The rare decay of $\Lambda_b\rightarrow \Lambda^0\mu^+\mu^-$ with the LHCb detector at CERN

The LHCb detector, one of the main particle physics detectors at the Large Hadron Collider (LHC) is purpose built for the study of interesting and rare particle physics events. One such rare event with an expected branching ratio of $\approx 10^{-6}$ is the decay of $\Lambda_b\rightarrow \Lambda^0\mu^+\mu^-$. This decay is interesting since it offers an opportunity to test our current understanding of particle physics and search for signs of new physics. In this thesis the background theory to the current model of particle physics (the Standard Model) and the main operational properties of the LHCb detector are summarized. The feasibility of observing this decay with LHCb is investigated and an estimated yield is calculated. A cut based selection is developed and optimized in order to select events according to this decay from the 2010 data set of approximately 1fb$^{-1}$ at a centre of mass energy of 7TeV. A clear indication of the decay is seen in the data with approximately 100 signal events and a significance of 4.8$\sigma$. The calculations of all required efficiencies are tabulated and are used to calculate a relative branching ratio to the resonant decay of $\Lambda_b\rightarrow J\psi\Lambda$, where $J\psi\rightarrow\mu^+\mu^-$, of $\mathcal{R}=1.89 x 10{-3}$.