Supersymmetry (SUSY) is currently one of the best motivated extensions of the Standard
Model (SM) of particle physics. Softly broken SUSY naturally stabilises the
electroweak scale against large quantum corrections, without the unnatural fine tuning
required in the SM. However, experimental searches for superpartners and the
observed 125 GeV Higgs mass now imply that large corrections again arise in the minimal
supersymmetric standard model (MSSM), reintroducing the need for fine tuning.
In this thesis, we study a class of non-minimal E₆ inspired SUSY models that
are partially motivated by solving these and other problems of the MSSM. A unified
E₆ gauge group at high energies is assumed to lead to a low-energy theory with one
or more additional U(1) gauge symmetries and extra matter content compared to the
MSSM. To facilitate the study of these and other Beyond the Standard Model theories,
we implement several extensions to existing automated tools, significantly improving
their capabilities and range of applicability.
In the simplest E₆ inspired models, additional contributions to the Higgs mass
reduce the need for large radiative corrections but introduce a new source of fine
tuning associated with a massive Z' boson. By considering several such models at low
energies, we show that experimental limits on the mass of this state imply a minimal
amount of fine tuning is required to reproduce the electroweak scale. The severity of
this fine tuning is also shown to depend strongly on the details of the gauge symmetry
breaking.
We next consider an alternative E₆ model with a single, exact custodial symmetry.
This custodial symmetry, combined with an automatically conserved matter parity,
implies the existence of two dark matter candidates in the model. We explore the
parameter spaces of constrained versions of this model and the MSSM in which one
dark matter candidate is a MSSM-like mixed bino-Higgsino or pure Higgsino state.
We find that the dark matter relic density may be reproduced while satisfying experimental
constraints, and that light exotics may be discoverable at the Large Hadron
Collider. We conclude by investigating the impacts of current and future direct detection
searches on the parameter spaces of both models.Thesis (Ph.D.) -- University of Adelaide, School of Physical Sciences, 201
