Contribution to the alignment of the LHCb tracking system and measurement of the mean lifetimes of $B_{d(s)} \to D_{(s)} \pi$, $D_{(s)}\to KK\pi$

The LHCb experiment is one of the four large experiment of the Large Hadron Collider (LHC) situated at CERN, on the swiss-french border near Geneva. The LHCb detector is a single-arm spectrometer dedicated to the study of rare $b$-hadrons decays and to precision CP violation measurements. The LHCb experiment has so far collected $1\mathrm{fb^{-1}}$ of data at a center of mass energy of $7\,\mathrm{TeV}$. This thesis addresses three topics related to the LHCb experiment. The first part concerns the alignment of the LHCb Inner Tracker with the first LHC data. Misalignments in the tracking system degrade the momentum measurement and flight distance determination of particles. Such quantities are vital for accurate lifetime and mass measurements. A standalone alignment of the Inner Tracker was performed using a method to stabilize the Inner Tracker alignment without the need of fixing elements. The Inner Tracker was aligned to a precision of $102\pm 10\,\mathrm{\mu m}$, with a bias of $0\pm 13\,\mathrm{\mu m}$. In the second part, a first optimization of the selection cuts of the Same Side Kaon tagger has been performed using $D_{s}^{+} \to \phi\pi^{+}$ 2010 data along with $B_{s}^{0}$ Monte Carlo data. The $D_{s}^{+} \to \phi\pi^{+}$ channel was shown to be suitable for this purpose in the absence of a large $B_{s}^{0}$ calibration sample. Compared to the initial section of kaon, tuned on Monte Carlo data, an improvement both in tagging power and mistag rate was observed. In the third part, a method to fit the $B_{s}^{0}$ lifetime in $B_{s}^{0} \to D_{s}^{-}\pi^{+}$ and $B^{0}$ lifetime in $B^{0} \to D^{-}\pi^{+}$ was developed using a global decay time acceptance function and per-event decay time uncertainty estimates. The precision of the fits result is found to be dominated by systematic uncertainty due to the precision to which the acceptance function can be modeled. The average $B_{s}^{0}$ lifetime is measured to be \begin{equation} \nonumber \tau_{B_{s}^{0}} = 1.515 \pm 0.015 (\mathrm{stat}) {}^{+0.041}_{-0.039} (\mathrm{sys})\,\mathrm{ps} \end{equation} This result has an accuracy comparable to the world average provided by the Particle Data Group using $B_{s}^{0} \to D_{s} X$ decays \begin{equation} \nonumber \tau_{B_{s}^{0}} = 1.425 \pm 0.041\, \mathrm{ps} \end{equation} In the case of the $B^{0}$, the average lifetime is measured to be \begin{equation} \nonumber \tau_{B_{d}^{0}} = 1.513 \pm 0.020 (\mathrm{stat}) {}^{+0.033}_{-0.037} (\mathrm{sys})\,\mathrm{ps} \end{equation} It is expected that the precision of these measurements can be improved by using per-event acceptances in place of a global function.