This thesis presents work carried out using data from the LHCb experiment during the first three years of data taking, 2010 - 2012. A study of the effects of radiation damage on the silicon sensors of the LHCb Vertex Locator is performed, with an emphasis on the implications for the long term performance of the detector. Following three years of operation the sensors have received a maximum delivered neutron equivalent fluence of approximately 1.6E12 per square centimeter, leading to a number of radiation induced effects. In particular the change in charge collection efficiency and signal/noise with fluence is compared to theoretical expectations, and the current trends are extrapolated to the fluences expected at the end of the LHCb detector lifetime. The development of an unexpected effect due to the structure of the routing lines in the sensors is described in detail. Searches for lepton flavour and baryon number violating decays of the tau lepton using the 2011 LHCb dataset are described. Observation of any lepton flavour or baryon number violation would be an unambiguous sign of new physics, whilst setting improved limits helps to constrain a number of Beyond the Standard Model theories. First LHCb limits are set on the branching fractions of the decays tau- to mu- mu+ mu-, tau- to anti-proton mu+ mu- and tau- to proton mu- mu-, with these results also representing the first limits on lepton flavour violating tau decays at a hadron collider. The limit on tau- to mu- mu+ mu- is expected to approach the world's best result from Belle in the coming years whilst the tau- to anti-proton mu+ mu- and tau- to proton mu- mu- results constitute the first limits on the branching fractions of these decays. The future prospects for these measurements with further data are briefly described.

CUORE is one of the world-leading experiments to search for neutrinoless double beta decay. The excellent energy resolution and the stability of the detectors at CUORE also allow for other rare event searches. This thesis describes an experimental analysis undertaken to search for baryon number violation in 130Te using the data acquired by the CUORE detector. The conservation of the baryon number in the Standard Model relies on an accidental symmetry rather than being deduced from fundamental principles. If there is evidence suggesting a breach of this symmetry, it would significantly impact our understanding of the universe, especially concerning the origin of the matter-antimatter asymmetry. One possible way for this conservation principle to be violated is through tri-nucleon decay, where three nucleons decay simultaneously within a nucleus. For 130Te, the resulting decay products would be emitted with energy in the GeV range, making them a promising signal for detection in the CUORE experiment. This thesis describes the search signatures, the relevant background, and the analysis techniques used in this investigation, and results for an exposure of 236.6 kg·yr are presented. The daughter nucleus of the decay (127In) is unstable, and its decay chain can offer an secondary signature coinciding with the emitted energy. The viability of adding this secondary signature is also presented. / Doctor of Philosophy / Since the beginning of scientific thought, humankind has asked why there is something in the Universe instead of nothing. As our understanding of the working principles of the Universe deepened, this question has been refined and focused on an intriguing imbalance easily ob- served around us: The imbalance of the quantity of matter over anti-matter. We have never observed anti-matter galaxies or stars, and we never observe anti-matter manifesting around us in our daily lives. There are many ideas physicists have developed to explain this mysteri- ous absence of anti-matter, and one of them involves searching for an extremely rare radioac- tive process called triple nucleon decay. This thesis uses the data acquired by the nuclear experiment CUORE, situated in the Gran Sasso mountains in Italy, to look for this process.