Measurement of the CP-violating phase $\phi_s$ using $B_s \rightarrow J/\psi \phi$ and $B_s^0 \rightarrow J/\psi \pi^{+} \pi^{-}$ decays with the LHCb experiment

This thesis presents a measurement of the CP-violating phase $\phi_s$, arising in the interference of $B_s^0$ mixing and the amplitudes of $B_s^0 \rightarrow J/\psi \phi$ and $B_s^0 \rightarrow J/\psi \pi^{+} \pi^{-}$ decays. The phase $\phi_s$ is an observable with very high sensitivity for physics phenomena beyond the Standard Model. New, heavy particles could contribute to the mixing process and influence the measured value of $\phi_s$. As the prediction for $\phi_s$ is very precise, already small deviations of the measured value would be a hint for new physics effects. \\ The presented measurement is done with a data set corresponding to an integrated luminosity of ${\mathcal{L}}=1.0 {\rm fb^{-1}}$, collected during 2011 with the LHCb experiment. The determination of $\phi_s$ with $B_s^0 \rightarrow J/\psi \phi$ decays requires a time-dependent analysis, depending also on the decay angles of the $B_s^0$ to separate the CP-eigenstates of the decay. A four-dimensional maximum likelihood fit, including as well information of the $B_s^0$ production flavour, is used to determine $\phi_s$ from the corresponding measured time and angular distributions. The measurement of the strong phase difference between $K^{+} K^{-}$ P-wave and S-wave amplitudes, as a function of the invariant $K^{+} K^{-}$ mass, allows to resolve a twofold ambiguity ($\phi_s \leftrightarrow \pi - \phi_s$) in the differential $B_s^0 \rightarrow J/\psi \phi$ decay rate. The measured value is $\phi_s = 0.069 \pm 0.091 \, ({\rm stat.}) \pm 0.014\, ({\rm syst.})\ {\rm rad}$. Performing a combined analysis of $B_s^0 \rightarrow J/\psi \phi$ and $B_s^0 \rightarrow J/\psi \pi^{+} \pi^{-}$ decays a value of $\phi_s = 0.043 \pm 0.076 \, ({\rm stat.}) \pm 0.014\, ({\rm syst.})\ {\rm rad}$ is determined. The obtained results are in agreement with the prediction.