Mass Resolution Study of the $B_s$-Meson with First LHCb Data

The rare decay $B^0_s \to \mu^+ \mu^-$ is very strongly suppressed in the Standard Model. As a flavour-changing neutral current, this decay is forbidden at the tree-level and can only be introduced by higher order loop processes. New physics models beyond the Standard Model typically include an extended particle spectrum, which might influence the loop processes measurably. The analysis of the $B^0_s \to \mu^+ \mu^-$ branching ratio at the LHCb experiment provides interesting possibilities to constrain the parameter space of some new physics models. The LHC at CERN Geneva is the most powerful ring accelerator at the moment. LHCb is one of the four main experiments at the LHC and is dedicated to physics in the B-meson sector. The work was divided in two main parts: an experimental part and an analysis part. The Tracker Turicensis was successfully installed and commissioned from 2006-2009. In parallel the slow control software for the Tracker Turicensis was developed and tested. Tuning of hardware and software parameters was achieved during the proton injection tests to the LHC before proton-proton collisions happened in the LHC. After the successful commissioning of the detector in October 2009, more than 99.7 % of about 143000 readout channels were working , which is of great importance for the precision measurements of the LHCb experiment. The second part of this work is related to the analysis to determine a limit on the branching ratio for $B^0_s \to \mu^+ \mu^-$ are described. However the main focus of this work lies on a novel method on the basis of error propagation to estimate the invariant mass resolution on an event-by-event basis for a two body decay from data. A correction factor on the relative error on the momentum of the decay particles was developed to achieve a proper calibration of the error on the momentum and the mass resolution from data. The systematic uncertainty on the mass resolution determined by this novel method, using the correction factor, was found to be 1.96%, which is lower than the systematic error of the methods currently used in the $B^0_s \to \mu^+ \mu^-$ analysis.