Measurement of the $B^0_s–\bar{B}^0_s$ Oscillation Frequency at LHCb using 1 fb$^{−1}$ of data taken in 2011

In this thesis the measurement of the $B^0_s-\bar{B}^0_s$ oscillation frequency, $\Delta m_s$, in the decay $B^0_s \rightarrow D^-_s \pi^+$ is presented. It is an important step to prove that the LHCb experiment is able to resolve the fast $B^0_s-\bar{B}^0_s$ oscillation and, thus, can perform precision measurements in the $B^0_s$ system to search for physics beyond the Standard Model. Examples for such searches are the measurement of the weak mixing phase, $\phi_s$, in the decays $B^0_s \ rightarrow J/\psi \phi$ and $B^0_s \rightarrow J/\psi \pi^+\pi^-$ and the CKM-angle, $\gamma$, in the decay $B^0_s \rightarrow D^{\pm}_s K^{\mp}$. For the measurement of $\Delta m_s$ presented in this thesis a data set, accumulated by the LHCb experiment at the CERN LHC in 2011, is used. The data sample corresponds to an integrated luminosity of 1fb$^{-1}$ and about 34,000 signal $B^0_s$ candidates are reconstructed with an average decay time resolution of 45 fs. To determine the production flavour of the $B^0_s$ candidates both opposite and same side kaon flavour tagging algorithms are used with effective tagging efficiencies $\epsilon^{OST}_{eff} = 2.4\pm 0.4\%$ and $\epsilon^{SST}_{eff} = 1.2 \pm 0.3\%$. Both, the excellent decay time resolution and performance by the flavour tagging algorithms are prerequisits for a precision measurement of $\Delta m_s$. The oscillation frequency is measured to be $\Delta m_s$ = 17.768 $\pm$ 0.023 (stat) $\pm$ 0.006 (syst) ps$^1$ which is the world's best measurement of this quantity.