Alignment of the LHCb Tracking Stations and Selection of $X(3872)$ and $Z(4430)^{\pm}$ in $pp$ Collisions at 14TeV

The LHCb experiment is one of the four large experiments located at the Large Hadron Collider (LHC) at CERN, close to Geneva, Switzerland. The LHCb detector is a single-arm forward spectrometer which is dedicated to precision measurements of CP violation, as well as to the study of rare $b$-hadron decays. Both the energy at which the proton-proton collisions will take place and the statistics of events that will be selected are unprecedented. The LHCb detector will start its measurements in November 2009 and operate for several years. Being an experiment for precision measurements, LHCb relies on excellent reconstruction and trigger efficiencies, outstanding proper-time and momentum resolutions, as well as on a reliable particle identification, both for the event selection and the flavour tagging of $B$-meson decays. These performances are however not possible without a precise construction and alignment of the detector. An extensive survey of the detector geometry has been performed. However these measurements, for instance for the Inner Tracker, a silicon-strip tracking device, are only precise to the order of the detector resolution. The first part of the thesis discusses the detector alignment. A software alignment method has been developed in order to improve the knowledge of the detector element position. The novelty of this method is that it uses the tracks from the standard track-fitting procedure, which is based on a K alman filter, and not on a global track model. The advantage of this method is that it is possible to properly take the multiple Coulomb scattering, the magnetic field and the energy loss corrections into account. It also allows to correctly take into account the correlations between the hits on tracks. This document presents two realistic running scenarios, using simulated data, in which the alignment of the Inner and Outer Trackers (IT and OT) will need to be performed. A general strategy is defined for the alignment in a multi-step manner, starting from a coarse granularity and descending step-by-step to a finer detector granularity. A dedicated track selection is also developed. In particular, an evolving cut on the $\chi^{2}$ of the track fit is shown to be essential in the alignment procedure. Starting from a misaligned detector, the two scenarios use tracks coming either from beam-gas collisions at an energy of 450\,GeV/c without magnetic field, or from proton--proton collisions at a centre-of-mass energy of $\sqrt{s} = 14$\,TeV and when the magnetic field of the experiment is turned on. It is shown that the alignment software is able to recover from misalignments of the order of 1-2\,mm with a precision better than 20\,\% of the single-hit resolution for the IT and 5\,\% for the OT, in both scenarios. The precision of this alignment is then validated by studying the mass distributions of reconstructed $J/\psi$ and $K^{0 }_{S}$ mesons and by showing that the mass resolution for these particles is not degraded by more than 2\,\% between the ideal case and the case after re-alignment of the detector. In the Summer of 2008 and 2009, data were taken at LHCb during LHC synchronisation tests. The alignment of the IT using these high track-multiplicity data is presented in this document. A dedicated pattern recognition and track selection are used in order to obtain a sample of good-quality tracks. The IT is aligned down to the lowest granularity with a precision of 20\,$\mu$m. This precision is obtained by studying the distributions of unbiased residuals with respect to the reconstructed tracks. It is also shown that the alignment results do not depend on the position of the detector before alignment. The second part of this thesis discusses the first studies at LHCb of the $X(3872)$ and $Z(4430)^{\pm}$ particles. Six years ago, the Belle collaboration discovered a new state called the $X(3872)$. Several theoretical models have been developed in order to include this state, and the many others discovered since then. On the other hand, several collaborations have repeated the observation of this resonance in several decay modes. However, the nature and the quantum numbers of this state remain uncertain. Belle also discovered a charged state called the $Z(4430)^{\pm}$, but this discovery has not been confirmed by any other experiment yet. For both thes e states, LHCb is expected to play an important role. A Monte Carlo feasibility study of the selections of the $X(3872)\to J/\psi\,\pi^{+}\pi^{-}$ decay in the $B^{\pm}\to X(3872) K^{\pm}$ channel and of the $B^{0}\to Z(4430)^{\pm} K^{\mp}$ with $Z(4430)^{\pm}$ decaying to $\psi(2S)\pi^{\pm}$ are presented in this document. A yield of 1'850 reconstructed, selected and triggered $B^{\pm}\to X(3872) K^{\pm}$ events is obtained per nominal year(corresponding to an integrated luminosity of 2\,$\mathrm{fb}^{-1}$), for a background-to-signal ratio in the interval [0.3, 3.4] at 90\,\% CL. With such statistics, half a nominal year will be sufficient to disentangle between the two remaining spin hypotheses for the $X(3872)$ state. For the $Z(4430)^{\pm}$, an annual yield of 6'200 reconstructed, selected and triggered $B^{0}\to Z(4430)^{\pm} K^{\mp}$ events is obtained for a $B/S$ ratio within the interval [2.7, 5.3] at 90\,\% CL. Hence, the confirmation or ruling out of the Belle discovery will be possible, even in the early running phase of the LHC proton collider at $\sqrt{s} = 7-10$\,TeV.