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The nature of the dark matter particle is one of the most prevalent outstanding questions in particle physics. Over the past several decades, direct detection experiments have been trying to measure the properties of the dark matter particle on earth. The Global Argon Dark Matter Collaboration (GADMC) has several large-area detectors in development designed for this purpose. Due to their better cryogenic performance and higher radiopurity, Silicon PhotoMultipliers (SiPMs) are increasingly considered in these experiments over PhotoMultiplier Tubes (PMTs) to measure the scintillation light produced in particle interactions within the liquid argon detectors used. The development of passively quenched, analogue SiPMs has supported this transition. Looking forward into the future to GADMC's flagship experiment, ARGO, there is interest in applying active quenching technology in a new generation of digital SiPMs with better timing resolution and on-chip signal digitization for better signal to noise for this detector. One such device is the prototype U. Sherbrooke and Teledyne Dalsa Photon to Digital Converter (PDC). The dark noise sources and rates of this device were studied using TRIUMF's Microscope for the Injection and Emission of Light (MIEL) experiment, with the intent to better understand dark noise sources in general and to analyse the current state of digital SiPMs in the context of large-area direct dark matter detectors.

The NA62 experiment aims at measuring the branching ratio of the ultra-rare decay K⁺ → π⁺νν ̄ with 10% precision. To achieve the desired precision, high levels of background rejection must be accomplished using techniques such as high-resolution timing, kinematic rejection, particle identification, and hermetic vetoing of photons. K⁺ → π⁺π0 (Kπ₂) decays, one of the largest background sources, are mainly rejected by kinematics reconstruction and photon vetoing in NA62. To evaluate Kπ₂ background rejection capabilities of the NA62 system, we studied the inefficiency of these two techniques. Kπ₂ and K⁺ → μ⁺ν (Kμ₂) events were selected from 2015 minimum bias data runs using Kπ₂/Kμ₂ separation cuts whose efficiency was also studied in details. The inefficiency of kinematics suppression was found to be (2.16 ± 0.21) × 10-³, and the upper limit of the photon veto inefficiency was 7 × 10-⁷ at 90% confidence level. Combined with correction factors from Monte Caro simulations, a preliminary result, S/B > 0.2, was estimated for Kπ₂ background in the measurement of K⁺ → π⁺νν ̄. Also, an upper limit on the branching ratio of the invisible decay π0 → νν ̄, 4.3×10-⁷, was obtained at 90% confidence level.

The branching ratio of pions decaying to positrons and muons R = (π→eυ + π→eυγ)/(π→μυ + π→μυγ) has been calculated with very high precision in the Standard Model of particle physics. So far, the theoretical value of R = 1.2352(1) x 10-⁴ is 40 times more precise than the current experimental value of R = 1.230(4) x 10-⁴. To test this variable with respect to deviations from the Standard Model, the experimental precision needs to be improved, which is why the PIENU experiment aims at a precision of less than 10-³, i.e. an improvement of an order of magnitude over the current precision. At this level, mass scales ∼ TeV/c² can be probed for evidence of new pseudo-scalar interactions. The data collected with the experimental setup also allows for a search of sterile neutrinos. When determining the branching ratio, various systematic corrections are applied. The largest among these is due to electro-magnetic shower leakage out of the calorimeters and radiative decays. It was calculated to be (2.25 ± 0.06) % in this thesis.In the second part of the thesis, an experiment on the direct radiative capture of muons in zirconium is described. One theoretical extension to the Standard Model involves a new light and weaklyinteracting particle in the muon sector which does not conserve parity. This can be studied experimentally with polarized muons that undergo the direct radiative capture into the 2S state of a medium mass target nucleus. During this capture, longitudinal muon polarization is conserved and the muons instantly undergo the 2S-1S transitionemitting a second photon. Studying the angular distribution of this second photon indicates whether or not the process is parity violating, which would manifest physics beyond the Standard Model. The direct radiative capture of a muon into an atom in the 1S or 2S state has not been observed yet. Therefore, data was taken in 2012 to studythe radiative capture of muons in zirconium. The analysis method of this data set is described with a blind analysis technique.

Electric field calculations and ionization signal simulations in a liquid xenon detector for Positron Emission Tomography have been performed. The electric field was calculated using Opera 3D, a Finite Element Method application software. The uniformity of the electric field inside of the detector was evaluated by calculating the deviation of drifting electrons under the applied electric field. The ionization signals of the detector have been simulated. The comparison between simulation results and measurement signals was made.

The capabilities and system performance of a high-resolution micro-PET system based on liquid xenon have been studied. Monte-Carlo simulations of scintillation events within a single sector of a twelve-sector prototype have been performed, and the results have been analyzed using Neural Network algorithms. The ability of the system to distinguish interaction points using scintillation information has been analyzed and presented. Monte-Carlo simulations of a full scale prototype have also been performed using NEMA standard mouse and rat phantoms. A novel scatter suppression scheme based on weighted Line of Response data is presented, and the effects on scatter fraction and background noise are analyzed.