Search for heavy neutrinos and characterisation of silicon sensors for the VELO upgrade

Many theories beyond the Standard Model predict the existence of heavy neutral leptons to explain the smallness of neutrino masses. A search is performed for a heavy neutrino in the mass range $5-50$ GeV using the data collected with the LHCb detector at the centre of mass energy of 8 TeV. The decay process $W \to \mu \textrm{N}$ with the heavy neutrino decaying promptly as $\textrm{N} \to \mu \, \textrm{jet}$ is investigated exploiting the large branching ratio expected to this final state and the full reconstruction of the $W$ from its decay products. Both final states with opposite-sign and same-sign muon pairs are considered, since both processes are allowed if the neutrino is a Majorana particle. Upper limits on the coupling of a heavy neutrino with the Standard Model neutrino of the order of $10^{-3}$ for lepton-number-conserving decays and of the order of $10^{-4}$ for lepton-number-violating heavy-neutrino decays are set at 95% confidence level. The second part of the thesis is dedicated to the characterisation of novel silicon pixel sensors in view of the upgrade of the Vertex Locator of the LHCb experiment. A wide range of prototype sensors has been tested with a charged particle beam using the Timepix3 telescope, prior to and after different types of irradiation up to $8 \times 10^{15} 1 \, \textrm{MeV}\, \textrm{n}_{\textrm{eq}}\, \textrm{cm}^{-2}$. Among the several aspects tested, the behaviour of the sensor at the edge is particularly important, since this is the point closest to the beam (about 5 mm). Two of the prototypes tested exhibited an unexpected behaviour, driving the choice for the final design of the detector. Innovative methods for bulk studies of the sensor have been further developed. The device under test is placed almost parallel to a beam of minimum ionising particles such that particle tracks traverse it longitudinally, known as grazing angle or edge on technique. In this way, charge is liberated at a known depth in the bulk material. This method is shown to be a powerful tool to investigate not only the charge collection, but also the time-to-threshold properties as a function of the depth at which the charges are liberated.