An approach to new physics at LHCb: study of penguin pollution to $\phi_s$($B_s^0{\to}J/\psi{\phi}$) using $B_s^0{\to}J/\psi{\bar{K}^{*0}}$ decays, and search for a light $A_1^0$ Higgs boson in the NMSSM.

This LHCb Thesis consists of three main parts. First, characterisation studies of Medipix3 silicon detectors using charged-particle beams in the context of the VELO upgrade: average cluster size and resolution versus threshold have been found to not change significantly between irradiated and non-irradiated assemblies, proving that Medipix3 assemblies are hard-radiation suitable for the development of Timepix3 and Velopix assemblies. Second, measurement of penguin pollution to the $CP$-violating $\phi_s$ phase using $B_s^0{\to}J/\psi{\phi}$ decays: polarisation fractions and direct CP violation have been found to be in agreement with SM predictions, while penguin pollution have been found to be small and under control. Third, a search of $A_1^0{\to}\mu^+\mu^-$ decays where $A_1^0$ is the light $CP$-odd Higgs boson in the NMSSM: the analysis is not finished yet, however, it is in good shape and a sensible improvement with respect to previous estimations is expected - updates can be found in the LHCb analysis note numbered LHCb-ANA-2017-004.