Measurement of $CP$ Observables in $B^0_s \rightarrow J/\psi \phi$ decays at LHCb experiment

The symmetries and conservation laws have played an important role in the development of the Standard Model (SM). However, not all symmetries are strictly conserved. In particular, the symmetry with respect to the charge-conjugation-parity operator ($\mathcal{CP}$) is not conserved in weak interactions. This leads to differences in behaviour of particles and anti-particles. In the SM the $\mathcal{CP}$ violation arises through a single phase in the Cabibbo-Kobayashi-Moskawa quark mixing matrix, describing the interactions among quarks and the charged carrier of the weak force. In neutral $B$ meson decays to a final state which is accessible to both $B$ and $\bar{B}$ mesons, the interference between the amplitude for the direct decay and the amplitude for decay after oscillation, leads to a time dependent $\mathcal{CP}$-violating asymmetry between the decay time distributions of $B$ and $\bar{B}$ mesons. The decay $B^{0}_{s}\to J/\psi\phi$ allows for a measurement of such an asymmetry, which can be expressed in terms of the decay width difference $ \Delta\Gamma_{s}$ and a single phase $\phi_{s}$. The objective of this thesis is the measurement of the $\mathcal{CP}$- violating parameters in the $B^{0}_{s}\to J/\psi\phi$ decays with $e^{+}e^ {-}$ final state for $J/\psi$ meson decay and $K^{+}K^{-}$ pair for $\phi$ meson decay. Using a dataset corresponding to an integrated luminosity of 3.0 fb$^{-1}$ recorded at a center-of-mass energies of $\ sqrt{s}$ = 7 and 8 TeV collected with the LHCb detector at CERN Large Hadron Collider during 2011 and 2012, a tagged time dependent angular analysis of $B^{0}_{s}\to J/\psi\phi$ decays is performed. The selected sample corresponds to 12195$\pm$497 decay candidates. The $\mathcal{CP}$- violating phase of the $B^{0}_{s}$ system is measured to be $\phi_{s}=- 0.18^{+0.37}_{-0.39}(\mathrm{stat.})\pm0.25(\mathrm{syst.})$ rad that is consistent with the SM predictions and measurement results of other channels. This is the first time that the $\mathcal{CP}$-violating parameters have been measured in a decay with electron final state. The result allows to increase the data statistics and to improve the knowledge of a possible systematic effects. In addition to physics results, the alignment studies of the LHCb tracking stations are presented. The investigations are focused on the variation of the detector positions dependence on magnetic field polarizations and lead to improved alignment of tracking detectors. The study results are discussed in the thesis.