Pushing the boundaries of the LHCb rare decays program: search for the $\Lambda_{b} \to \Lambda \gamma$ decay

This thesis presents the study of radiative b-hadron and rare strange decays using data collected by the LHCb detector in Run 1 and 2 of the LHC, with the purpose of testing the Standard Model. A dedicated inclusive trigger selection of radiative decays has been developed for Run 2 based on multivariate techniques and exploiting the common properties of these decays. An absolute efficiency gain of around $20\%$ has been obtained for the main radiative decays, with improvements of up to $70\%$ for cases with special topology. For rare strange processes, the feasibility of observing the mode $K_{S}^{0} \to \pi^{+}\pi^{-}e^{+}e^{-}$ at LHCb has been studied using simulation samples. An expected yield of $120^{+280}_{-100}/fb^{-1}$ has been obtained in Run 1 conditions, while no signal has been observed in 2012 data. Using pseudoexperiments it has been shown that an observation is feasible exploiting state-of-the-art multivariate techniques to separate further signal and background. Trigger improvements for Run 2 have been introduced, achieving an expected signal yield of $620^{+290}_{-120}/fb^{-1}$, which guarantees an observation of this mode in Run 2. In the area of radiative b-decays, a search for the radiative decay $\Lambda_{b}^{0} \to \Lambda \gamma$ has been performed for the first time at LHCb, using 2016 data. Exploiting a dedicated reconstruction and high performance multivariate techniques a first observation of this decay has been obtained, with a signal yield of $(64 \pm 13)$ events and a signal significance of $5.7\sigma$ observed. Exploiting the well-known radiative mode $B^{0} \to K^{*}\gamma$ as normalization, the branching ratio of the $\Lambda_{b}^{0} \to \Lambda \gamma$ decay has been measured to be $\mathcal{B}(\Lambda_{b}^{0} \to \Lambda \gamma) = (2.59 \pm 0.52 \pm 0.28 \pm 0.33) \times 10 ^{-6}$, where the first uncertainty is statistical, the second systematic and the third the systematic associated to the ratio of hadronization fractions between $\Lambda_{b}^{0}$ and $B^{0}$.