Theory and Phenomenology Beyond the Standard Model and Dark Matter Physics

This thesis is dedicated to the study of theories of physics Beyond the Standard Model (BSM), specifically minimal extensions in which the Standard Model (SM) gauge group is extended by a new U(1)’ factor. We study the implications and applications of such U(1)’ extensions in the context of BSM and, in particular, in connection to Dark Matter (DM). We consider the possibility that DM interactions with the SM states are mediated though a new Z’ gauge boson which couples only to top quarks and DM. We call this scenario the Top-philic Vector Portal. We present a comprehensive study of top-philic DM models which can reproduce the correct DM relic density via the conventional freeze-out mechanism and which satisfy the current constraints from: the Large Hadron Collider (LHC), direct detection, indirect detection and electroweak precision tests. Additionally, we develop a method for identifying whether a vector is truly top-philic, or couples to both t and b, by considering the ratio of cross sections in the mono-jet and mono-photon searches for DM at the LHC. Subsequently, we discuss the case that the Z’ gauge boson only has axial couplings to the SM fermions. Such axial vector mediators are particularly interesting as portals between the SM and DM, as the direct detection constraints on such models are weak. However, additional U(1)’ gauge groups, under which the SM states are charged, generically lead to gauge anomalies unless new exotic anomaly cancelling fermions are introduced. We provide explicit examples and general methods for constructing anomaly free spectra and argue that in certain classes of models the axial vector Z’ mass is expected to be comparable to the fermion exotics, in which case these models may be tested at current and forthcoming experiments.