LHCb Vertex Locator Upgrade Development and Rare b-quark Decays in LHCb

This work describes contributions and results obtained within the scope of the LHCb collaboration. Analysis of two decays of b hadrons using the LHCb detector are discussed: $\Lambda_b^0 \rightarrow pK J/\psi(\mu\mu)$ and its use to probe lepton universality and the very rare $B^+\rightarrow a_1^+(1260)(\pi\pi\pi) \mu\mu$ and its feasibility in LHCb. The development and testing of the LHCb Vertex Locator(VELO) upgrade pixel sensors and readout chips is presented, with a discussion of the challenges and solutions of a silicon detector operating at 5.1 mm from the LHC interaction region. There is an extensive discussion on the testing of different silicon sensor designs both before and after irradiation up to a fluence of $8 \times 10^{15}\,1\,\mathrm{MeV}\, \mathrm{n}_{eq} \, \mathrm{cm}^{-2}$. Results obtained in the laboratory and in a testbeam environment are shown, proving the chosen solution, a planar n-on-p, 200 $\mu$m thick, 450 $\mu$m guard-ring sensor design meets LHCb's requirements. The testing methods for sensors and readout chips for the module production are presented together with a new method to bias hybrid pixel assemblies under vacuum before wire-bonding. This work was part of the campaign to deliver the VELO upgrade detector for a 2020 installation and physics operation in the LHC in 2021.