No abstract

The gauged U (1) Lµ−Lτ extension of the Standard Model is a very simple framework that can alleviate the discrepancy in the anomalous magnetic dipole moment of the muon, reinforced by the recent Fermilab measurement. In this thesis, we introduce a dark matter (DM) candidate to the theory and proceed to study experimental probes of the model's parameter space with a general treatment of kinetic mixing between the Z ′ gauge boson of the U (1) Lµ−Lτ symmetry and the Standard Model photon. The physical value of the total kinetic mixing depends on a free parameter of the model and the energy scale of a given process. Specifically, after addressing the (g − 2) µ anomaly with the Z ′ boson, L µ − L τ charged dark matter with a thermal origin is explored, where we demonstrate that existing DM direct detection constraints are sensitive to the freedom in the kinetic mixing and can be substantially weakened if the total mixing parameter approaches zero in the low momentum transfer limit. Furthermore, we show for the same kinetic mixing scenario that this model predicts a novel recoil energy spectrum in future direct detection experiments. Finally, the effects of a general treatment of kinetic mixing on neutrino probes of the parameter space of the Z ′ are quantified. We find that constraints derived from the Borexino experiment (measuring solar electron-neutrino scattering), several experiments (both current and future) that study the process of coherent elastic neutrino nucleus scattering (CEνNS), and white dwarf cooling, are collectively not strong enough to rule out the region of the U (1) Lµ−Lτ parameter space that alleviates the (g − 2) µ tension. This is a positive result, since the avoidance of these constraints allows for a simultaneous explanation of both DM and the muon (g − 2) µ anomaly in this model.The joint efforts of future neutrino and DM experiments along with precision spectral measurement will be the key in testing such a theory. i Statement of OriginalityAll of the work presented and contained within this thesis is original material and has been solely created and written by myself, unless explicitly stated and/or referenced from external sources. I acknowledge Carleton's statement regarding academic integrity and recognize the consequences should this policy be breached. iii 6.10 Current and future reach (upper bound) on g µτ from neutrino experiments, including Borexino and white dwarfs (first row) and the CEνNS experiments (second row). In addition to the future CEνVS experiments depicted here, the proposed PIP-II linac at Fermilab expects to probe the Z ′ parameter space region favoured by (g − 2) µ through this interaction channel [116]. The dashed curves correspond to the kinetic mixing scenario with ε UV = 0, and the solid curves correspond to the kinetic mixing scenario with ε IR = 0 which are much weaker. . . . . . 111 xiv