A Novel Flavour Tagging Algorithm using Machine Learning Techniques and a Precision Measurement of the $B^0 - \overline{B^0}$ Oscillation Frequency at the LHCb Experiment

This thesis presents a novel flavour tagging algorithm using machine learning techniques and a precision measurement of the $B^0 -\overline{B^0}$ oscillation frequency $\Delta m_d$ using semileptonic $B^0$ decays. The LHC Run I data set is used which corresponds to $3 \textrm{fb}^{-1}$ of data taken by the LHCb experiment at a center-of-mass energy of 7 TeV and 8 TeV. The performance of flavour tagging algorithms, exploiting the $b\bar{b}$ pair production and the $b$ quark hadronization, is relatively low at the LHC due to the large amount of soft QCD background in inelastic proton-proton collisions. The standard approach is a cut-based selection of particles, whose charges are correlated to the production flavour of the $B$ meson. The novel tagging algorithm classifies the particles using an artificial neural network (ANN). It assigns higher weights to particles, which are likely to be correlated to the $b$ flavour. A second ANN combines the particles with the highest weights to derive the tagging decision. An increase of the opposite side kaon tagging performance of 50% and 30% is achieved on $B^{+} \rightarrow J/\psi K^{+}$ data. The second number corresponds to a readjustment of the algorithm to the $B^0_{s}$ production topology. This algorithm is employed in the precision measurement of $\Delta m_d$. A data set of $3.2 \times 10^6$ semileptonic $B^0$ decays is analysed, where the $B^0$ decays into a $D^- (K^+ \pi^- \pi^-)$ or $D^{*-} (\pi^- \overline{D^0}(K^+ \pi^-))$ and a $\mu^+ \nu_{\mu}$ pair. The $\nu_{\mu}$ is not reconstructed, therefore, the $B^0$ momentum needs to be statistically corrected for the missing momentum of the neutrino to compute the correct $B^0$ decay time. A result of $\Delta m_d = 0.503 \pm 0.002 (\textrm{stat.}) \pm 0.001 (\textrm{syst.}) \textrm{ps}^{-1}$ is obtained. This is the world's best measurement of this quantity.