$B^{0}_{s} \to J/\psi(\mu^+ \mu^-) \eta'(\pi^+ \pi^-\eta(\gamma\gamma))$ decays and sensitivity to the $B^{0}_{s}$ mixing phase at LHCb

The \lhcb experiment is one of four main experiments to be setup at IP8 point of the proton-proton Large Hadron Collider (\lhc) at \cern, Geneva. The data taking is scheduled to start end 2007. The \lhcb detector is a forward single-arm spectrometer conceived to study \cp violation and rare phenomena in the \textit{b}-quark sector with very high precision. \lhcb should provide a profound understanding of flavour physics in the framework of Standard Model (SM), so that the SM will be over-constrained, hopefully, it will exhibit some inconsistencies which may reveal a sign of New Physics beyond the SM.\\ The physics studies being considered by the \lhcb collaboration offer the possibility of furthering in the SM description of \cp violation. The SM provides the theoretical framework for the violation of the \cp symmetry in neutral B mesons as well as in neutral K mesons. The neutral \bsmix system stays at a privileged position in the quest for \cp violation evidences. The \bsmix mixing phase, $\phi_s$, has never been measured. This mixing phase has its origins in the interference between the decay and the mixing of those neutral mesons. \bccs quark-level transitions decaying to \cp eigenstates, may directly probe this electroweak phase by performing a time-dependent measurement of mixing-induced \cp violation.\\ Among those quark level transitions, we have the golden-plated channel to perform such a measurement that is \Bsjpphi and that requires an angular analysis to disentangle its \cp eigenstates components. On the other hand, \bccs transitions to pure \cp eigenstates provide another probe to the $\phi_s$ not requiring such angular studies. In this dissertation we will be consider the \Bsjpetapmmppgg decays which are \bccs transitions to pure \cp even eigenstates. The reconstruction and selection of those decays will be presented here using full Monte Carlo simulations. An annual event yield of $\sim 2000$ is assured with a background-over-signal level close to unity. The mass and proper time resolution will be also presented and some methods searching to improve those performances. In the last chapter of the dissertation, we will also present a study of the statistical sensitivity of \Bsjpetapmmppgg to the \bsmix mixing parameters, using a fast parameterised Monte Carlo simulation. Those simulations takes into account in a realistic manner the outputs from the full Monte Carlo simulations. Specifically, we will be simulate the background-over-signal levels, the time dependent acceptance efficiency and tagging and reconstruction performances for that decay mode. It will also take as inputs the event-by-event proper time errors obtained from the full MC. The likelihood fit performed to extract the physics parameters requires a flavour-specific control sample, \BsDspi, which allows for the extraction of the \bsmix mixing frequency, $\Delta M_s$. The sensitivity achieved by our channel decay will be then combined to other \bccs quark level transitions to pure \cp eigenstates and finally also to the \Bsjpphi decay to admixture of \cp eigenstates. The sensitivity obtained from the pure \cp modes is $\sigma(\phi_s) = 0.056$~rad whereas if we combine all decay channels into a single sensitivity measurement we achieve $\sigma(\phi_s) = 0.021$~rad. The contribution from the pure \cp modes is non-negligible, $\sim 14\%$, so that it is expected that these channels will certainly help in the measurement of $\phi_s$