifold. We have assumed that there is a fermion doublet
and two singlets located at the xed points of the extra dimension, which pointed
to some interesting phenomenology in this toy model. We then explicitly test in a
simpli ed 5-dimensional model with SU(5), SU(5) U(1)0 and G2 gauge symmetries,
the evolution of the gauge couplings, by assuming that all the matter elds
are propagating in the bulk, and consider orbifolds based on Abelian discrete groups
which lead to 5-dimensional gauge theories compacti ed on an S1=Z2. The gauge
couplings evolution is derived at one-loop level and used to test the impact on lower
energy observables, in particular the Weinberg angle. For our numerical calculations
we have assumed that the fundamental scale is not far from the scope of the Large
Hadron Collider, where we choose the compacti cation radii to be the following
benchmark values: 1TeV, 4TeV, 5TeV, 8TeV, 10TeV, 15TeV and 20TeV.
As these gauge-Higgs uni cation models can also contain many additional particles,
we sought to use these particles as dark matter (DM) candidates. As many studies
have already been done on various spin DM particles, we chose to focus on the more
exotic spin-3/2 fermionic DM. We have allowed interactions with standard model
fermions through a vector mediator in the s-channel in our rst considerations. An
interesting feature of the spin-3/2 nature of the standard model particles is that
there exists a minimum value of the DM mass for a given coupling and mediator
mass, below which the decay width of the mediator exceeds the mediator mass. We
nd that for pure vector couplings almost the entire parameter space in DM and
mediator mass is consistent with the observed relic density, and is ruled out by the
direct detection observations through DM-nucleon elastic scattering cross-section. In
contrast, for pure axial-vector coupling, the most stringent constraints are obtained
from mono-jet searches at the Large Hadron Collider.
We have also considered a spin-3/2 fermionic DM particle interacting with the standard
model quarks through the exchange of a charged and coloured scalar or vector
mediator in a simple t-channel model. It is found that for the vector mediator case
almost the entire parameter space allowed by the observed relic density is already
ruled out by the direct detection LUX data. There are no such bounds which exist
on the interaction mediated by scalar particles. Monojet + missing energy searches
at the Large Hadron Collider provide the most stringent bounds on the parameters
of the model for this case. The collider bounds put a lower limit on the allowed DM
masses.
These studies have shown a variety of particle phenomenology beyond the standard
model, where such models can be constrained from both collider and astrophysical
data. === MT 2018
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