Radiation damage studies in the LHCb VELO detector and searches for lepton flavour and baryon number violating tau decays

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 $\sim1.6 \times 10^{12}$ per square centimetre, 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 $\tau^-\rightarrow \mu^-\mu^+\mu^-$, $\tau^-\rightarrow \overline{p}\mu^+\mu^-$ and $\tau^-\rightarrow p\mu^-\mu^-$, with these results also representing the first limits on lepton flavour violating tau decays at a hadron collider. The limit on $\tau^-\rightarrow \mu^-\mu^+\mu^-$ is expected to approach the world's best result from Belle in the coming years whilst the $\tau^-\rightarrow \overline{p}\mu^+\mu^-$ and $\tau^-\rightarrow p\mu^-\mu^-$ results constitute the first limits on the branching fractions of these decays. The future prospects for these measurements with further data are briefly described.