LHCb detector momentum calibration with the first year data and a performance study of CP violation measurement with the $B^{0}_{s} \to J/\psi\phi$ decays

A new area in particle physics has begun with the start of the Large Hadron Collider (LHC) at CERN at the end of 2009, which collides protons at energies never reached before. To detect the products of the collisions, four main experiments are located around the LHC, among which the LHCb experiment. LHCb has been designed as a single- arm forward spectrometer and is dedicated to measurements of CP violation and rare decays of B hadrons. These searches could also potentially lead to the discovery of phenomena that cannot be described by the model used to date, called the Standard Model. The physics beyond the Standard Model is referred to as New Physics. A measurement of the phase of the $\rm B_s^0 - \bar{\rm B}_s^0$ oscillation amplitude with respect to that of the ${\rm b} \rightarrow {\rm c^{+}}{\rm W^{-}}$ tree decay amplitude, called $\rm \phi_s^{J/\psi\phi}$, is one of the key goals of the LHCb experiment with first data. In the Standard Model, this phase equals $-2\beta_s $, with $\beta_s$ the smallest angle of the unitary triangle of the CKM matrix relevant to $B^{0}_{s}$. The $\rm \phi_s^{J/\psi\phi}$ phase is hence predicted to be small, $\phi_{\rm s}^{\rm J/\psi\phi}\equiv-2 \beta_s=-0.0360^{+0.0020}_{-0.0016}$ $\rm rad$. However, possible contributions of New Physics to the $\rm B_s^0 - \bar{\rm B}_s^0$ box diagram, such as new particles entering into it, could modify the $ \phi_{\rm s}^{\rm J/\psi\phi}$ value from its Standard Model expectation. Due to its very small theoretical uncertainty in the Standard Model, $\phi_{\rm s}^{\rm J/\psi\phi}$ is therefore a very sensitive probe to detect the presence of New Physics. The $\phi_{\rm s}^{\rm J/\psi\phi}$ phase will be measured from a time-dependent angular analysis to $\rm B_s^0\rightarrow J/\psi\phi$ events with tagging the initial flavor of the $\rm B_s^0$ mesons. Due to the pseudo-scalar to vector-vector particle nature of the decay, an angular analysis is required to disentangle statistically the CP- even and CP-odd components present in the final state. Already with 2 fb$^{-1}$ of data taken at the nominal luminosity ${\cal L}=2 \cdot 10^{32}$ cm$^2$s$^{-1}$, corresponding to $\sim 117,000$ $\rm B_s^0\rightarrow J/\psi\phi$ signal events, the LHCb experiment is expected to achieve a statistical uncertainty $\sigma(\phi_{\rm s}^ {\rm J/\psi\phi})\simeq 0.03$ rad, similar to the value predicted by the Standard Model. On the way to this measurement, we present prospects for the time- dependent angular analysis to $\rm B_s^0\rightarrow J/\psi\phi$ events without tagging the initial flavor of the $\rm B_s^0$ mesons. This analysis is less sensitive to $\phi_{\rm s}^{\rm J/\psi\phi}$, but it has the advantages of being independent of the tagging calibration and less stringent about the proper time resolution, as it does not have to resolve the fast $\rm B_s^0 - \bar{\rm B}_s^0$ oscillations. Consequently, it can be applied on first data. Sensitivity results for $\phi_{\rm s}^{\rm J/\psi\phi}$, but also for the other parameters entering in the analysis are given. In particular, the amplitudes of the CP-even and CP-odd components and the $\rm B_s^0$ meson lifetime can already be measured with a better precision than the latest CDF results (June 2010) with only 0.2 fb$^ {-1}$ of data at nominal luminosity with the untagged analysis. To perform this analysis, the trajectories through the spectrometer of the particles coming from the $\rm B_s^0\rightarrow J/\psi (\mu^+ \mu^-)\phi (K^+K^-)$ decay, the muons and kaons, need to be reconstructed very precisely. Indeed, from the curvature of their trajectory in the magnetic field, the momentum of the particles is obtained, which is then used in the calculation of the angles forming the basis for the angular analysis to $\rm B_s^0\rightarrow J/\psi\phi $ events. For particles flying in the innermost part of LHCb, the Inner Tracker is the detector that provides information about the tracks. It consists of twelve detector boxes fixed on three tracking stations located downstream of the magnet in a cross-shaped configuration around the beam pipe. They are each filled with four layers of silicon microstrip sensors. We have assembled the twelve Inner Tracker detector boxes in a clean environment at CERN. By summer 2008, they were all assembled and installed in the LHCb cavern. To reconstruct track trajectories very accurately, two ingredients are essential: a good alignment description of the detectors used for tracking and an accurate description of the magnetic field. Before closing the Inner Tracker detector boxes, we organized with the survey team at CERN measurements of the silicon sensor positions. Once installed in the LHCb cavern, the Inner Tracker detector boxes were aligned as close to their nominal position as possible on the tracking stations previously adjusted. From the final measurements, we provided to the LHCb software a first realistic geometry description of the Inner Tracker, which was validated using particles coming from LHC injection tests of September 2008 and June 2009. The magnetic field map used initially in the LHCb software had been generated with a model based on finite element calculation. To obtain a better magnetic field map description, we developed a method for parameterizing magnetic field measurements that were recorded in December 2005 in the LHCb cavern using Hall probes. This new map replaced the former field map in the LHCb software. However, the magnetic field measurements showed some different features compared to the simulated magnetic field values, which needed to be validated with real data. As an example, an asymmetry of the magnetic field between the lower and upper parts of the magnet is observed in the measurements, while simulated values do not have this by design of the dipole magnet. Using reconstructed masses of $\rm K_s\rightarrow \pi^+\pi^-$, $\rm \Lambda\rightarrow p^+\pi^-$ and $\bar{\Lambda} \rightarrow \rm p^-\pi^+$ decays coming from 2009 and early 2010 real data, we validated the magnetic field map based on the measurements against the one based on simulated values according to several criteria, one of which being the confirmation of the up-down asymmetry in the field. From the same studies, we calculated a factor to correct globally for the momentum scale. As this factor should be universal, it can be calculated for one resonance and validated using the results for other resonances