Gauge higgs unification in extra dimensions and spin-3/2 dark matter

Khojali, Mohammed Omer Ahmednoor
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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.
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