Alignment with Kalman filter fitted tracks and reconstruction of $B^{0}_{s} \to J/\psi \phi$ decays

The LHC at CERN provides a new testing ground for the Standard Model of elementary particles as well an opportunity to further explore the mysteries and expand our knowledge of Nature. The Standard Model is a theory based on experimental observations of particle interactions at collider experiments and at cosmic ray experiments. Despite the successes of the Standard Model it does not provide a complete picture of the beautiful intricately woven tapestry called Nature. To further explore the finest threads of this tapestry and to validate or exclude the Standard Model or extensions thereof, so-called New Physics Models, particle physicists at the LHC have built precision instruments to measure fundamental parameters, which may reveal New Physics, with the highest possible precision. A case in point is the weak mixing phase s, a key measurement of the LHCb experiment, which can be accessed via $B^{0}_{s} \to J/\psi\phi$ decays. According to the Standard Model this phase is expected to small, approximately $\phi_{s}$ = -0.04 mrad. However, New Physics contributions may augment this phase, yielding a larger value. To be able to attribute the observed magnitude of the phase to New Physics, the LHCb experiment has been designed to measure s with a precision of $0.024 mrad$ after one nominal year of data taking. To achieve this sensitivity on $\phi_{s}$ requires high precision tracking detectors. Furthermore, to determine charged particle trajectories and observables with a high precision, the positions of the tracking detectors need to be known well within their respective hit resolutions. To determine the positions of the detectors well within their hit resolutions, a generic track based alignment framework for the LHCb detector has been developed. The novelty of this framework is that it uses a Kalman filter track model and fit in the so-called global method of alignment procedure. In this procedure alignment offsets are determined through a global least squares method, in which not only the hits themselves are considered but also the correlations between the hits. This has the advantage that only a few iterations are required to determine the alignment offsets. Furthermore, the framework uses the same track model and fit as the standard LHCb reconstruction and physics analyses procedures. The obtained alignment offsets are therefore expected to be consistent with the track model and fit used in these procedures. An additional advantage of this alignment framework is the possibility to align all of the LHCb sub-detectors simultaneously or each sub-detector individually at any granularity.