Development of "same side" flavour tagging algorithms for measurements of flavour oscillations and $CP$ violation in the $B^0$ mesons system

In this thesis new developments of $\textit{Flavour Tagging}$ algorithms for the $LHCb$ experiment are presented. The $\textit{Flavour Tagging}$ is a very usefull tool which allows to determine the flavour of the reconstructed particles, such as the $B^0$ mesons. A correctly identification of the flavour is fundamental in certain measurements such as time-dependent $CP$ violation asymmetries or the $B^0 \leftrightarrow \overline{B}^0$ oscillations. Both these type of measurements are exploited by LHCb experiment in the research of new physics beyond the Standard Model. The new developments achieved in this work concern an optimization of the $\textit{Same Side Tagger}$ algorithms, using protons and pions correlated in charge with the signal $B^0$ to infer its initial flavour. Then two combinations are implemented: the first is a combination of the $\textit{SS Pion Tagger}$ ($SS\pi$) and the $\textit{SS Proton Tagger}$ ($SSp$) in a unique $\textit{Same Side}$ ($SS$) tagging algorithm; the second one is the final combination ($SS+OS$) of this new $\textit{SS Tagger}$ with the $\textit{Opposite Side}$ ($OS$) $\textit{Tagger}$ combination already implemented. To unfold the signal from the background events it has taken advantage of the sPlot technique, which allows to calculate a per-event sWeight exploiting a discriminant variable, i.e. the invariant mass of the $B^0$ meson. The new SS taggers are implemented by means a multivariate analysis based on a $\textit{Boost Decision Tree}$ ($BDT$) algorithm. The goal of this BDT is to optimize the separation between ``signal'' (right charge correlated) and ``background'' (wrong charge correlated) particles and to identify the most probable tagger candidate. The input variables used to $\textit{train}$ the BDT include both kinematic and geometric variables. Then the sample is divided in categories according to the BDT output value and for each one a mistag probability is estimated by means an unbinned fit on the asymmetry oscillations. This procedure allows to predict the mistag value ($\eta$) of a certain event directly from the BDT response. This analysis is performed on the data sample collected by the $\textit{LHCb}$ experiment in 2012, corresponding to the $B^0 \longrightarrow D^- (\rightarrow K^+ \pi^- \pi^-) \pi^+$ decay channel. Then the data samples collected in the 2011, corresponding to the same decay channel and using two different event selections, are used to obtain a validation of the flavour oscillation calibration. In order to verify the goodness of the calibration both samples are divided in categories and the true mistag ($\omega$) is calculated through an unbinned fit. Thus a plot $\eta$ vs $\omega$ can be used to check the corrected calibration. An additional validation is performed on a different data sample corresponding to the $B^0 \longrightarrow K^- \pi^+$ decay mode. As last step the systematic effects are studied to check the dependence of the tagging response on the event properties. The new $SS\pi$ provides a tagging effective efficiency $\varepsilon_{eff} = 1.64 \pm 0.07 \%$, showing an improvement of the performance by about $20 \%$ with respect to previous tuning. On the other hand the new $SSp$ yields a tagging power compatible to the result achieved with the previous tuning (i.e. $\varepsilon_{eff} = 0.47 \pm 0.04 \%$). The two combinations $SS$ and $SS+OS$ provide a tagging effective efficiency $\varepsilon_{eff} = 1.97 \pm 0.10 \%$ and $\varepsilon_{eff} = 5.09 \pm 0.15 \%$ respectively. The algorithms developed in this thesis will be available as new taggers for the next $CP$ violation measurements at the LHCb experiment.