Development and calibration of a same side kaon tagging algorithm and measurement of the $B_s^0$--$\bar{B}_s^0$ oscillation frequency $\Delta m_s$ at the LHCb experiment

This thesis presents a so called same side kaon tagging algorithm, which is used in the determination of the production flavour of \Bs mesons. The measurement of the $B_s^0$--$\bar{B}_s^0$ oscillation frequency $\Delta m_s$ in the decay $B_s^0\rightarrow D_s^- \pi^+$ is used to optimise and calibrate this algorithm. The presented studies are performed on a data set corresponding to an integrated luminosity of $\mathcal{L} = 1.0 fb^{-1}$ collected by the LHCb experiment in 2011. The same side kaon tagging algorithm, based on multivariant classifiers, is developed, calibrated and tested using a sample of about $26,000$ reconstructed $B_s^0\rightarrow D_s^- \pi^+$ decays. An effective tagging power of $\varepsilon_{\rm eff}=\varepsilon_{\rm tag}(1-2\omega)^2=2.42\pm0.39\%$ is achieved. Combining the same side kaon tagging algorithm with additional flavour tagging algorithms results in a combined tagging performance of $\varepsilon_{\rm eff}=\varepsilon_{\rm tag}(1-2\omega)^2= 5.13\pm0.54\%$. With this combination, the $B_s^0$--$\bar{B}_s^0$ oscillation frequency is measured to be $\Delta m_s = 17.745\pm0.022\,\mathrm{(stat.)}\,\pm0.006\,\mathrm{(syst.)}\,ps^{-1}$, which is the most precise measurement to date.