Search for baryon and lepton number violation in heavy baryon decays and the background studies for exotic searches

The thesis describes searches for baryon and lepton number violation in $X_{b} \rightarrow K^{-} \mu^{+} (X_{b} = \Lambda^0_{b}, \Xi_{b}^{0})$ decays. The study is performed in the \mbox{LHC\textit{b}} experiment using data sample corresponding to an integrated luminosity of $3.0 fb^{-1}$ of proton-proton collisions at the centre-of-mass energy of $7$TeV $8$TeV, collected in 2011 (2012), respectively. No statistically significant signal of the decays in question has been found. As a result, the upper limits have been set: $\cal B ( \Lambda^0_{b} \rightarrow K^{-} \mu^{+} ) < 3.6 \times 10^{-9}$ and $\cal B (\Xi_{b}^{0} \rightarrow K^{-} \mu^{+} ) < 1.8 \times 10^{-8}$ at the $95\%$ confidence level. The second part of the thesis presents the background studies for exotic searches. The measurement of $\sigma(b\overline b)$ and $\sigma(c\overline c)$ production cross-sections with $b- (c-)$ hadron inclusive final states has been performed with data collected by the \mbox{LHC\textit{b}} experiment in 2010 in proton-proton collisions at the centre-of-mass energy of $7$TeV. The author of this thesis has prepared the interface to the Next-To-Leading-Order POWHEG simulation framework into the \lhcb software chain. All the kinematic characteristics of the hadron production in proton-proton collisions have been studied. The resulting angular and momentum correlations indicate a possible contribution from other mechanisms of LHCb production than the $\textit {flavour}$ $\textit {creation}$, mainly the $\textit {gluon}$ $\textit {splitting}$.