Testing the Standard Model with radiative beauty and rare strange decays at LHCb

This thesis focuses in the analysis of radative b-decays and rare strange decays, using data recorded by the LHCb, at the LHC during the Run 2 period. Two analyses are presented in the thesis, both flavour changing neutral currents, known to be very sensitive to new physics effects beyond the Standard Model. A first preliminary analysis focusing in the decay of $K_S^0\to\pi^{+} \pi^{-} e^{+} e^{-}$ followed by an angular analysis of the radiative decay $\Lambda_b^0\to\Lambda^0\gamma$. The decay of the $K_S^0$ to two pions and two electrons is quite challenging to reconstruct by the LHCb detector. Nevertheless, the decay is very interesting as it can be used as a control mode for much rarer decays of $K_S^0$ decaying into four leptons, never observed before, and very sensitive to new physics. The first analysis in this thesis presents the first working steps towards the usage of this mode inside the LHCb. The angular analysis of the $\Lambda_b^0\to\Lambda^0\gamma$ decay mode is performed to measure the polarization of the final state photon, by exploiting the weak decay of the $\Lambda$ baryon to a pion and proton pair. The proton angular distribution gives full access to the photon polarization, known to be very sensitive to new physics effects. This study presents the strategy and performs the first ever measurement of the photon polarization in radiative b-baryon decays.