Study of the very rare decay $B_s\rightarrow\mu^{+}\mu^{-}$ in LHCb

This thesis shows the strategy to extract the $B_s\rightarrow\mu^{+}\mu^{-}$ branching ratio from the LHCb data, calibrating all the steps using control channels and not relying on the simulation. This branching ratio is very sensitive to New Physics effects, and can get large enhancements within SuperSymmetry or other Standard Model extensions. The signal is separated from background according to three properties: the invariant mass, the muon identification, and the geometrical properties of the decay. The multivariate analysis designed to combine the geometrical properties is also shown here. The ration of offline reconstruction efficiencies between signal ($B_s\rightarrow\mu^{+}\mu^{-}$) and normalization channels ($B^{+}\rightarrow J/\psi(\mu^{+}\mu^{-}K^{+}$ and/or $B_d\rightarrow K ^{+}\pi^{-}$ ) can be extracted using the ratio of different control channels (for instance, $B_d\rightarrow J/\psi (\mu^{+}\mu^{-}) K^{*0}(K^{+}\pi^{-}))$ with a few percent precision. The ratio of trigger efficiencies can be extracted using events triggered independently of the signal, which with enough integrated luminosity will give a few percent precision. The invariant mass and the geometrical properties can be extracted using $B\rightarrow h^{+}h^{-}$ events as signal candidates and the events in the sidebands of the mass distribution as background candidates, without relying on the simulation. There are several good control channels (f or instance $J/\psi\rightarrow \mu^{+}\mu^{-} and \Lambda\rightarrow p\pi^{-})$ to be able to calibrate the muon identification efficiency and the muon misidentification probability. This strategy will allow LHCb to perform a measurement of the $B_s\rightarrow\mu{+}\mu{-}$ branching ratio that should not depend on how well our simulation reproduces real data. The strategy is tested with a sophisticated toy MC analysis for a hypothetical integrated luminosity of 150 pb$^{-1}$. The potential of all LHC experiments in this measurement is also studied, showing that LHCb has the best performance for a given integrated luminosity. From this study, LHCb could overtake Tevatron’s limit with the data of 2010 having already an important impact on New Physics searches. Within five nominal years, LHCb could observe values even smaller than SM prediction. Finally, the first data produced by the LHC at the end of 2009 is used for validate, to first order the potential described in this thesis using MC simulations.