Measurement of strange hadron production ratios and perspectives for the search of $D^0 \to \mu^+ \mu^-$ decay at LHCb

The study of $V^{0}$ particles in $pp$ collisions is important for the comprehension of soft processes involved in strange quark production. Baryon asymmetry, measured as the $\bar \Lambda/\Lambda$ production ratio, is crucial to understand the mechanism with which the baryon number information of the initial state is transported to the final state. Strange baryon over meson suppression, measured as the $\bar \Lambda/K^0_S$ production ratio, is an important probe of the hadronisation mechanisms in high energy collisions. In this dissertation we report measurements of $\bar \Lambda/\Lambda$ and $\bar \Lambda/K^0_S$ production ratios as obtained by the LHCb experiment in $pp$ collisions at $\sqrt{s} = 0.9$ and $7$ TeV. Some theoretical aspects, the analysis procedure and results are presented and compared with phenomenological models using predictions based on Monte Carlo simulations. We also present a measurement of the transverse polarisation of $\Lambda$ baryons, which is important to understand the role of spin in high energy collisions. Furthermore a preliminary outlook of the search of the very rare $D^0 \to \mu^{+} \mu^{-}$ decay is reported. This process involving flavour changing neutral currents is sensitive to contributions from different new physics scenarios. A selection for this decay and its possible background contributions are presented as obtained from the study of $pp$ collisions at $\sqrt{s} = 7$~TeV. We present the results and discuss the prospects for the detection of this decay and the possibility to constraint the parameters of new physics scenarios.