Phenomenology of new physics beyond the Standard Model: signals of Supersymmetry with displaced vertices and an extended Higgs sector at colliders

Our current understanding of matter and its interactions is summarised in the Standard Model (SM) of particle physics. Many experiments have tested the predictions of the SM with great success, but others have brought our ignorance into focus by showing us there are new phenomena that we can not describe within the framework of the SM. These include the experimental observations of neutrino masses and dark matter, which confirms there must be new physics. What this new physics may look like at colliders motivates the original work in this thesis, which comprises three studies: the prospects of future electron-positron colliders in testing a model with an extended Higgs sector with a scalar triplet, doublet and singlet; the discovery potential at the Large Hadron Collider (LHC) of a non-minimal Supersymmetric model via conventional sparticle searches and via searches for displaced vertices; and the experimental search for long-lived massive particles via a displaced vertex signature using data of proton-proton collisions collected at a collider center of mass energy of 8 TeV in 2012 by the ATLAS detector operating at the LHC.