Exploiting angular correlations in the rare decay $B\rightarrow K^{*}\mu^{+}\mu^{-}$ at LHCb

In this thesis, methods for studying the flavour-changing neutral current decay $B\rightarrow K^{*}\mu^{+}\mu^{-}$ at LHCb are investigated. The decay proceeds via a $b\rightarrow s$ loop, and will be sensitive to the effects of new particles, predicted in many models of beyond-the-Standard-Model physics. The formalism used to describe the decay will be introduced, and a number of observables available in its angular distribution presented. In the first few years of LHCb data taking, the number of signal events available will be relatively small and measurements must be optimized for experimental sensitivity. The vanishing point of the angular observable $S_{5}$ will be of particular interest; it has reduced theoretical uncertainties from hadronic form factors and can be extracted with high precision at LHCb. It provides a complementary measurement to that of $A_{FB}$ and $F_{L}$, already considered by BaBar, Belle, and CDF. Once $\mathcal{O}(10^{4})$ $B\rightarrow K^{*}\mu^{+}\mu^{-}$ signal events have been collected, a full-angular analysis can be performed that will give the maximum available sensitivity to new physics in the decay. It will also provide access to many other observables with reduced theoretical uncertainties that are optimized for sensitivity to particular classes of new physics. It is shown that the full-angular analysis will be a sensitive probe of the decay, and can provide power to distinguish between mo dels if physics beyond the Standard Model is discovered at the LHC. Many of the conceptual issues associated with making this measurement are explored. Finally, a new decay model of $B\rightarrow K^{*}\mu^{+}\mu^{-}$ is presented for the decay simulator EvtGen that allows the model independent simulation of new physics. This model is used to investigate the current state of $b\rightarrow s$ observables, and it is shown that their 2009 experimental values are in excellent agreement with the Standard model.