The year 2010 saw the Large Hadron Collider (LHC) collect 35:1 pb-1 of 7TeV proton-proton collision data. This thesis reports on the work carried out by the candidate as part of the calculation of the first constraints placed upon the supersymmetric parameter space using measurements made with this data. In particular, the development and application of the kinematic techniques used to ensure that the search was robust to detector mismeasurements, inherent in any early phase of data-taking, are discussed. The Constrained Minimally Supersymmetric Standard Model (CMSSM) is introduced to demonstrate how supersymmetry may extend the Standard Model of particle physics, and is used as the benchmark signal to investigate how supersymmetry may appear in 7TeV proton-proton collisions. The role of kinematics in early searches for such signals is then discussed; given the final state topology of interest (particle jets and large missing transverse momentum), particular attention is paid to errors that are due to detector mismeasurements, and how these may be accounted for with an appropriate choice of observable. A search strategy based upon these principles and applied to the Compact Muon Solenoid (CMS) experiment is then described, as used in the first published search for supersymmetry with LHC data reported in Phys. Lett. B 698 (2011) 196. The kinematic characterisation of events discussed above is exploited to ensure that the search is robust to mismeasurement. The thesis concludes with a summary of the search results. The observed number of events fulfilling the signal criteria is compatible with that expected from the Standard Model alone. The subsequent exclusion limits, given at the 95% Confidence Level, place significantly greater constraints upon the supersymmetric parameter space than those of previous experiments.

Inorganic scintillators are playing an ever increasing role in the search for rare events. Progress in the use of cryogenic phonon-scintillation detectors (CPSD) has allowed for a rapid increase in sensitivity and resolution of experiments using this technique. It is likely that CPSD will be used in future dark matter searches with multiple scintillator materials. Further improvements in the performance of CPSD can be expected if the amount of light collected is increased. In this thesis, two approaches are used to look at ways of maximising the amount of light collected in CPSD modules. The first approach is to obtain a detailed understanding of the spectroscopic properties in the crystal to identify ways of increasing their scintillation intensity. The second is to simulate the light collection properties using a Monte-Carlo simulation program. This requires a detailed understanding of the optical properties of inorganic scintillators and obtaining this information is the focus of the current work. Two new methods have been developed to evaluate the scintillation decay time and the intrinsic light yield of scintillators. These methods are tested on CRESST CaWO₄ crystals so that all the input parameters necessary for the simulation of CRESST modules is available. These input parameters are used to successfully explain features of the light collection in CRESST CPSD modules and to suggest possible improvements to the design of the modules. In summary, the current work has contributed to the development of a standardised method to maximise the light yield that can be obtained from CPSD for application to rare event searches.